# 2005 IncorporatingNonLocalInformatio

## Quotes

### Abstract

Most current statistical natural language processing models use only local features so as to permit dynamic programming in inference, but this makes them unable to fully account for the long distance structure that is prevalent in language use. We show how to solve this dilemma with Gibbs sampling, a simple Monte Carlo method used to perform approximate inference in factored probabilistic models. By using simulated annealing in place of Viterbi decoding in sequence models such as HMMs, CMMs, and CRFs, it is possible to incorporate non-local structure while preserving tractable inference. We use this technique to augment an existing CRF-based information extraction system with long-distance dependency models, enforcing label consistency and extraction template consistency constraints. This technique results in an error reduction of up to 9% over state-of-the-art systems on two established information extraction tasks.

### 1 Introduction

Most statistical models currently used in natural language processing represent only local structure. Although this constraint is critical in enabling tractable model inference, it is a key limitation in many tasks, since natural language contains a great deal of non-local structure. A general method for solving this problem is to relax the requirement of exact inference, substituting approximate inference algorithms instead, thereby permitting tractable inference in models with non-local structure. One such algorithm is Gibbs sampling, a simple Monte Carlo algorithm that is appropriate for inference in any factored probabilistic model, including sequence models and probabilistic context free grammars (Geman and Geman, 1984). Although Gibbs sampling is widely used elsewhere, there has been extremely little use of it in natural language processing.[1] Here, we use it to add non-local dependencies to sequence models for information extraction.

Statistical hidden state sequence models, such as Hidden Markov Models (HMMs) (Leek, 1997; Freitag and McCallum, 1999), Conditional Markov Models (CMMs) (Borthwick, 1999), and Conditional Random Fields (CRFs) (Lafferty et al., 2001) are a prominent recent approach to information extraction tasks. These models all encode the Markov property: decisions about the state at a particular position in the sequence can depend only on a small local window. It is this property which allows tractable computation: the Viterbi, Forward Backward, and Clique Calibration algorithms all become intractable without it.

However, information extraction tasks can benefit from modeling non-local structure. As an example, several authors (see Section 8) mention the value of enforcing label consistency in named entity recognition (NER) tasks. In the example given in Figure 1, the second occurrence of the token Tanjug is mislabeled by our CRF-based statistical NER system, because by looking only at local evidence it is unclear whether it is a person or organization. The first occurrence of Tanjug provides ample evidence that it is an organization, however, and by enforcing label consistency the system should be able to get it right. We show how to incorporate constraints of this form into a CRF model by using Gibbs sampling instead of the Viterbi algorithm as our inference procedure, and demonstrate that this technique yields significant improvements on two established IE tasks.

### 2 Gibbs Sampling for Inference in Sequence Models

In hidden state sequence models such as HMMs, CMMs, and CRFs, it is standard to use the Viterbi algorithm, a dynamic programming algorithm, to infer the most likely hidden state sequence given the input and the model (see, e.g., Rabiner (1989)). Although this is the only tractable method for exact computation, there are other methods for computing an approximate solution. Monte Carlo methods are a simple and effective class of methods for approximate inference based on sampling. Imagine we have a hidden state sequence model which defines a probability distribution over state sequences conditioned on any given input. With such a model M we should be able to compute the conditional probability $PM(\bf{s}|\bf{o})$ of any state sequence s = {s0, . . . , sN } given some observed input sequence o = {o0, . . . , oN }. One can then sample sequences from the conditional distribution defined by the model. These samples are likely to be in high probability areas, increasing our chances of finding the maximum. The challenge is how to sample sequences efficiently from the conditional distribution defined by the model.

Gibbs sampling provides a clever solution (Geman and Geman, 1984). Gibbs sampling defines a Markov chain in the space of possible variable assignments (in this case, hidden state sequences) such that the stationary distribution of the Markov chain is the joint distribution over the variables. Thus it is called a Markov Chain Monte Carlo (MCMC) method; see Andrieu et al. (2003) for a good MCMC tutorial. In practical terms, this means that we can walk the Markov chain, occasionally outputting samples, and that these samples are guaranteed to be drawn from the target distribution. Furthermore, the chain is defined in very simple terms: from each state sequence we can only transition to a state sequence obtained by changing the state at any one position i , and the distribution over these possible transitions is just

PG(s(t )|s(t−1)) = PM(s(t )
i |s(t−1)
−i , o). (1)


where s−i is all states except si . In other words, the transition probability of theMarkov chain is the conditional distribution of the label at the position given the rest of the sequence. This quantity is easy to compute in any Markov sequence model, including HMMs, CMMs, and CRFs. One easy way to walk the Markov chain is to loop through the positions $i$ from 1 to N, and for each one, to resample the hidden state at that position from the distribution given in Equation 1. By outputting complete sequences at regular intervals (such as after resampling all N positions), we can sample sequences from the conditional distribution defined by the model.

This is still a gravely inefficient process, however. Random sampling may be a good way to estimate the shape of a probability distribution, but it is not an efficient way to do what we want: find the maximum. However, we cannot just transition greedily to higher probability sequences at each step, because the space is extremely non-convex. We can, however, borrow a technique from the study of non-convex optimization and use simulated annealing (Kirkpatrick et al., 1983). Geman and Geman (1984) show that it is easy to modify a Gibbs Markov chain to do annealing; at time t we replace the distribution in (1) with

PA(s(t )|s(t−1)) =
PM(s(t )
i |s(t−1)
−i , o)1/ct
Pj PM(s(t )
j |s(t−1)
−j , o)1/ct
(2)


where c = {c0, . . . , cT } defines a cooling schedule. At each step, we raise each value in the conditional distribution to an exponent and renormalize before sampling from it. Note that when c = 1 the distribution is unchanged, and as c ! 0 the distribution

To verify the effectiveness of Gibbs sampling and simulated annealing as an inference technique for hidden state sequence models, we compare Gibbs and Viterbi inference methods for a basic CRF, without the addition of any non-local model. The results, given in Table 1, show that if the Gibbs sampler is run long enough, its accuracy is the same as a Viterbi decoder.

## References

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volumeDate ValuetitletypejournaltitleUrldoinoteyear
2005 IncorporatingNonLocalInformatioIncorporating Non-local Information Into Information Extraction Systems by Gibbs Sampling10.3115/1219840.12198852005
1. Prior uses in NLP of which we are aware include: Kim et al. (1995), Della Pietra et al. (1997) and Abney (1997).
 Author Jenny Rose Finkel +, Trond Grenager + and Christopher Manning + doi 10.3115/1219840.1219885 + title Incorporating Non-local Information Into Information Extraction Systems by Gibbs Sampling + year 2005 +