1. Introduction
We are interested in question generation (QG) – the task of automatically generating reading comprehension questions and their correct answers from given declarative sentences. If made readily available, such a QG system could be used by second-language learners to test their understanding of a text they have read, or by teachers to quickly generate reading comprehension questions to be used in class. Numerous methods have been proposed for solving the QG task, most of which have been aimed at the English language. Early methods, mostly based on context-free grammars, relied on the strict word order and the limited inflectional morphology of English. These traits made it relatively straightforward to craft hand-written templates based on these grammars. State-of-the-art QG methods are data-driven and rely on the availability of large-scale data sets, such as SQuAD (Rajpurkar et al. Reference Rajpurkar, Zhang, Lopyrev and Liang2016) – a question-answering data set repurposed for QG. At the core of these methods for English are modern language models based on the transformer architecture, such as BERT (Devlin et al. Reference Devlin, Chang, Lee and Toutanova2019) or GPT-3 (Brown et al. Reference Brown, Mann, Ryder, Subbiah, Kaplan, Dhariwal, Neelakantan, Shyam, Sastry, Askell, Agarwal, Herbert-Voss, Krueger, Henighan, Child, Ramesh, Ziegler, Wu, Winter, Hesse, Chen, Sigler, Litwin, Gray, Chess, Clark, Berner, McCandlish, Radford, Sutskever and Amodei2020). It is well known that the training of such language models requires large resources, both in terms of computing power and available text material in digital form. The above-mentioned idiosyncracies and the unique availability of large-scale resources for English leave a number of open challenges for developing QG methods applicable to languages other than English.
The first challenge is the scarcity of textual resources for pre-training of large-scale language models, for example, BERT or GPT-3, for languages other than English. Training data for English BERT consisted of the BooksCorpus (800M words) and English Wikipedia (2500M words at that time). Currently, English Wikipedia is the largest Wikipedia in the world containing around 6.1 million articles and 3.6 billion words.Footnote a In contrast, Wikipedias for languages with a richer inflectional morphology are significantly smaller, for example, Russian (1.7 million articles and 0.8 billion wordsFootnote b), Finnish (0.5 million articles and 0.14 billion wordsFootnote c) or Turkish (0.4 million articles and 0.11 billion wordsFootnote d). There are no guarantees that pre-trained BERT models on much smaller textual resources will result in as useful representations as those for English, especially for languages with richer morphology. Furthermore, GPT-3, currently available only for English, was trained on a substantially larger data set than BERT with English Wikipedia comprising only 0.6% of all training data tokens (although it was oversampled as a high-quality data set).
The second challenge is the lack of large-scale training data sets for QG and a prohibitively high cost of obtaining such resources. State-of-the-art QG methods for English train their models on the previously mentioned SQuAD data set, which contains more than 100,000 questions. Obtaining a good-quality data set of a similar size is very expensive, especially for languages with fewer native speakers around the world.
The third challenge is knowing how well available methods developed for English would generalise to other languages, especially synthetic ones with a richer inflectional morphology and a less strict word order (e.g., Finnish, Turkish or Russian). To the best of our knowledge, not much research has been done on QG for these kinds of languages.
The fourth challenge is assessing the obtained performance results. Evaluation results in isolation do not provide a comprehensive picture of the method’s performance, especially when using only automatic evaluation metrics, such as BLEU (Papineni et al. Reference Papineni, Roukos, Ward and Zhu2002). Researchers that developed the first statistical QG methods for English could compare their results to rule-based baselines. However, most other languages lack QG baselines, leaving researchers to wonder if the obtained performance is worth the computational resources spent on training the model.
In this article, we are addressing all of the mentioned challenges by proposing a novel, mostly deterministic method, called QuinductorFootnote e (Question inductor), for automatically generating question-answer pairs from data. Quinductor is based on dependency trees and can also be used for languages other than English, due to the Universal Dependencies (UD) framework (Nivre et al. Reference Nivre, de Marneffe, Ginter, Hajič, Manning, Pyysalo, Schuster, Tyers and Zeman2020) offering more than 200 treebanks in 100 languages (substantially more than the number of languages with the pre-trained BERT or GPT-3). The method does require a language-specific QG data set, but its size can be orders of magnitude smaller than SQuAD. Quinductor thus provides a middle ground between data-hungry computationally expensive methods based on neural networks and methods based on manually crafted templates. Hence, we believe that Quinductor can serve as a strong QG baseline for less-resourced languages.
2. Related work
Rus, Cai, and Graesser (Reference Rus, Cai and Graesser2008) broadly defined QG as automatic generation of questions from inputs such as text, raw data or knowledge bases. In this article, we are interested in generating reading comprehension questions from textual data, with their respective correct answers, and we want to do this in multiple languages. We exclude Yes/No-questions and fill-in-the-blank questions, as those can be generated with less sophisticated methods (Gates Reference Gates2011; Agarwal, Shah, and Mannem Reference Agarwal, Shah and Mannem2011; Mostow and Jang Reference Mostow and Jang2012). Hence, we limit the scope of related works only to articles exploring a similar QG setup.
To the best of our knowledge, no other work has proposed an automatic multilingual QG method relying on dependency parsing. The closest by spirit is the work by Afzal and Mitkov (Reference Afzal and Mitkov2014), where sentences are matched against a set of automatically extracted semantic patterns from the GENIA Event Annotation corpus using a Named Entity Recognizer (NER). These patterns are used to extract relevant parts of the dependency tree, which are then transformed into the question by abstracting away the information constituting the correct answer (which should not be a part of the question). The method requires resources that are often lacking for other languages, such as a NER system and a corpus which would be very expensive to annotate.
Mazidi and Nielsen (Reference Mazidi and Nielsen2015) also relied on a dependency parser, a semantic role labeler and discourse cues. However, their method only generated questions without the correct answers, requiring the manual creation of question templates, and relying on language-specific information. Similarly, Khullar et al. (Reference Khullar, Rachna, Hase and Shrivastava2018) proposed a method using a dependency parser and three manually crafted rule sets for transforming statements into questions (without exploring the generation of correct answers).
Rodrigues (Reference Rodrigues2020) induced patterns relying on both constituency and dependency parsers to generate questions in English. On top of that, their system uses a plethora of other resources, such as a named entity recognizer, WordNet (Miller Reference Miller1995), FrameNet (Baker, Fillmore, and Lowe Reference Baker, Fillmore and Lowe1998) and VerbNet (Kipper et al. Reference Kipper, Dang and Palmer2000). These resources are of high quality, but most of them are very expensive and labour-intensive to construct and are thus unavailable for languages other than English.
Other non-neural QG methods utilised hand-written templates based on context-free grammars. One example is the work by Heilman and Smith (Reference Heilman and Smith2009), which used an overgenerate-and-rank strategy for QG without generating correct answers. Another example is the work by Bernhard et al. (Reference Bernhard, De Viron, Moriceau and Tannier2012), which is based on constituent trees and a NER system to generate questions (and their correct answers) in French. Such methods require linguists to create context-free grammars, which is an expensive process, especially for languages with less strict word order and a richer morphology than English.
The most recent QG methods are based on neural networks, and thus require both large-scale data sets in the language of interest, as well as vast computational resources to train the models. Impressive performance for English have been demonstrated by both transformer-based masked language models (Chan and Fan Reference Chan and Fan2019; Dong et al. Reference Dong, Yang, Wang, Wei, Liu, Wang, Gao, Zhou and Hon2019; Liao et al. Reference Liao, Jiang and Liu2020) and auto-regressive models based on encoder–decoder architectures (Du, Shao, and Cardie Reference Du, Shao and Cardie2017; Song et al. Reference Song, Wang, Hamza, Zhang and Gildea2018; Zhao et al. Reference Zhao, Ni, Ding and Ke2018; Bahuleyan et al. Reference Bahuleyan, Mou, Vechtomova and Poupart2018; Kim et al. Reference Kim, Lee, Shin and Jung2019; Liu et al. Reference Liu, Zhao, Niu, Lai, He, Wei and Xu2019). Note that neural models typically do not generate correct answers, but instead use them as an input along with the sentence to generate questions. However, we are not going into more details on the neural methods, as our proposed method is not neural.
To the best of our knowledge, only a very limited number of neural methods explore QG in other languages than English, or multilingual QG. One such example is the work by Kumar et al. (Reference Kumar, Joshi, Mukherjee, Ramakrishnan and Jyothi2019) exploring joint cross-lingual training aimed at reusing the large-scale SQuAD data set for Hindi and Chinese.
3. Methodology
Let D be a data set consisting of triples
$(c_i, q_i, a_i)$
, where
$c_i$
is a context (a text passage),
$q_i$
is a question created based on
$c_i$
, and
$a_i$
is a contiguous phrase in
$c_i$
, answering
$q_i$
. A pair of
$(q_i, a_i)$
will be referred to as a question-answer pair (QA-pair). The aim is then to be able to generate QA-pairs
$(q_j^{\prime}, a_j^{\prime})$
given a previously unseen context
$c_j^{\prime}$
.
Our method, Quinductor, automatically induces QA-templates from the data set D using dependency parsing based on the UD framework. More formally, let
$s_i$
be the sentence from the context
$c_i$
in which the answer
$a_i$
appears (
$s_i$
can be found using a sentence segmenter, a tokenizer, and simple string matching). The QA-pair
$(q_i, a_i)$
is recast into a template in a specific formal language (defined in Section 3.1), using parts of the dependency tree for the sentence
$s_i$
. For instance, suppose
$s_i$
is ‘Tim plays basketball with friends and family every Tuesday’ (with its dependency tree shown in Figure 1), and
$q_i$
is ‘When does Tim play basketball with friends and family?’. Assuming r represents the root of the dependency tree (i.e., the dependent of the ‘root’ pseudonode; the word ‘plays’ in this example),
$q_i$
can now be expressed using the question template (1) and the answer ‘every Tuesday’ could be expressed using the answer template (2). For a formal definition of these expressions, we refer to the Section 3.1.
-
(1)
-
(2)
Figure 1: The dependency tree for the sentence ‘Tim plays basketball with friends and family every Tuesday’.
Figure 2: The dependency tree for the sentence ‘Ericsson pays dividends to the shareholders every first quarter of the year’.
Such a transformation can be applied only if certain conditions are met, and therefore each QA-template has an associated guard (described in its own formal language defined in section 3.2). After inducing both QA-templates and associated guards, we can then apply them to any previously unseen context c
$^{\prime}$
by processing its every sentence s
$^{\prime}$
using the following procedure.
-
Sept 1 Perform dependency parsing on s
$^{\prime}$
and get a dependency tree T
$^{\prime}$
. -
Sept 2 Find all satisfied guards for T
$^{\prime}$
and get a set of corresponding QA-templates
$QA_{T^{\prime}}$
. -
Sept 3 Apply all templates from
$QA_{T^{\prime}}$
to s
$^{\prime}$
, in order to get a set of generated question-answer pairs QA
$^{\prime}$
. Note that many QA-pairs will be unsatisfactory, which is why the next step is introduced. -
Sept 4 Rank QA
$^{\prime}$
so that a QA-pair (q
$^{\prime}$
,a
$^{\prime}$
) is ranked highly if it is likely to be relevant, grammatical, and where a
$^{\prime}$
is likely to be the correct answer to q
$^{\prime}$
. The ranking is done according to the method presented in Section 3.5.
As an example of this procedure, consider s
$^{\prime}$
to be the sentence ‘Ericsson pays dividends to the shareholders every first quarter of the year’ (with a dependency tree in Figure 2), then using the question template (1) and the answer template (2), the following QA-pair can be generated:
-
(3) When does Ericsson pay dividends to the shareholders? – Every first quarter of the year
The key to our method is to make templates as generic as possible to allow a certain amount of variation in their dependency structures. For instance, we want to avoid using adverbial clauses word by word, but instead matching adverbial clauses more generally. This generalisation is addressed by a novel shift-reduce algorithm, described in Section 3.3. Automatic induction of guards is described in Section 3.4. However, before describing the induction algorithms, let us first explain and motivate the designed template and guard languages. In the sections below, we use a bold font in the expression definitions to indicate metalinguistic variables which are not part of the defined languages.
3.1. Template language
Let T be an arbitrary dependency tree and r denote the root of the dependency tree, that is, the dependent of the ‘root’ pseudonode of T. In the example sentence in Figure 1 r corresponds to the word ‘play’ (all further examples will also be given for this sentence). Let n be an arbitrary node of T, then the following definitions are introduced.
-
• n.rel#id denotes a dependent of n with a dependency relation rel and index id of this dependent of n (starting from 0 for the ‘root’ pseudonode). For instance, r.obj#3 denotes the node for the word ‘basketball’.
-
• n.rel1#id1.rel2#id2 ….relN#idN denotes a node n
$^{\prime}$
such that there exists a directed path between nodes n and n’ with each edge having a corresponding dependency relation from a relation chain rel1#id1.rel2#id2 ….relN#idN. The node n
$^{\prime}$
will be referred to as a node at the end of the chain and a whole relation chain will be shortened to relchain. For instance, r.obl#5.case#4 denotes the node for the word ‘with’. This node can then be referred as the node at the end of the chain obl#5.case#4. The ID of the last element of relchain is later referred to as the ID of a template expression.
The IDs are included in the template expressions above to be able to distinguish between different dependents having the same dependency relation. To illustrate when this could be necessary, imagine the dependency relation between the words ‘plays’ and ‘Tuesday’ is obl instead of obl:tmod (an inaccuracy that could be produced by the dependency parsers in practice, especially for languages other than English). Then the question ‘When does Tim play basketball with friends and family?’ with the answer ‘every Tuesday’ would result into the following QA-template (assuming IDs are excluded):
-
(4)
-
(5)
It is impossible to distinguish <r.obl> in the question template (4) from the one in the answer template (5). However, if the IDs are introduced, then one immediately understands that those expressions correspond to different nodes. Note that differentiating between nodes with the same dependency relations is the only purpose of IDs, that is, we do NOT require the new sentences using QA-templates to have exactly the same IDs, as it would obviously hinder generalisation.
Let us define the following operators for selecting substructures from a dependency tree T:
-
• [n] extracts the token at the node n (for instance, [r] extracts the token ‘plays’);
-
• [n.relchain1] extracts the token of the node at the end of relchain1 (for instance, [r.obl#5.conj#7] extracts the token ‘family’);
-
• [n.lemma] ([n.relchain.lemma]) extracts the lemma of the token at the node n (the node at the end of relchain1). Either of these will be referred to as a lemma-expression. For instance, [r.lemma] extracts the string ‘play’ and [r.obl#5.lemma] extracts ‘friend’.
-
• <n> extracts the text string of the subtree rooted at the node n (for instance, <r> extracts the whole sentence);
-
• <n.relchain1> extracts the text string of the subtree rooted at the node at the end of relchain1 preserving the linear order (for instance, <r.obl#5.conj#7> extracts the string ‘and family’);
-
• <n.relchain1 - relchain2> extracts the text string of the subtree rooted at the node at the end of relchain1 except the text string of the subtree rooted at the node at the end of relchain2 (if such a subtree exists). Relchains that are subtracted in any template expression will be referred to as negatives. For instance, <r.obl#5.conj#7 - cc#6> extracts the string ‘family’. However, non-existing negatives do not influence the result, hence <r.obl#5.conj#7 - case#6> extracts the string ‘and family’, since there is no child of r.obl#5.conj#7 with a dependency relation case.
-
• <n.relchain1 - relchain2*> extracts the text string of a subtree rooted at the node at the end of relchain1 except the contents of the node at the end of relchain2 (if it exists). For instance, <r.obl#5 - conj#7 *> extracts the string ‘with friends and’. Note that the extracted string is not guaranteed to be a contiguous substring of the sentence.
Template expressions surrounded by square brackets ([]) will be referred to as node-level expressions and those surrounded by angle brackets (<>) as subtree-level expressions.
To distinguish the answer from the question, we use an additional binary infix operator q => a, denoting that the first operand is the question template, and the second one is the answer template. For instance, the question ‘When does Tim play basketball with friends and family?’ with the answer ‘every Tuesday’ could be represented as the following QA-template.
-
(6)
Note that words from the question that do not appear in the original sentence will not form any template expressions. Instead, they will be considered constant and rendered as a plain text, for example, ‘When’ and ‘does’ in the template (6).
3.2. Guard language
Recall that a guard is an expression specifying conditions for using a specific template. Formally, let T be an arbitrary dependency tree, and n denote a node in T. Then:
-
• n.pos denotes the part-of-speech (POS) tag assigned to the word associated with n (below referred to as a pos-property);
-
• n.morph denotes a set of morphological features, as defined by UD, associated with n (below referred to as a morph-property).
Each guard consists of clauses separated by a comma operator (,) denoting logical AND. Let us introduce operators defining the conditions for the guard clause to be satisfied:
-
• the unary operator exists can be applied exclusively to relchains in order to only accept sentences having a specified relchain;
-
• a binary operator is (is_not) can be applied merely to pos-properties to only accept sentences with a specific node having (lacking) a specified POS-tag;
-
• a binary operator has (has_not) can be applied to morph-properties exclusively to only accept sentences with a specific node having (lacking) specified morphological properties (in the UD format).
To specify which template should be used if all guard clauses are satisfied, we use an additional infix operator guard -> t denoting that if the first operand (guard) is satisfied, the template found by the unique identifier t can be used.
To exemplify, the guard for the template (6) could look as follows.
-
(7) n.pos is VERB, n.nsubj exists, n.obj exists, n.obl exists,
n.obl:tmod exists -> template3
Note that no requirement on the exact IDs of the nodes is present in the guards, since the IDs are only used during the template induction phase.
After having described both template and guard languages, we are now ready to explain the algorithms for automatically inducing templates (Section 3.3) and guards (Section 3.4).
3.3. Template induction
Recall that a datapoint is a triple
$(c_i, q_i, a_i)$
, where
$c_i$
is a context,
$q_i$
is a question asked on the basis of
$c_i$
, and
$a_i$
is a contiguous phrase in
$c_i$
constituting the correct answer to
$q_i$
. The goal is to induce templates for every
$(q_i, a_i) \in D$
, allowing to generalise to syntactically similar QA-pairs
$(q^{\prime}_j, a^{\prime}_j) \not\in D$
. This is achieved by merging template expressions into subtree-level expressions as much as possible, using the novel shift-reduce algorithm described below.
The preprocessing step is to find all triples
$(s_i, q_i, a_i)$
such that
$a_i$
is a contiguous phrase in
$s_i \in S(c_i)$
, where
$S(c_i)$
is the set of sentences of the context
$c_i$
. Recall that this step is trivially performed using a sentence segmenter, a tokenizer, and simple string matching.
The next step is to select only satisfactory triples, where
$s_i$
and
$q_i$
have at least one word in common (if not, then generalisation is impossible). After obtaining a number of satisfactory triples
$(s_i, q_i, a_i)$
, the induction of a template for transforming
$s_i$
into a pair of
$(q_i, a_i)$
can be described as the following 3-step process applied twice (once for
$q_i$
and once for
$a_i$
).
-
(1) Sentence transformation. Describe every word of
$q_i$
(
$a_i$
) in terms of dependency structures present in
$s_i$
using the formal template language presented in Section 3.1. When finished, proceed to step 2. -
(2) Shift-reduce. Simplify the template obtained at the previous step using the novel shift-reduce algorithm described in Section 3.3.2. In the rare case when the resulting template consists only of a single template expression (and would therefore generalise poorly), return the sentence transformation from step 1 as the final template, otherwise, proceed to step 3.
-
(3) Merging negatives. If possible, merge negatives (the subtracted relchains) in every template expression using the algorithm described in Section 3.3.3. Return the template with merged negatives as final.
Recall that words from the question that do not appear in the original sentence will be considered constant and rendered as a plain text. Templates containing only constants will not generalise and are thus removed after all templates have been induced. The remaining templates (i.e., with at least one non-constant template expression) are post-filtered to exclude templates with rare words (since those will not generalise well). We define a word as rare if it appeared in less than 25% of the documents and detect it based on the inverse document frequency (IDF), that is, we exclude all templates with a maximal IDF among their constant words exceeding
$\log\left(\frac{N}{\frac{N}{4}}\right)=\log(4)$
, where N is the number of documents in the corpus.
For demonstrating the algorithm, we consider the sentence ‘The longest river in Brazil is the Amazon river’ and the QA-pair ‘What is the longest river in Brazil?’ – ‘Amazon river’, which we will refer to as an example QA-pair.
3.3.1. Sentence transformation
The goal of this step is to describe every word in
$q_i$
and
$a_i$
in terms of dependency structures of
$s_i$
(shown in Figure 3). The sentence transformation applied to question from the example QA-pair would then take the following form:
-
(8)
Figure 3: Illustration of the sentence transformation step on the question from the example QA-pair.
Whereas sentence transformation applied to the answer of the example QA-pair would be:
-
(9)
To perform sentence transformation, first, both
$s_i$
and
$q_i$
should be parsed to get the dependency trees
$T_{s_i}$
and
$T_{q_i}$
, respectively (for example, see dependency trees in Figure 3).
$T_{q_i}$
is then traversed in linear order
$L_{T_{q_i}}$
. For each node
$n_q$
in
$L_{T_{q_i}}$
, the algorithm attempts to find a matching node in
$T_{s_i}$
with the same FORM or LEMMA. If no matching nodes are found,
$n_q$
is replaced by its FORM. If matching nodes are found,
$n_q$
is replaced by the list of template expressions corresponding to those nodes in
$T_{s_i}$
(using the template language presented in Section 3.1). This list is sorted in the ascending order by the distance from the root node of
$s_i$
in edges. The resulting list of lists of template expressions will be referred to as LLTE. The reason behind introducing LLTE is that certain words might appear more than once in
$s_i$
, for instance, the word ‘river’ (appearing as both r and r.nsubj#3 in Figure 3). We therefore need the heuristic method for finding the correct occurrence of the word. This heuristic, called LLTE resolution, is presented below. We provide an example for the LLTE of the question from the example QA-pair in the grey box marked ‘LLTE’ in Figure 3. Note that generation of lemma-expressions (e.g., [r.lemma]) is subject to the availability of a lemmatizer, in the absence of which the algorithm will simply insert a constant expression (i.e., the FORM of the token itself).
A template will generalise if many syntactic structures can be merged into subtree-level expressions, which is the goal of the next shift-reduce step of Quinductor. Hence, the result of sentence transformation should contain as many long contiguous phrases as possible. Achieving this goal imposes two requirements on LLTE: each list of LLTE should contain only one expression, and the resulting LLTE should contain a maximal possible amount of contiguous phrases. To address both requirements, we designed a heuristic for LLTE resolution that filters out template expressions from these lists until both of them contain one template expression each. To perform the filtering, we use the sum of absolute ID differences for the whole of question given each candidate pair of template expressions in positions under consideration. To construct candidate pairs, we process the lists from the left to right and combine every expression with every other in the order of their appearance. To give an abstract example, if we have two lists [1, 2] and [3, 4], then we would construct the following candidate pairs [(1, 3), (1, 4), (2, 3), (2, 4)].
To exemplify the heuristic, consider LLTE shown in Figure 3. As we can see, most of the words already have one corresponding template expression, except for the words ‘the’ and ‘river’ with 2 template expressions each. For these words, we need to apply our heuristic. The sums of absolute ID differences for different combinations of the template expressions for the words ‘the’ and ‘river’ are presented in Table 1. To exemplify these calculations, for the candidate template expressions [r.det#7] and [r#9] (for the words ‘the’ and ‘river,’ respectively). First, we skip the constant ‘What’, since it is not a template expression. Then we calculate the difference between the IDs of the template expressions in the next two adjacent positions, that is, r.cop#6 and r.det#7, which amounts to
$|7 - 6| = 1$
. Then we take template expressions in the next two adjacent positions, that is, r.det#7 and r.nsubj#3.amod#2. Recall that we defined the ID of a template expression to be the ID of the last element of the relchain, hence the absolute difference in this case amounts to
$|2 - 7| = 5$
. And we continue this procedure until we reached the end of the question, which in total amounts to
$|7 - 6| + |2 - 7| + |9 - 2| + |4 - 9| + |5 - 4| = 19$
, which corresponds to the value in the first row of Table 1.
Table 1. Sums of absolute ID differences for alternative representations of the words ‘the’ and ‘river’ for resolving LLTE in Figure 3
We assume that the question with most contiguous phrases should have LLTE with the minimal sum of absolute ID differences. In our example, two candidate pairs have exactly the same sum of 9, in which case we pick the pair that comes first in the list (recall that the list is sorted in the ascending order by the distance from the root node of
$s_i$
in edges), that is, [w.det#7] for ‘the’ and [w.nsubj#3] for ‘river’, resulting in the following sentence transformation
-
(10)
As can be seen, the algorithm chose the right expression for the word ‘river’ and the wrong one for the word ‘the’. Such errors depend on the order of expressions in each list in LLTE (recall, that those are ordered by the distance from the root, in edges). We want to stress that this is a heuristic and will not result in the optimal ordering all the time. Furthermore, we believe that there is no universal order that will result in choosing the right expressions all the time for all the languages.
3.3.2. Shift-reduce
The goal of this step is to make templates generalisable, which is achieved by merging template expressions into subtree-level expressions as much as possible using a novel shift-reduce algorithm. At every algorithm step, a current template (starting with the template obtained after the sentence transformation) is divided into a LIFO stack, where all seen items reside, and a FIFO buffer, containing the remainder. Depending on the stack-buffer configuration, one of the following two actions can be chosen:
-
• SHIFT, that removes the top expression from the buffer and adds it to the stack.
-
• REDUCE, that checks the topmost and the second topmost expressions on the stack and merges them into a subtree-level expression.
While SHIFT action is self-explanatory, REDUCE can be described as a 3-step procedure, operating on the topmost (stackTop) and the second topmost (stackTop2) template expressions on the stack.
-
Step 1 Extract relchains from stackTop and stackTop2 and find their longest common prefix, referred to as the common relchain. The node at the end of the common relchain is the closest common ancestor of the nodes corresponding to stackTop and stackTop2.
-
Step 2 The second step is to ensure that the two merging conditions are satisfied:
-
a. the common relchain is not empty;
-
b. the common relchain differs from either relchain of stackTop or stackTop2 by at most one dependency relation.
-
We have empirically found that these merging conditions increase generalisation chances.
-
Step 3 If the aforementioned conditions are met, stackTop and stackTop2 can be replaced by the subtree-level template expression of their common relchain with a number of subtracted negatives corresponding to all tokens of the induced subtree except those necessary to keep: stackTop, stackTop2, any node from the sentence transformation, and any whole subtree containing any of these nodes.
Figure 4: Illustration of the shift-reduce step on the question from the example QA-pair.
To exemplify, shift-reduce is applied to the template (10), obtained in Section 3.3.1, as follows. All the configurations, referred to in the description below, can be found in Figure 4.
-
(1) Put the whole template on the buffer, the stack is empty (the configuration A).
-
(2) Perform shifts until the two topmost elements on the stack are template expressions (3 SHIFTs were needed in our case, leading to the configuration B).
-
(3) stackTop is [r.det#7] and stackTop2 is [r.cop#6], their common relchain is empty, hence the first merging condition fails. Perform a number of SHIFTs until the merging conditions succeed (2 SHIFTs in our case, leading to the configuration C).
-
(4) Now stackTop is [r.nsubj#3] and stackTop2 is [r.nsubj#3.amod#2], their common relchain is nsubj#3 and it differs from the relchains of both elements by at most one dependency relation. Both merging conditions are satisfied, perform a REDUCE and replace these two node-level expressions by one subtree-level expression containing their common relchain, that is, <r.nsubj#3>. Check if there are any more nodes in this subtree except the ones whose node-level expressions we just removed. In this case, The, in and Brazil belong to the same subtree, so we should subtract them. This results in the subtree-level template expression <r.nsubj#3 - det#1 - nmod#5.case#4 - nmod#5* > (dubbed <TE3>) and leads to the configuration D. REDUCE is finished, perform a SHIFT, leading to the configuration E.
-
(5) stackTop is [r.nsubj#3.nmod#5.case#4] and stackTop2 is the result of the step (4). Their common relchain, nsubj#3, differs from relchain of stackTop by 2 dependency relations. Merging conditions failed, perform a SHIFT, leading to the configuration F.
-
(6) Now stackTop2 is [r.nsubj#3.nmod#5.case#4] and stackTop is [r.nsubj#3.nmod#5], their common relchain is nsubj#3.nmod#5. Merging conditions are satisfied, the REDUCE action is triggered, replacing both node-level expressions by <r.nsubj#3.nmod#5>. There are no unaccounted nodes in this subtree, hence there is nothing to subtract, leading to the configuration G. The buffer is empty, so the algorithm terminates. The resulting template (11) is on the stack in the reversed order.
-
(11)
3.3.3. Merging negatives
Recall that negatives are relchains subtracted in any template expression. The goal of this step is to merge negatives in the resulting template after the shift-reduce step, in order to make templates even more generic and generalisable.
The step can be performed only if we have a template expression with more than one negative (otherwise there is nothing to merge). To perform this step, we need to create a mapping for the dependency tree of the original sentence between each node and its direct children, referred to as a direct children mapping, DCM. Then, for every template expression, check if any subset of negatives matches any set of children from the mapping. In case of a match, all matched negatives should be swapped for the corresponding subtree root.
To exemplify, consider template (11), obtained after shift-reduce in the previous section. There is only one template expression with negatives: <r.nsubj#3 - det#1 - nmod#5* - nmod#5.case#4>. Indeed, this template expression has 3 negatives: - det#1, - nmod#5* and - nmod#5.case#4. Hence, we can attempt merging negatives. The step of merging negatives for the template (11) is illustrated in Figure 5. The direct children mapping for every node in the original dependency tree is marked as ‘DCM X’.
Figure 5: Illustration of merging negatives on the question from the example QA-pair.
As mentioned previously, we can attempt merging negatives only on one template expression: <r.nsubj#3 - det#1 - nmod#5* - nmod#5.case#4>. Now we need to examine every DCM and check whether it contains any subset of negatives from the given template expression. Indeed, the mapping ‘DCM 5’ contains two negatives (- nmod#5* , and - nmod#5.case#4) marked with a red dashed line in Figure 5. Hence, these two expressions can be swapped for the expression of their subtree, nmod#5. The resulting template expression then becomes <r.nsubj#3 - det#1 - nmod#5> (dubbed <TE3’>) and the final induced template is template (12)
-
(12)
The advantage of the resulting template expression after merging negatives is that it makes no assumptions on the structure of a nominal modifier nmod#5. Indeed, the original template assumed that by subtracting nmod#5* and nmod#5.case#4, the whole subtree corresponding to nmod#5 is removed. While this is true for this particular example, nominal modifiers (and many other constructs) can, however, vary in structure and thus the template without merging negatives will generalise poorly to sentences with nominal modifiers (or other constructs) of different structure. To address this problem, the negatives of each template expression should be merged as much as possible to their common parent.
3.4. Guard induction
A template can have multiple guards. Consider two sentences ‘John is playing basketball’ and ‘John has played basketball’. Both questions ‘What is John playing?’ and ‘What has John played?’ would result in the same template (supported by the previously mentioned sentences). However, the morphological properties of the root of each sentence (‘playing’ and ‘played’, respectively) are different. Hence, there are 2 different cases when this template could be applied, and thus 2 guards.
Motivated by the example above, guards consist of base and complementary guards. A base guard contains the requirements for using templates and is created in the following 3 steps:
-
(1) Create an exists-clause for the relchain of every template expression present in the question or answer (excluding the negatives).
-
(2) If a template for the answer contains a nominal subject (nsubj) as a non-negative expression, add the clause n.nsubj.morph has_not PronType=Rel ensuring that the subject is not a relative pronoun (e.g., ‘which’). This is motivated by the fact that no reading comprehension question would ask about a relative pronoun.
-
(3) If a root is involved in the creation of a template, and it is a verb without an auxiliary verb, add a clause n.aux not_exists. The rationale behind this step is to separate templates for questions with either copula or tenses requiring a modal verb, from those questions that do not exhibit these features.
Complementary guards contain requirements specific to the sentences supporting the generated template. Complementary guards are induced by creating an is-clause for the pos-property and has-clause for the morph-property of the root of every sentence from the corpus supporting the current template.
To get a final set of guards for the template, add the base guard to each complementary guard and use an infix operator -> to point each guard from the induced set to the template of interest.
For instance, the guard for the template (12) would look as (13), and n.morph has Number=Sing, n.pos is VERB are the only complementary guards.
-
(13) n.morph has Number=Sing, n.pos is NOUN, n.cop exists, n.det exists, n.nsubj exists, n.nsubj.nmod exists, n.nsubj.morph has_not PronType=Rel -> template12
3.5. Ranking and filtering
After all templates and guards have been generated, they can be applied to unseen data to produce a number of QA-pairs. With the purpose of down-voting undesirable QA-pairs, we use the following two models that serve as a proxy to grammaticality of the questions for ranking and filtering.
-
(1) An n-gram model based on any pos-morph-tagged UD-compliant corpus. For instance, we use a 3-gram model, which could give the following probability P(NOUN/Number=Sing
$|$
DET/Definite=Def, ADJ/Number=Sing). -
(2) A question-word model calculating the count
${\textit c}(qw,r)$
for each pair of question word qw and pos-morph expression of the root r of the corresponding answer, for example, (when,NOUN/Number=Sing).
Both models operate on pos-morph expressions (i.e., words are substituted by their POS-tag together with UD morphological features, if applicable). For instance, the pos-morph expression for the word ‘basketball’ is NOUN/Number=Sing and for the word ‘on’ is ADP.
The first step is basic filtering and involves two procedures. The first one aims at filtering out QA pairs with a single-word answer, whose pos-morph expression has never occurred in the training corpus as an answer. The procedure prevents generating single-word answers containing only function words (e.g., ‘the’, ‘himself’, ‘to’). The second one ensures that a pair of question word and pos-morph expression of the root of the corresponding answer appeared in the training data at least once using a question-word model. This procedure contributes towards minimising the obvious mismatches between the question word and the answer (e.g., ‘where’-question with a date as the answer).
The second step is to rank every remaining QA pair j according to the score
$r_{qa}^{(j)}$
using Equations (1)–(3). Equation (1) is a convex combination using the n-gram model, where
$p^*$
denotes the backoff probability, in which each word
$w_i$
is substituted by its pos-morph expression (or by a POS-tag only if the former does not exist).
$N_j$
is the number of trigrams in the question
$q_j$
, since we use a 3-gram model. In our experiments,
$\lambda_4 = 0.000001, \lambda_3 = 0.01 - \lambda_4, \lambda_2 = 0.1 - \lambda_3, \lambda_1=0.9$
. Note that the values of
$\lambda_i, i \in [1, 4]$
can be estimated from data, as described by Jurafsky and Martin (Reference Jurafsky and Martin2018, Section 3.5.3); however, we opted for setting them heuristically as those estimates will be unreliable for low-resourced languages with small amounts of textual data.
\begin{equation} r_{ng}^{(j)} = \frac{1}{N_j} \sum_{i=1}^{N_j}\lambda_1 p^*(w_{i}|w_{i-2}, w_{i-1}) + \lambda_2 p^*(w_{i}|w_{i-1}) + \lambda_3p^*(w_i) + \lambda_4\end{equation}
Equation (2) uses the question-word model to get the frequency of the pair of the question word qw and the root token of the answer
$r_{a_j}$
.
\begin{equation} r_{qw}^{(j)} = \frac{{\textit c}(qw,r_{a_j})}{\sum_i{\textit c}(qw,r_i)}\end{equation}
Equation (3) provides the final score, which is a convex combination between the scores calculated in Equations (1) and (2). For our experiments, we have performed a manual search for
$\alpha \in [0.1, 0.9]$
and found that
$\alpha=0.8$
ranked grammatically correct questions with suitable answers highest more frequently than the other alternatives.
\begin{equation} r_{qa}^{(j)} = \alpha \cdot r_{ng}^{(j)} + (1 - \alpha) \cdot r_{qw}^{(j)};\end{equation}
Using the aforementioned n-gram and question-word models, a generated QA-pair is given a high score
$r_{qa}$
if the question is made of a likely sequence of pos-morph expressions, and the question word (e.g., ‘when’) matches the answer well.
The final step is referred to as mean filtering. This step ensures that only questions scoring higher than (or equal to) the mean of the scores for all generated questions for all sentences will be returned. Such filtering allows Quinductor to drop generated questions of potentially poor quality, and thus sometimes choose not to generate any QA-pairs for a given sentence.
4. Data
To evaluate Quinductor in a multilingual setting, we have utilised a data set called TyDi QA (Clark et al. Reference Clark, Choi, Collins, Garrette, Kwiatkowski, Nikolaev and Palomaki2020). The data set is a question-answering benchmark based on Wikipedia articles for 11 typologically diverse languages. Eight of these languages have available UD treebanks and trained dependency parsers in Stanza package (Qi et al. Reference Qi, Zhang, Zhang, Bolton and Manning2020), which we have utilised for inducing templates in all languages. For both training and evaluation, we have excluded Yes/No-questions resulting in the filtered training/development sets of the sizes reported in Table 2. Due to limited resources, we have performed a human evaluation only on a subset of languages, while reporting automatic evaluation metrics for all languages with the available UD treebanks.
Table 2. Language-specific information along with the sizes of filtered training and development sets (the number of QA-pairs along with a proportion of the original sets in parentheses) and the associated UD treebanks (UDT size, in tokens) used by the pre-trained Stanza parsers for the languages in the TyDi QA data set. Question phrase positions are either obligatorily initial (OI), or not OI, or mixed, as defined by Dryer (Reference Dryer2005)
To compare Quinductor to previous work, we have also used the SQuAD data set (Rajpurkar et al. Reference Rajpurkar, Zhang, Lopyrev and Liang2016) for English, specifically the training/validation/test split provided by Du et al. (Reference Du, Shao and Cardie2017).
5. Evaluation
Essentially, automatic evaluation metrics, such as BLEU (Papineni et al. Reference Papineni, Roukos, Ward and Zhu2002), ROUGE (Lin Reference Lin2004), METEOR (Agarwal and Lavie Reference Agarwal and Lavie2008) and CIDEr (Vedantam, Lawrence Zitnick, and Parikh Reference Vedantam, Lawrence Zitnick and Parikh2015), rely on comparing word overlap between a generated question and a reference question. Such metrics can yield a low score even if the generated question is valid but just happens to be different from the reference question, or a high score even though the question is ungrammatical but happens to have a high word overlap with the reference question (see the article by Callison-Burch, Osborne, and Koehn (Reference Callison-Burch, Osborne and Koehn2006) for a further discussion). Nonetheless, Amidei, Piwek, and Willis (Reference Amidei, Piwek and Willis2018) reports that 32% of the surveyed papers on automatic QG used only automatic evaluation metrics, although Nema and Khapra (Reference Nema and Khapra2018) found that there is only a weak correlation between the automatic evaluation metrics and human judgements on answerability of the generated questions. For a broader discussion on the relationship between automatic evaluation metrics and human judgements, an interested reader is referred to Gatt and Krahmer (Reference Gatt and Krahmer2018, Section 7.4.1). In this article, we report automatic evaluation metrics for the following two reasons. First, for the sake of comparability to other results reported in the literature, and giving a point of reference to researchers lacking resources to conduct human evaluations. Second, to assess the degree of the word overlap of the questions generated by Quinductor and the reference questions, as well as the quality of this overlap (e.g., if it contains mostly stop words).
The conducted human evaluation aims at providing insights about strengths and weaknesses of Quinductor as well as directions for future research. Unfortunately, there exist no standardised questionnaires and/or guidelines for human evaluation of automatically generated questions and answers. Amidei et al. (Reference Amidei, Piwek and Willis2018) report 22 different criteria used by researchers to evaluate QG systems. Evaluations differ both on the number of criteria used and on the granularity of the rating scales for human judgements (Amidei et al. Reference Amidei, Piwek and Willis2018, Table 7). The number of human judges ranges from 1 to 364 (with an average of 4 and a mode of 2), and the number of sampled questions to be evaluated ranges from 60 to 2186 (with an average of 493). Amidei et al. (Reference Amidei, Piwek and Willis2018) note that often the papers provide only little information about the evaluation guidelines as well.
For this article, we have tried to combine best practices from the reported evaluation guidelines for QG, notably (Heilman and Smith Reference Heilman and Smith2009; Rus et al. Reference Rus, Wyse, Piwek, Lintean, Stoyanchev and Moldovan2010), and more generally, best practices in human evaluation for NLG, as consolidated by van der Lee et al. (Reference van der Lee, Gatt, van Miltenburg and Krahmer2021). On that basis, we propose to conduct human evaluation using a 9-item questionnaire. Each questionnaire item is rated on a 4-point Likert-type scale (see more information and design motivation in Appendix A).
A subset of automatic evaluation metrics (BLEU-N, ROUGE-L and CIDEr) was calculated using the nlg-eval package (Sharma et al. Reference Sharma, El Asri, Schulz and Zumer2017) and METEOR using METEOR-1.5 packageFootnote f (Denkowski and Lavie Reference Denkowski and Lavie2014). For all experiments, we have used dependency parsers trained on UD treebanks as a part of Stanza package (Qi et al. Reference Qi, Zhang, Zhang, Bolton and Manning2020). All templates were induced and then processed using UDon2 (Kalpakchi and Boye Reference Kalpakchi and Boye2020) – an efficient package for manipulating dependency trees, written in C++ with Python bindings.
5.1. Multilingual setting
In order to support the claim about Quinductor’s applicability to multiple languages, we have performed an evaluation on the subset of the TyDi QA data set containing 8 typologically diverse languages (see more information about the subset in Section 4). Different languages required somewhat different pre-processing steps, which are documented in Appendix B.
5.1.1. Automatic evaluation
We have evaluated Quinductor on all languages present in the TyDi QA data set with available UD treebanks and pre-trained dependency parsers in Stanza. The templates were induced using the training sets, and the questions were generated on the development sets of the TyDi QA data set. Only the top-ranked generated question (if any) was considered for automatic evaluation with the respective automatic evaluation metrics reported in Table 3. The proportion of source sentences (the ones where the correct answer is found), for which Quinductor could generate anything at all is reported in Table 6.
Table 3. Automatic evaluation on the filtered TyDi QA development sets only for generated questions ranked first
Quinductor was able to induce templates for all of these languages, but failed to generate any questions on the development sets for Telugu and Korean. The main reason is that QA-pairs for these languages contain answers that use smaller parts of some words (dubbed subwords) in the original sentence. As can be seen in Table 4, such cases constitute 53% and 60% of the training QA-pairs for Telugu and Korean, respectively, whereas the corresponding proportions for other languages are much lower. For instance, the word “
” (‘Israel’) is used as the answer for one of the QA-pairs in Korean, whereas the original sentence contains the word ”
” (“Israeli”). Given that the number of possible questions not using subwords in the provided answers is only 19%, and the data set for Korean is the smallest (only 1638 QA-pairs), it is no surprise that Quinductor managed to generate only 9 templates. The same proportion for Telugu is 35%, resulting in a larger number of templates, but only 1 generated question. This can most probably be attributed to the small size of Telugu’s treebank (only 6K tokens), which might result in a less generalisable dependency parser.
Table 4. Descriptive statistics of the TyDi QA training data for different languages. Recall that ‘satisfactory questions’ have at least one word in common with the original sentence
Table 5. Descriptive statistics of the templates produced using the filtered training set of the TyDi QA data set for different languages. Support per template is the number of sentences from the training set that yield the same template
While it is no surprise that subwords are used in agglutinative languages (e.g., Telugu, Korean, Japanese, Finnish, Indonesian) or fusional languages (e.g., Arabic), such cases are more surprising for English and Russian. For these languages, the cases are due to differences in tokenization between the original sentences and the provided answers (which can happen, since Stanza’s tokenizers are based on neural networks). For example, the answer ‘
$\$$
102 million’ was tokenized as ‘
$\$$
102’, ‘million’ for the answer and as ‘
$\$$
’, ‘102’, ‘million’ in the original sentence.
Note, however, that even with a very limited set of induced templates Quinductor managed to find source sentences (152 for Telugu and 92 for Korean, as reported in Table 6), for which at least one template was applicable (meaning the guard was passed and the question could be induced). However, the questions were not deemed to be of sufficient quality, since most of them did not pass even basic filtering. This highlights the important property of Quinductor: sometimes the method will choose not generate anything if the question is obviously of insufficient quality (which basic and mean filtering attempt to capture). This is in contrast to some neural question generation methods, which are often forced to generate something for all input data.
Table 6. Descriptive statistics of the questions induced on the filtered development set of the TyDi QA data set for different languages using the templates, mentioned in Table 5. ‘SS’ stands for ‘source sentence(s)’, that is, the sentence in which the correct answer is found. ‘
$\ge 1$
applicable template’ means that at least 1 question was induced from the given SS
Russian and Japanese are two best performing languages in terms of BLEU-1 scores, meaning the induced questions have the highest word overlap with the reference questions. However, while Russian performs the best in terms of BLEU-4 (4-grams overlap), Japanese performs the worst (the other agglutinative languages, Finnish and Indonesian, perform similarly to Japanese in terms of BLEU-4). Note, however, that Quinductor managed to induce templates for both Russian and Japanese on a smaller subset of the development sets than for other languages, except Telugu and Korean (10% for Russian and 14% for Japanese). So these performance differences might be attributed to the types of questions available in the data set and not to the Quinductor method itself.
Performance in METEOR scores (which have been shown by Agarwal and Lavie Reference Agarwal and Lavie2008 to correlate with human judgements better than BLEU scores) is roughly similar between all languages except a considerably higher score for Russian (should be treated with caution, as mentioned previously). This shows that while 4-gram precision is lower for some languages, the number of aligned matches is comparable.
Performance in ROUGE-L scores varies significantly with Japanese and Russian performing on-par at the top of the list, while Indonesian and Finnish are at the bottom of the list. While this clearly indicates that the length of the longest common matched subsequence varies across languages, the reasons behind this variation are unclear.
The final metric, CIDEr takes into account if the matched words are frequent or rare (and thus more informative) using inverse document frequency (IDF). The more rare the matched words, the higher the score. The CIDEr score for Russian is significantly higher than for all other languages meaning that word overlap with reference questions contains more rare words. By contrast, the score CIDEr for Finnish is significantly lower than for all the other languages, meaning that most of the matched words are frequent ones (such as question words, prepositions or common verbs). This makes both Russian and Finnish interesting candidates for human evaluation to see whether such significant difference in CIDEr scores results in significant difference in the quality of the questions according to human judges.
The only available fusional language, Arabic, exhibits similar performance to the agglutinative languages (except CIDEr in Finnish). The notable difference is the significantly higher number of induced templates. It is also interesting that no templates could be generated without the prior removal of punctuation as a pre-processing step. This calls for additional investigation of the quality of the output of Arabic’s dependency parser and potentially further tweaks of Quinductor to suit fusional languages better.
Finally, the performance for Indonesian is on-par with Arabic, which is interesting, given that Indonesian is the only language in TyDi QA with a mixed question phrase position (meaning that some question phrases are obligatorily initial and some are not). However, the templates for Indonesian have been induced assuming that the first word of the reference question is a question word. Hence, the obtained performance might be due to specific properties of the data set and requires further investigation on other data sets.
5.1.2. Human evaluation
As mentioned previously, Finnish and Russian were interesting candidates for human evaluation and were chosen along with English. For evaluation, we randomly sampled 50 sentences for each language and generated QA-pairs for them using the induced templates. Fifty generated QA-pairs were combined with 50 original QA-pairs from the corpus (later referred to as gold QA-pairs), corresponding to the same sampled sentences, and presented for evaluation in a random order to 5 human judges via the Prolific platform.Footnote g Each triple of a sentence and a QA-pair was judged using a questionnaire comprising 9 criteria (formulated as statements) to be evaluated on a 4-point Likert-type scale (from ‘Disagree’ to ‘Agree’). Further details about the questionnaires, guidelines and evaluation process in general are provided in Appendix A.
The score of each judge per criterion is treated as a judgement on an ordinal scale, instead of treating all criteria together as an interval scale. The rationale behind such treatment is that a single aggregated quality score of questions and/or answers (over judgement criteria) is not very informative and will not help in pinpointing the exact problems observed in generated QA-pairs.
Following the work of Amidei, Piwek, and Willis (Reference Amidei, Piwek and Willis2019), we assess inter-annotator agreement (IAA) using Fleiss’
$\kappa$
(Fleiss Reference Fleiss1971) and Goodman–Kruskall’s
$\gamma$
(Goodman and Kruskal Reference Goodman and Kruskal1979). However, keeping in mind that we deal with ordinal data, the following two slight differences from Amidei et al. (Reference Amidei, Piwek and Willis2019) are introduced in our approach.
First, Fleiss’
$\kappa$
(Fleiss Reference Fleiss1971) measures the level of agreement compared to agreement by chance, originally defined by Fleiss through the marginal distribution of scores over categories (hence another name of this statistics – fixed-marginal
$\kappa$
). However, using Fleiss’
$\kappa$
is appropriate only if judges know a priori how many cases should be distributed into each category (see Randolph Reference Randolph2005) for an extensive discussion on the matter). In our case, it would not make sense to require judges to rate in this way, making the original Fleiss’
$\kappa$
inappropriate for our purposes. Instead the free-marginal alternative
$\kappa$
, introduced by Randolph (Reference Randolph2005) and later referred to as Randolph’s
$\kappa$
, should be used. In Randolph’s
$\kappa$
the probability of agreement by chance is assumed to be uniform and thus suitable in our case.
Second, Goodman-Kruskall’s
$\gamma$
(GK
$\gamma$
) was designed to measure rank correlation between ordinal judgements of two judges. Amidei et al. (Reference Amidei, Piwek and Willis2019) averaged GK
$\gamma$
over pairs of judges, which is not interpretable from a statistical perspective, given that correlation coefficients are not additive (see Appendix C for a discussion on the matter). Instead of computing the mean, we propose a generalisation of GK
$\gamma$
to multiple raters, dubbed
$\gamma_N$
(derived in Appendix C).
\begin{equation} \Pi_N = \{(i, j) | i \in U, j \in U, i < j \} \end{equation}
\begin{equation} C_N = \sum_{(i, j) \in \Pi_N} C_{ij}; \ \ D_N = \sum_{(i, j) \in \Pi_N} D_{ij}; \ \ \gamma_N = \frac{C_N - D_N}{C_N + D_N} \end{equation}
where U is the set of indices corresponding to human judges,
$C_{ij}$
(
$D_{ij}$
) is the number of concordant judgement pairs (i.e., ranked in the same order by judges i and j) or discordant judgement pairs (ranked in the reversed order by judges i and j).
Inter-annotator agreement (IAA) for the conducted human evaluations are reported in Table 7 per criterion for gold and generated QA-pairs separately. On the scale for Fleiss’ kappa proposed by Landis and Koch (Reference Landis and Koch1977), there is a slight agreement between judges for most of the criteria for English and a moderate agreement for Finnish and Russian. Following Amidei et al. (Reference Amidei, Piwek and Willis2019), we use the scale for GK
$\gamma_N$
proposed by Rosenthal (Reference Rosenthal1996). On this scale, there is a large correlation between the judgements on most of the criteria for English and a very large correlation for Finnish and Russian. A notable observation is that IAA for English is substantially lower on all criteria, no matter the IAA metric, or whether the QA-pairs were generated or gold. Another observation of interest is that the generated QA-pairs get lower Randolph’s
$\kappa$
, but higher GK
$\gamma_N$
compared to the gold ones in the vast majority of cases. This means that the exact scores for generated questions differ more than for gold ones, but the ranking order is more consistent.
Table 7. Inter-annotator agreement per criterion. Q stands for ‘Question’ and SA – for ‘Suggested answer’
To break down the results even further, we report the aggregated scores per each criterion using bi-variate histograms in Figure A.3 in Appendix A Recall that we treat human judgements as ordinal data. Valid measures of central tendency for ordinal data are median (the value separating a higher half from the lower half of a sample) and mode (the most frequent value of a sample), whereas mean is not a valid measure for ordinal scales (see Blaikie Reference Blaikie2003, Chapter 3 for more information). Hence, the scores have been aggregated by median (on x-axis) and mode (on y-axis) over all 5 judges. If there are multiple modes, the worst one was taken, meaning if the ideal value for a criterion is ‘Agree’ (corresponding to the numeric value of 4), then the smallest mode was considered, otherwise the largest. The rationale behind this handling of multi-modal distributions is to penalize cases where the human judges could not come to a definite agreement. To aid reader in understanding this presentation format, we provide an annotated histogram in Figure A.1 in Appendix A
As established before, GK
$\gamma_N$
is higher than Randolph’s
$\kappa$
, meaning we should trust the exact ratings less and the relative rankings more. Then we are interested in QA-pairs ranked better than all other pairs by most of the judges, preferably that both median and mode for these QA-pairs are either equal to 4 if the best rating for the given criterion is 4, or to 1 if the best rating is 1. The proportion of such cases per criterion per language is presented in Table 8.
Table 8. Proportion of generated QA pairs where both median and mode are the same
The majority of generated questions for English and Finnish are borderline (given 2 or 3) in terms of grammaticality, whereas the majority of questions in Russian were given a 4. It should be noted, though, that a considerable number of questions were evaluated as being grammatically incorrect (see Section 5.1.3 for error analysis). A similar pattern holds as to whether the question makes sense. The vast majority of the questions are not overinformative across all languages, and would not benefit from more information (except for English). Most of the cases for English and Finnish were borderline, whereas a substantial majority of questions were judged as relevant to the given sentence for Russian.
Focusing on the suggested answers, the majority of them have been reported to answer the question correctly for Finnish and Russian, whereas most of the cases were borderline for English. It should be noted that a substantial number of the suggested answers did not answer the question correctly. A breakdown of such cases is presented in Section 5.1.3. A considerable number of answers would benefit from rephrasing for English and Russian, whereas the majority of answers for Finnish would not (which is surprising given that Finnish is an agglutinative language with rich inflectional morphology). Almost none of the suggested answers are overinformative, and a majority of them would not benefit from more information either (except for English).
5.1.3. Error analysis
Exploring the questions that obtained a mode of 1 or 2 for the grammaticality criterion, we have identified three most frequent types of errors, which are summarised in Table 9. As can be seen, the types of errors are different across languages, suggesting that Quinductor’s performance might be boosted for each individual language by applying language-specific post-processing (e.g., determiner correction for English). Some of the errors are connected to the errors in dependency parsing, such as split proper names in Russian, calling for a principled error analysis for these parsers beyond the provided development treebanks.
Another interesting issue pertains to questions that were judged grammatically correct (mode and median of 4 on the grammaticality criterion), but exhibited problems with respect to other criteria. Such cases are presented in Tables 10 and 11.
Table 9. Three most frequent types of grammatical mistakes for questions that received a mode of 1 or 2 for the criterion ‘The question is grammatically correct’
Table 10. Examples of QA-pairs judged grammatically correct (median and mode of 4), but exhibiting problems in other criteria
As can be seen in Table 11, most of the questions also make sense, but would benefit from including more information. The suggested answers exhibit much more variation in human judgements, both in terms of them being correct, requiring rephrasing or more information. Most of the suggested answers are not over-informative (see samples in Table 10).
Table 11. Human judgements of the examples in Table 10. If only one number is specified, then mode and median are equal, otherwise the format is median/mode
5.2. Comparison to other methods on the SQuAD data set
To support the claim of Quinductor being a strong baseline, we compare our method to previously reported results for both state-of-the-art and baseline methods. Most of the previous work is done for the SQuAD data set (Rajpurkar et al. Reference Rajpurkar, Zhang, Lopyrev and Liang2016), although the training/development/test split varies among articles, since the original SQuAD test set is hidden. We have found a number of articles relying on the SQuAD splitFootnote h made by Du et al. (Reference Du, Shao and Cardie2017) and others relying on the split made by Zhou et al. (Reference Zhou, Yang, Wei, Tan, Bao and Zhou2018).
In this article use the split by Du et al. (Reference Du, Shao and Cardie2017), composed of 70,484 QA-pairs in the training set and 11,877 QA-pairs in the test set (note that we did not use development set in our experiments). Hence, we compare only to the articles that have explicitly reported to use of the same split to ensure a fair comparison between the methods. CIDEr is not provided in all other publications and is thus not reported. We induce templates based on the provided training set and evaluate on the test set. Note that we use both the splits, the provided tokenizations and the extracted source sentences for each question as provided in the data/processed folder of the original repository. The default Quinductor implementation (dubbed QA-templates) also needs the correct answers, so we have extracted those from the provided raw files and followed the same tokenization procedure as described by Du et al. (Reference Du, Shao and Cardie2017). We have also tried inducing templates only for questions without correct answers (dubbed Q-templates). This is to see whether the induced templates will end up being more generalisable as a consequence of more relaxed guards (not having constraints related to the correct answer).
For SQuAD we have used only automatic evaluation metrics, since some articles did not perform human evaluation at all (Zhao et al. Reference Zhao, Ni, Ding and Ke2018; Song et al. Reference Song, Wang, Hamza, Zhang and Gildea2018; Kim et al. Reference Kim, Lee, Shin and Jung2019; Dong et al. Reference Dong, Yang, Wang, Wei, Liu, Wang, Gao, Zhou and Hon2019), and others (Du et al. Reference Du, Shao and Cardie2017; Bahuleyan et al. Reference Bahuleyan, Mou, Vechtomova and Poupart2018) used different criteria and evaluation guidelines making a fair comparison impossible.
Only the top-ranked generated question (if any) was considered for automatic evaluation. As can be seen our method performs better than all baselines reported by Du et al. (Reference Du, Shao and Cardie2017) (shown in italics in Table 12) in terms of METEOR and ROUGE-L, and substantially better on BLEU-4 compared to the vanilla seq2seq model reported by Du et al. (Reference Du, Shao and Cardie2017). Indeed, this cements the position of our as a rather strong baseline that could be used as a point of reference for languages other than English. However, the performance lags behind to a substantial degree, compared to most other methods reported in literature, which is, again, not an unexpected quality for the baseline method.
Table 12. Comparison to state-of-the-art QG methods and other reported baselines (shown in italics) on the test set of the SQuAD split made by Du et al. (Reference Du, Shao and Cardie2017). Note that the cases when Quinductor did not generate any question were excluded when calculating all metrics. Best results for methods and baselines from related work, as well as for Quinductor are indicated in bold
1The result for this model as reported by Du et al. (Reference Du, Shao and Cardie2017).
2The result for the model by Heilman and Smith (Reference Heilman and Smith2009), as reported by Du et al. (Reference Du, Shao and Cardie2017).
When comparing two variations of Quinductor itself, we see no substantial performance differences. We note, however, that the variation with Q-templates induced substantially more templates with a roughly similar support per template on average. The version with Q-templates also managed to apply templates to about 6.5 percentage points more source sentences than the default version (as can be seen in Table 14), which might explain a slight dip in BLEU scores in Table 12. We note that METEOR score was slightly higher for the variation with Q-templates, indicating that the matches between the generated and the gold questions are slightly better aligned. ROUGE-L score were also slightly higher, indicating that the longest common subsequences between the generated and gold questions were slightly longer. These two observations along with the fact that the variation with Q-templates managed to generate questions for substantially more source sentences, hint that this variation might be a viable alternative if only questions are of interest.
Table 13. Descriptive statistics of the templates produced using the training set of the SQuAD data set (split by Du et al. Reference Du, Shao and Cardie2017). Support per template is the number of sentences from the training set that yield the same template. ‘SD’ stands for ‘standard deviation’
Table 14. Descriptive statistics of the questions induced on the test set of the SQuAD data set (split by (Du et al. Reference Du, Shao and Cardie2017)) using templates, mentioned in Table 13. ‘SS’ stands for ‘source sentence(s)’, that is, the sentence in which the correct answer is found. ‘
$\ge 1$
applicable template’ means that at least 1 question was induced from the given SS. ‘SD’ stands for ‘standard deviation’
5.3. Comparison to other methods on the Monserrate benchmark
Many data sets used for benchmarking in QG provide only a few questions to be evaluated against for each source passage/sentence. This is problematic, as discussed previously, since one can pose many valid questions to each and every sentence (and many more to a passage as a whole). Rodrigues, Nyberg, and Coheur (Reference Rodrigues, Nyberg and Coheur2022) contribute towards overcoming this limitation by releasing the Monserrate QG benchmark, which attempts at providing an exhaustive list of possible questions for each source sentence. In this setting, the previously discussed automatic evaluation metrics become clearly more relevant, since every generated question will be compared to more than 1 alternative (on average 26 alternatives in the Monserrate corpus). We have applied Quinductor’s guards and templates generated on the SQuAD data set (which was also used for the evaluation in Section 5.2). The results for both QA-templates and Q-templates are reported in Table 15. For calculating the evaluation metrics, we have used the runMaluuba.py script provided in the GitHub repository for Monserrate.Footnote i Only the top-ranked generated question (if any) was considered for automatic evaluation. Note that, contrary to Table 12, we include the cases when Quinductor did not generate any questions when calculating the metrics reported in Table 15. This is because we did not manage to make the evaluation script run without errors otherwise, which also gives us confidence that the metrics reported in Rodrigues et al. (Reference Rodrigues, Nyberg and Coheur2022) on this benchmark were obtained in this way (contrary to the results in Table 12). As previously, we report the descriptive statistics of the induced questions in Table 16.
Table 15. Comparison to state-of-the-art QG methods on the Monserrate benchmark. Note that the cases when Quinductor did not generate any question were included when calculating all metrics. Best results for methods from related works and Quinductor are indicated in bold
1The result for this model as reported by Rodrigues et al. (Reference Rodrigues, Nyberg and Coheur2022).
Table 16. Descriptive statistics of the questions induced on the Monserrate benchmark using templates, mentioned in Table 13. ‘SS’ stands for ‘source sentence(s)’, that is, the sentence in which the correct answer is found. ‘
$\ge 1$
applicable template’ means that at least 1 question was induced from the given SS. ‘SD’ stands for ‘standard deviation’
As can be seen from Table 15, Quinductor performs much better on this benchmark with the less-restrictive Q-templates than QA-templates. In fact, Table 16 shows that the Quinductor variation with QA-templates generated questions for 79.45% of the source sentences, which is 17.81 percentage points fewer than the one with Q-templates. This shows the conservative side of our default approach, where we prefer not to generate a QA-pair at all if either question or answer are deemed of insufficient quality. Evidently, generating only questions appears to be easier than QA-pairs.
Notably, the Quinductor variation with QA-templates performs worse than most other methods on all metrics (except METEOR for GEN SubT system). The variation with Q-templates performs substantially better, and in fact outperforms the system by Du et al. (Reference Du, Shao and Cardie2017) on all metrics except ROUGE-L. Both the system by Heilman and Smith (Reference Heilman and Smith2009) and all versions of GEN system perform better than Quinductor with Q-templates in BLEU-1 and ROUGE-L. However, Quinductor with Q-templates performs better or on par with GEN SubT and GEN FlexSubT and is not that far behind the other systems in terms of BLEU-4 and METEOR, proving Quinductor to be a reasonably strong baseline method. Bearing in mind that the system by Heilman and Smith (Reference Heilman and Smith2009), as well as the GEN system were both designed with English-specific knowledge or components (e.g., a named-entity recognizer), it is not unexpected that their performance is better than Quinductor’s. Even though Quinductor uses no language-specific knowledge or components, it yet demonstrates a performance on par or not far behind in terms of BLEU-4 and METEOR, making Quinductor a promising candidate for the baseline QG method for languages other than English.
6. Discussion
We have shown that the Quinductor method is a strong baseline method as concerns automatic evaluation metrics, outperforming baselines for English reported previously in the literature in terms of METEOR and ROUGE-L scores and performing better (or not far behind) some of the previously proposed QG methods. In addition, our method is inexpensive to train both in terms of time and textual resources, and thus applicable to languages other than English.
Quinductor has been successfully applied to 5 typologically diverse less-resourced languages with limited training data. Most agglutinative languages (with a rich morphology and a free word order) performed similarly in terms of automatic evaluation metrics. Agglutinative languages with data sets relying on subwords in either questions or answers are proven to not work well with Quinductor (e.g., Korean and Telugu in TyDi QA data set). Generated questions for Finnish performed better than English in terms of human judgements. Russian performed substantially better than all other languages both in terms of automatic evaluation metrics and human judgements, which might be a merit of a specific data set and requires further investigation.
However, Quinductor has a number of limitations. Our method relies on the correctness of the dependency parser’s output, or rather on the consistency of its errors. This assumption, although weaker than correctness, is still a limitation and does not always hold. We have noticed that some language-specific preprocessing techniques make the output of dependency parsers more consistent, but this requires further investigation.
Our method also incorporates a number of heuristics, such as mean filtering, selecting of contiguous template expressions in sentence transformation and ranking models, which seems to result in a comparable performance across languages. While only empirical evidence supports the applicability of these heuristics, we believe it is enough to make Quinductor a strong multilingual baseline and set the lower bar for neural methods.
Another limiting factor of Quinductor is that every generated question will be based on a single sentence. Thereby, the questions will be of the information-locating kind, which is the basic and least advanced rung on the reading comprehension ladder (OECD 2019, p. 34). However, the ability of quickly scanning a text and locating the answer to a specific question is a very important component in reading comprehension (Dreher and Guthrie Reference Dreher and Guthrie1990; Moore Reference Moore1995; Rouet and Coutelet Reference Rouet and Coutelet2008). It is also a non-trivial task for second-language learners, as it requires knowledge of decoding, the vocabulary, and the grammar of the language to be learnt, all important aspects of second-language reading comprehension (Jeon and Yamashita Reference Jeon and Yamashita2014). We therefore believe that the questions generated by Quinductor can be highly useful in language teaching and training.
It might be said that Quinductor still requires the use of a dependency parser to be trained on a sizeable data set, and thereby moving the problem rather than solving it. However, first, the Universal Dependencies framework includes 200 treebanks for over 100 languages (and counting). Second, we have shown that Quinductor could induce templates even for Telugu, whose dependency parser is trained on a treebank with only 6K tokens. Third, less-resourced languages have much smaller corpora of raw text, making pretraining of large-scale neural language models challenging (let alone fine-tuning them for QG). Finally, Quinductor method is a yet another use case for a dependency treebank, adding to the motivation of expanding UD to other languages.
Acknowledgements
This work was supported by Vinnova (Sweden’s Innovation Agency) within project 2019-02997. We would also like to thank Lisse-Lotte Hermansson for helping with translating instructions for human evaluation in Finnish, Kristiina Savola for help in assessing results of human evaluation for Finnish and Bram Willemsen for helpful comments and discussions on the matter of evaluation. We are very grateful to the anonymous reviewers for their detailed and insightful comments that helped improving this article substantially.
Conflicts of interest
The authors declare none.
Appendix A. Human evaluation details
Human evaluation has been conducted on the Prolific platform.Footnote j We used Prolific’s pre-screening feature and required each human judge to have the language of interest as the first language and hold at least a high school diploma (A-levels).
Figure A.1 An annotated example of a bi-variate histogram.
Figure A.2 Evaluation guidelines and questionnaire for English.
Figure A.3 Bi-variate histograms of human judgements (the order of criteria is the same for all languages).
Figure A.4 Evaluation guidelines and questionnaire for Finnish.
Figure A.5 Evaluation guidelines and questionnaire for Russian.
The exact guidelines for human evaluation are presented in Figures A.2, A.4, A.5. The instructions and 9 evaluation criteria are the same, but are translated into every language. Each criterion is evaluated on a 4-point Likert-type scale with the ends labelled as ‘Disagree’ and ‘Agree’. A neutral option is excluded, to force judges to make a decision. We opted out of a more typical ‘Strongly disagree’ – ‘Strongly agree’ scale to give judges some alternatives in the middle, such as, ‘Somewhat (dis)agree’. Otherwise, the scale would be interpreted as ‘Strongly disagree’ – ‘Disagree’ – ‘Agree’ – ‘Strongly agree’, which effectively collapses it to a binary scale.
The detailed results of human judgements for questions in English, Finnish and Russian are presented in Figure A.3. To aid reader in understanding the presentation format, we provide an annotated histogram in Figure A.1.
Appendix B. Data pre-processing steps
The applied pre-processing steps for every language are specified in Table B.1. Note that Arabic is written from right to left, but we found that processing sentences from left to right yielded better results with Quinductor.
Table B.1. Language-specific pre-processing steps before template induction. S denotes processing from the start of the sentence, E denotes processing from the end of the sentence
Appendix C. Derivation of multi-rater Goodman-Kruskall’s
$\gamma_N$
Let us start by presenting the original derivation of GK
$\gamma$
, proposed by Goodman and Kruskal (Reference Goodman and Kruskal1979), applied to the case of human evaluation. Assume that we have two judges independently assigning scores from 1 to
$\alpha$
to the same set of M items. Let
$s_{aj}$
denote a random variable associated with scores of judge a to the item j. Let
$c_{1,2}$
denote the event that a randomly selected pair of items will be ordered in the same way by judges 1 and 2 (such pair is called concordant). The probability of such event can then be calculated using Equation (C.1), given that the judgements are independent.
\begin{equation} P(c_{1,2}) = \sum_{(i,j) \in \Pi_M}P(s_{1i} < s_{1j})P(s_{2i} < s_{2j}) + P(s_{1i} > s_{1j})P(s_{2i} > s_{2j})\end{equation}
Let
$d_{1,2}$
denote the event that a randomly selected pair of items will be ordered differently by judges 1 and 2 (such pair is called discordant). The probability of such event can then be calculated using Equation (C.2), given that the judgements are independent.
\begin{equation} P(d_{1,2}) = \sum_{(i,j) \in \Pi_M}P(s_{1i} < s_{1j})P(s_{2i} > s_{2j}) + P(s_{1i} > s_{1j})P(s_{2i} < s_{2j})\end{equation}
Let
$t_{1,2}$
denote the event that a randomly selected pair of items will be get the same scores with each other (be tied) by both judges. Then the probability of ties is calculated using Equation (C.3) given that the judgements are independent.
\begin{equation} P(t_{1,2}) = \sum_{(i,j) \in \Pi_M}P(s_{1i} = s_{1j}) + P(s_{2i} = s_{2j})\end{equation}
In all equations above,
$\Pi_M$
is a 2-combination of the set of item indices between 1 and M. The conditional probability of concordant orders given no ties (
$\widetilde{t_{12}}$
) then equals to:
\begin{equation} P(c_{1,2}|\widetilde{t_{1,2}}) = \frac{P(\widetilde{t_{1,2}}|c_{1,2}) P(c_{1,2})}{P(\widetilde{t_{1,2}})} = \frac{1 \cdot P(c_{1,2})}{1 - P(t_{1,2})} = \frac{P(c_{1,2})}{1 - P(t_{1,2})}\end{equation}
Similarly, the conditional probability of discordant orders given no ties equals to
$P(d_{1,2}|\widetilde{t_{1,2}}) = \frac{P(d_{1,2})}{1 - P(t_{1,2})}$
. GK
$\gamma$
was then proposed by Goodman and Kruskal (Reference Goodman and Kruskal1979) to be computed as
\begin{equation} \gamma_{1,2} = \frac{P(c_{1,2}) - P(d_{1,2})}{1 - P(t_{1,2})}\end{equation}
Observe that
$P(c_{1,2}|\widetilde{t_{1,2}}) + P(d_{1,2}|\widetilde{t_{1,2}}) = 1$
, since if there are no ties, there can be either concordant or discordant orders, then the following derivation holds:
\begin{align} P(c_{1,2}|\widetilde{t_{1,2}}) + P(d_{1,2}|\widetilde{t_{1,2}}) = 1 \end{align}
\begin{align} \frac{P(c_{1,2})}{1 - P(t_{1,2})} + \frac{P(d_{1,2})}{1 - P(t_{1,2})} = 1 \end{align}
\begin{align} \frac{P(c_{1,2}) + P(d_{1,2})}{1 - P(t_{1,2})} = 1 \end{align}
\begin{align} P(c_{1,2}) + P(d_{1,2}) &= 1 - P(t_{1,2}) \end{align}
Using this observation, GK
$\gamma_{1,2}$
can be rewritten to a more familiar form:
\begin{equation} \gamma_{1,2} = \frac{P(c_{1,2}) - P(d_{1,2})}{P(c_{1,2}) + P(d_{1,2})}\end{equation}
Now assume we have a third judge as well and we calculate
$\gamma_{1,2}$
,
$\gamma_{1,3}$
, and
$\gamma{2,3}$
. Then to evaluate the agreement between three judges, we simply take an average of them. Let us see what it amounts to.
\begin{align} \gamma_{1-3} &= \frac{\gamma_{1,2} + \gamma_{1,3} + \gamma_{2,3}}{3}\end{align}
\begin{align} = \frac{\frac{P(c_{1,2}) - P(d_{1,2})}{P(c_{1,2}) + P(d_{1,2})} + \frac{P(c_{1,3}) - P(d_{1,3})}{P(c_{1,3}) + P(d_{1,3})} + \frac{P(c_{2,3}) - P(d_{2,3})}{P(c_{2,3}) + P(d_{2,3})}}{3}\end{align}
The quantity in Equation (C.12) cannot be simplified further resulting neither in a valid probability nor in a generalized version of GK
$\gamma$
.
Instead the derivation process can easily be extended to N judges (
$N > 2$
), as follows, resulting in a generalized version of GK
$\gamma$
, dubbed
$\gamma_N$
. Let
$c_N$
,
$d_N$
and
$t_N$
be the events that a randomly selected pair of items is concordant, discordant or tied (respectively) by any pair selected from N judges, then the following holds.
\begin{align} P(c_N) = \sum_{(a,b) \in \Pi_N}\sum_{(i,j) \in \Pi_M}P(s_{ai} < s_{aj})P(s_{bi} < s_{bj}) + P(s_{ai} > s_{aj})P(s_{bi} > s_{bj})\end{align}
\begin{align} P(d_N) &= \sum_{(a,b) \in \Pi_N}\sum_{(i,j) \in \Pi_M}P(s_{ai} < s_{aj})P(s_{bi} > s_{bj}) + P(s_{ai} > s_{aj})P(s_{bi} < s_{bj})\end{align}
\begin{align} P(t_N) &= \sum_{(a,b) \in \Pi_N}\sum_{(i,j) \in \Pi_M}P(s_{ai} = s_{aj}) + P(s_{bi} = s_{bj})\end{align}
\begin{align} P(c_N|\widetilde{t_N}) &= \frac{P(c_N)}{1 - P(t_N)}\end{align}
\begin{align} P(d_N|\widetilde{t_N}) &= \frac{P(d_N)}{1 - P(t_N)}\end{align}
\begin{align} \gamma_N &= \frac{P(c_N) - P(d_N)}{P(c_N) + P(d_N)} = \frac{\sum\limits_{(a,b) \in \Pi_N} P(c_{a,b}) - \sum\limits_{(a,b) \in \Pi_N} P(d_{a,b})}{\sum\limits_{(a,b) \in \Pi_N} P(c_{a,b}) + \sum\limits_{(a,b) \in \Pi_N} P(d_{a,b})}\end{align}
$\Pi_M$
is a 2-combination of the set of item indices between 1 and M,
$\Pi_N$
is a 2-combination of the set of judge indices between 1 and N,
Appendix D. Samples of generated questions
Here we present samples of generated questions for English, Finnish and Russian. All sentences, questions and suggested answers are lowercased, since we have empirically found Stanza’s tokenizers and dependency parsers to perform more consistently when text is lowercased. Both QA-pairs and sentences were also lowercased for human judges during evaluation.
Sentence: diphenhydramine was first made by George Rieveschl and came into commercial use in 1946
Question: who made diphenhydramine?
Suggested answer: George Rieveschl
Suggested: parallax (from ancient greek 
(parallaxis), meaning ’alternation’) is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or semi-angle of inclination between those two lines.
Question: what is a displacement in the apparent position of an object viewed along two different lines of sight?
Suggested answer: parallax
Sentence: the lowest temperatures are registered in July and August (18
$^{\circ}$
c–64
$^{\circ}$
f) and the highest in February (maximum temperature 28
$^{\circ}$
c–82.4
$^{\circ}$
f [1]), the summer season in the southern hemisphere.
Question: where are the lowest temperatures registered?
Suggested answer: july
Sentence: the nobel peace prize was first awarded in 1901 to Frédéric Passy and Henry Dunant – who shared a prize of 150,782 swedish kronor (equal to 7,731,004 kronor in 2008) – and, most recently, to Denis Mukwege and Nadia Murad in 2018
Question: where was the nobel peace prize awarded?
Suggested answer: Frédéric in 1901
Sentence: in 1986, the first statute aimed at defense contractor employee whistleblower protection was enacted.
Question:when was the first statute aimed at defense contractor employee whistleblower protection enacted?
Suggested answer: 1986
Sentence: 
Question: 
Suggested answer: 2008 
Sentence: 
Question: 
Suggested answer: 6
Sentence: 
Question: 
Suggested answer: 
Sentence: 
Question: 
Suggested answer: 1488
Sentence: 
Question: 
Suggested answer: 
Sentence: jäämerentie oli valmistuessaan 531 kilometriä pitkä ja viisi metriä leveä.
Question: kuinka pitkä jäämerentie oli?
Suggested answer: 531 kilometriä
Sentence: fennomania, suomenmielisyys, suomenkiihko[1] oli suomalaisten kansallisen heräämisen liike, joka syntyi 1800-luvun alkupuolella ja vaikutti erityisesti saman vuosisadan jälkipuolella.
Question: mitä fennomania oli?
Suggested answer: liike
Sentence: kaupungin väkiluku on noin 118000, ja sen pinta-ala on km
$^2$
, josta km
$^2$
on vesistöjä.[1] kuopion keskustaajama sijaitsee kallaveteen etelästä työntyvällä kuopionniemellä, joka jakaa kallaveden kahteen toisistaan lähes erilliseen osaan.
Question: paljonko on kaupungin väkiluku?
Suggested answer: 118000
Sentence: sen konsentraatio 25
$^{\circ}$
c:n lämpötilassa on noin 1,004
$\cdot$
10-7mol/l eli sen ph-arvo on 7,0
Question: paljonko on sen konsentraatio 25
$^{\circ}$
c:n lämpötilassa?
Suggested answer: 1,004
$\cdot$
10-7mol/l
Sentence: pegaso oli ajoneuvojen tuotemerkki, joka kuului vuonna 1945 generalissimus francisco francon valtiollistamaa espanjan ajoneuvoteollisuutta yhdistämällä vuonna 1946 syntyneeseen, madridissa kotipaikkaansa pitäneeseen enasa:an [empresa nacional de autocamiones s.a.).
Question: mitä pegaso oli?
Suggested answer: tuotemerkki
.
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