Denis and Muller, Predicting Globally-Coherent Temporal Structures from Texts via Endpoint Inference and Graph Decomposition, IJCAI 2011

Citation

Predicting Globally-Coherent Temporal Structures from Texts via Endpoint Inference and Graph Decomposition, by P. Denis, P. Muller. In Proceedings of IJCAI, 2011.

Online version

This Paper is available online [1].

Summary

Like Yoshikawa et al. (2009), this paper is a follow up paper to Chambers and Jurafsky (2008) that focuses on using global inference to improve local, pairwise temporal ordering of events in text. Similar to Chambers and Jurafsky (2008), this paper formulates the global inference of temporal ordering as a constraint optimization problem, which can be then given an exact solution using Integer Linear Programming (ILP). Chambers and Jurafsky (2008) however, restricts themselves to only predicting precedence relations (before/after) as ILP becomes impractical when considering all possible interval relations due to the combinatorial number of variables and constraints needed to represent them. The main contribution of this paper is in reducing the number of variables and constraints needed to represent all interval relations, by translating these temporal intervals into their end points, thus preserving the same temporal information while reducing the number of variables and constraints to handle. Additional gain in efficiency is achieved by decomposing the temporal graph and enforcing temporal coherence on the subsets of the graph.

The proposed method is evaluated through experiment on TimeBank Corpus and achieves similar accuracy as Tatu and Srikanth (2008) which infers temporal relations while preserving consistency. Tatu and Srikanth (2008) however, only performs classification on 6 of the 13 possible temporal relations. This paper on the other hand, classifies all 13 temporal relations. Chambers and Jurafsky (2008) achieves an accuracy of 70%, however they only perform classifications on 2 temporal relations.

Brief description of the method

The paper proposes two steps method for temporal ordering of events: (1) learn a classifier which outputs a score for each event pair and their temporal relation, (2) combine these local scores with coherence constraints on the temporal graph within a global optimization problem using Integer Linear Programming (ILP).

Being an NP-hard problem, inference in ILP is sensitive to its number of variables and constraints. In this case, these numbers are exponential in the number of temporal relations used. For ILP to be able to handle all 13 temporal relations specified in TimeBank Corpus, the paper proposes to first translate these temporal relations intervals into their end points; thus reducing the number of relations from 13 to 5. This reduced number of temporal relations result in 50 times less number of constraints needed to represent global temporal coherence in while preserving the temporal information. The translation between each pair of events' temporal relations to points are shown in the table below: (inverses and simultaneous relation are not shown)

Where the intervals are, in Allen (1983)'s notation: b as in BEFORE, m as in MEET (IBEFORE or immediately before), o as in OVERLAP, s as in START, d as in DURING, and f as in FINISH. For each event pair $({e_{1}},{e_{2}})\,\!$, four relations between their endpoints are considered: $({e_{1}^{-}},{e_{2}^{-}})$, $({e_{1}^{+}},{e_{2}^{-}})$, $({e_{1}^{-}},{e_{2}^{+}})$, $({e_{1}^{+}},{e_{2}^{+}})$ as shown in the table.

The variables in ILP can then be represented in terms of the endpoints as triplets: $(r,p,q)\,\!$ where p and q are endpoints and r is a possible temporal relation over them. The weights on the variables, ${c_{(r,p,q)}}\,\!$ are obtained from classifier scores. The objective function is defined as:

$max\sum _{(p,q)\in C}\sum _{r\in R}{c_{(r,p,q)}}*{x_{(r,p,q)}}\,\!$

subject to the constraints:

${x_{(r,p,q)}}\in {0,1}\,\!$

and the constraint that at most one base relation can hold between 2 points:

$\sum _{r\in R}{x_{(r,p,q)}}\leq 1\,\!$

and other constraints.

To achieve even more efficiency, the temporal graph is decomposed into subsets so as to restrict the constrained prediction to relevant subgroups of events. Two different decompositions are tried:

• decomposition based on human annotations - human annotations in the corpus are scattered and events appear in separate, self-connected components in the graph. The constrained prediction is restricted to these connected components
• decomposition based on dates that appear in the same sentence as the events - events are grouped based on dates they are closest to in the sentence

Experimental Result

The experiment is done on TimeBank Corpus using 5-fold cross validation. Three sets of experiments are conducted to evaluate:

• the effectiveness of relations inferred using only the transitive closure of original relations in the corpus (as described in Chambers and Jurafsky (2008))
• the effectiveness of using ILP point model on the entire temporal graph
• the effectiveness of using ILP point model with graph decompositions

When only transitive closure is done, an accuracy of 26% is achieved. When ILP is used, an accuracy of almost 50% is achieved. This is the accuracy achieved by Tatu and Srikanth (2008) on the temporal predictions where they preserve consistency. However, this paper uses the whole set of 13 relations while Tatu and Srikanth (2008) has only six. When predictions is limited on subsets of decomposed graph, ILP accuracy increases to 54%, perhaps benefiting from the more relevant context of the graph.

Related papers

The approach in this paper is similar to that of an earlier work by Chambers and Jurafsky (2008) that proposes to use global framework based on Integer Linear Programming (ILP) to jointly infer temporal relations between events. Chambers and Jurafsky (2008) show that adding global inference improves the accuracy of the inferred temporal relations. However they only focus on event-event temporal relations while this paper also jointly predicts temporal order between events and time expressions, and between events and document creation time.

Secondly, Chambers and Jurafsky (2008) combines the output of local classifiers using ILP framework while this paper uses Markov Logic Networks which represents global constraints through the addition of weighted first order logic formulae. The advantage is that it allows for representation of non-deterministic rules that tend to hold between temporal relations but do not always have to. For example, if A happens before B and B overlaps with C, then there is a good chance that A also happens before C, but this is not always the case. The learned weights of the rules allow for soft enforcement of the constraints.