Improved Induction of Narrative Chains via Cross-Document Relations (2022)

Abstract: The standard approach for inducing narrative chains considers statistics gathered per individual document. We consider whether statistics gathered using cross-document relations can lead to improved chain induction. Our study is motivated by legal narratives, where cases typically cite thematically similar cases. We consider four novel variations on pointwise mutual information (PMI), each accounting for cross-document relations in a different way. One proposed PMI variation performs 58% better relative to standard PMI on recall@50 and induces qualitatively better narrative chains.

## introduction narrative chains are sets of events centered around a common protagonist. they can be induced from corpora using various unsupervised methods, many using pointwise mutual information (pmi) between events. to our knowledge, no prior work has used the information available in relations between documents in a corpus when inducing narrative chains. to illustrate the potential for improved narrative chain induction based on document relations, we develop four novel variants of pointwise mutual information (pmi) that assume a directed graph structure between documents (i.e. relations that are edges). we test these 1 on a corpus of all u.s. federal court cases, which has a readily accessible relation between documents: citation. one case will cite prior cases as precedent in explaining its decision. we find that one of our four variants of pmi performs particularly well in the standard event cloze evaluation @xcite and in inducing meaningful narrative chains. ## background unsupervised narrative chain induction from a corpus was introduced by chambers and jurafsky 1 code is at https://github.com/blairstanek/ cross-doc @xcite , inspired by the notion of scripts owing to @xcite . coreference chains were extracted over the gigaword corpus @xcite to extract event chains with the same protagonist. a syntactic parser identified each event in which the protagonist was involved, defined as the combination of a verb and dependency relation, such as (convict, obj). they then calculated the pointwise mutual information (pmi) @xcite for each combination of two events and used this pmi to do agglomerative clustering to induce narrative chains. we follow the basic approach of @xcite , with the major extension that we take relations between the documents into account for the first time. there have been numerous improvements on the @xcite approach, including using language modeling approaches @xcite , neural networks @xcite , and graphs where events are the vertices @xcite . none of these improvements has considered relations between documents in the corpus. ## alternative measures much of the narrative chain induction literature, following @xcite , has used pmi. specifically, for any given coreference chain c anywhere in the corpus, the standard pmi of two events e 1 and e 2 is defined by, pmi standard (e 1 , e 2 ) = log p (e 1 ∈ c ∧ e 2 ∈ c) p (e 1 ∈ c)p (e 2 ∈ c) pmi provides a measure of how often e 1 and e 2 actually occur together, as compared to what we would expect if they were independent. if they were independent, then: p (e 1 ∈ c ∧ e 2 ∈ c) = p (e 1 ∈ c)p (e 2 ∈ c) note that the definition of pmi standard has the equation above's left hand side in the numerator and right hand side in the denominator. given some relation between the documents making up the corpus, e.g. case citations, we consider four different ways to define an extension of pmi. one is document-by-document, and three are chain-by-chain. to develop the three chain-by-chain measures, we define a and b to be documents with a relation (e.g. case a cites case b), and define c a to be a chain of events in document a, and c b to be a chain of events in document b. thus, assuming independence between all occurrences of e 1 and e 2 , we can derive four equivalent expressions: these are the probabilities that, if you randomly select a chain c a and a chain c b where case a cites case b, that these chains have these events. for example, if you've randomly selected c a and c b , then p (e 1 ∈ c a ) is the probability that the event e 1 appears in c a . by taking the first expression above as the numerator and using the last three expressions above as the denominators, we get three different extensions of pmi: a fourth approach can come from considering an analogous measure that works document-bydocument, rather than chain-by-chain. given related documents a and b (e.g. case a cites case b), if we assume that occurrences of e 1 and e 2 are independent, then the following must be true: this expression, unlike the chain-by-chain expression, cannot be further factored into two other alternatives. why? there can be (and typically are) multiple chains in each document. within a document, there may exist no chains with both e 1 and e 2 , even though there exists a chain with e 1 and another chain with e 2 . we can get the fourth extension of pmi by dividing the two sides of the equation directly above: we used all u.s. federal court cases since 1970 that have at least 800 total characters and that either cite to or are cited by another u.s. federal court case. all text came from the caselaw access project (cap). cases with under 800 characters and cases neither cited to or by other federal were summary dispositions or procedural rulings that lacked meaningful description of the underlying facts of the case. the resulting corpus had 965,467 cases. (each case is exactly one document.) ## conclusion we have explored four new measures of pmi that can take advantage of relationships between documents in corpora. applying them to the corpus of federal cases, we find that one such measure, pmi cross shows substantial improvement over standard pmi. future work may consider the use of these new pmi measures on other corpora where the documents may have relationships that can be characterized as directed edges, including hyperlinks and references. 5 we focused on a pmi-based approach to inducing narrative chains owing to its familiarity within the community. based on these results demonstrating the benefits of utilizing document-to-document relations, future work can consider extensions such as using temporal relations, causality, and neural modeling.