Aggregate and mixed-order Markov models for statistical language processing

We consider the use of language models whose size and accuracy are intermediate between different order n-gram models. Two types of models are studied in particular. Aggregate Markov models are classbased bigram models in which the mapping from words to classes is probabilistic. Mixed-order Markov models combine bigram models whose predictions are conditioned on different words. Both types of models are trained by ExpectationMaximization (EM) algorithms for maximum likelihood estimation. We examine smoothing procedures in which these models are interposed between different order n-grams. This is found to significantly reduce the perplexity of unseen word combinations. 1 Introduction The purpose of a statistical language model is to assign high probabilities to likely word sequences and low probabilities to unlikely ones. The challenge here arises from the combinatorially large number of possibilities, only a fraction of which can ever be observed. In general, language models must le..

Topic-based mixture language modelling

This paper describes an approach for constructing a mixture of language models based on simple statistical notions of semantics using probabilistic models developed for information retrieval. The approach encapsulates corpus-derived semantic information and is able to model varying styles of text. Using such information, the corpus texts are clustered in an unsupervised manner and a mixture of topic-specific language models is automatically created. The principal contribution of this work is to characterise the document space resulting from information retrieval techniques and to demonstrate the approach for mixture language modelling. A comparison is made between manual and automatic clustering in order to elucidate how the global content information is expressed in the space. We also compare (in terms of association with manual clustering and language modelling accuracy) alternative term-weighting schemes and the effect of singular value decomposition dimension reduction (latent semantic analysis). Test set perplexity results using the British National Corpus indicate that the approach can improve the potential of statistical language modelling. Using an adaptive procedure, the conventional model may be tuned to track text data with a slight increase in computational cost

Clustering via kernel decomposition

Spectral clustering methods were proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this letter, the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership. Hyperparameters are selected using standard cross-validation methods

A Machine learning approach to POS tagging

We have applied inductive learning of statistical decision trees and relaxation labelling to the Natural Language Processing (NLP) task of morphosyntactic disambiguation (Part Of Speech Tagging). The learning process is supervised and obtains a language model oriented to resolve POS ambiguities. This model consists of a set of statistical decision trees expressing distribution of tags and words in some relevant contexts. The acquired language models are complete enough to be directly used as sets of POS disambiguation rules, and include more complex contextual information than simple collections of n-grams usually used in statistical taggers. We have implemented a quite simple and fast tagger that has been tested and evaluated on the Wall Street Journal (WSJ) corpus with a remarkable accuracy. However, better results can be obtained by translating the trees into rules to feed a flexible relaxation labelling based tagger. In this direction we describe a tagger which is able to use information of any kind (n-grams, automatically acquired constraints, linguistically motivated manually written constraints, etc.), and in particular to incorporate the machine learned decision trees. Simultaneously, we address the problem of tagging when only small training material is available, which is crucial in any process of constructing, from scratch, an annotated corpus. We show that quite high accuracy can be achieved with our system in this situation.Postprint (published version

Optimal Kullback-Leibler Aggregation via Information Bottleneck

In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost; The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a sub-optimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.Comment: 13 pages, 4 figure