We present an extensive empirical comparison of several smoothing techniques in the domain of language modeling, including those described by Jelinek and Mercer (1980), Katz (1987), and Church and Gale (1991). We investigate for the first time how factors such as training data size, corpus (e.g., Brown versus Wall Street Journal), and n-gram order (bigram versus trigram) affect the relative performance of these methods, which we measure through the cross-entropy of test data. In addition, we introduce two novel smoothing techniques, one a variation of Jelinek-Mercer smoothing and one a very simple linear interpolation technique, both of which outperform existing methods. 1

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We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected number of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infinite---consider, for example, symbols being possible words appearing in English text.

In certain contexts, maximum entropy (ME) modeling can be viewed as maximum likelihood training for exponential models, and like other maximum likelihood methods is prone to overfitting of training data. Several smoothing methods for maximum entropy models have been proposed to address this problem, but previous results do not make it clear how these smoothing methods compare with smoothing methods for other types of related models. In this work, we survey previous work in maximum entropy smoothing and compare the performance of several of these algorithms with conventional techniques for smoothing n-gram language models. Because of the mature body of research in n-gram model smoothing and the close connection between maximum entropy and conventional n-gram models, this domain is well-suited to gauge the performance of maximum entropy smoothing methods. Over a large number of data sets, we find that an ME smoothing method proposed to us by Lafferty [1] performs as well as or better tha...

Unsupervised learning of linguistic structure is a difficult problem. A common approach is to define a generative model and maximize the probability of the hidden structure given the observed data. Typically, this is done using maximum-likelihood estimation (MLE) of the model parameters. We show using part-of-speech tagging that a fully Bayesian approach can greatly improve performance. Rather than estimating a single set of parameters, the Bayesian approach integrates over all possible parameter values. This difference ensures that the learned structure will have high probability over a range of possible parameters, and permits the use of priors favoring the sparse distributions that are typical of natural language. Our model has the structure of a standard trigram HMM, yet its accuracy is closer to that of a state-of-the-art discriminative model (Smith and Eisner, 2005), up to 14 percentage points better than MLE. We find improvements both when training from data alone, and using a tagging dictionary. 1

Abstract—In certain contexts, maximum entropy (ME) modeling can be viewed as maximum likelihood (ML) training for exponential models, and like other ML methods is prone to overfitting of training data. Several smoothing methods for ME models have been proposed to address this problem, but previous results do not make it clear how these smoothing methods compare with smoothing methods for other types of related models. In this work, we survey previous work in ME smoothing and compare the performance of several of these algorithms with conventional techniques for smoothing-gram language models. Because of the mature body of research in-gram model smoothing and the close connection between ME and conventional-gram models, this domain is well-suited to gauge the performance of ME smoothing methods. Over a large number of data sets, we find that fuzzy ME smoothing performs as well as or better than all other algorithms under consideration. We contrast this method with previous-gram smoothing methods to explain its superior performance. Index Terms—Exponential models, language modeling, maximum entropy, minimum divergence,-gram models, smoothing.

Language modeling is the art of determining the probability of a sequence of words. This is useful in a large variety of areas including speech recognition, optical character recognition, handwriting recognition, machine translation, and spelling correction (Church, 1988; Brown et al., 1990; Hull, 1992; Kernighan et al., 1990; Srihari and Baltus, 1992). The most commonly used language models are very simple (e.g. a Katz-smoothed trigram model). There are many improvements over this simple model however, including caching, clustering, higherorder n-grams, skipping models, and sentence-mixture models, all of which we will describe below. Unfortunately, these more complicated techniques have rarely been examined in combination. It is entirely possible that two techniques that work well separately will not work well together, and, as we will show, even possible that some techniques will work better together than either one does by itself. In this...

The standard method for training Hidden Markov Models optimizes a point estimate of the model parameters. This estimate, which can be viewed as the maximum of a posterior probability density over the model parameters, may be susceptible to overfitting, and contains no indication of parameter uncertainty. Also, this maximummay be unrepresentative of the posterior probability distribution. In this paper we study a method in which we optimize an ensemble which approximates the entire posterior probability distribution. The ensemble learning algorithm requires the same resources as the traditional Baum--Welch algorithm. The traditional training algorithm for hidden Markov models is an expectation-- maximization (EM) algorithm (Dempster et al. 1977) known as the Baum--Welch algorithm. It is a maximum likelihood method, or, with a simple modification, a penalized maximum likelihood method, which can be viewed as maximizing a posterior probability density over the model parameters. Recently, ...

Building models of language is a central task in natural language processing. Traditionally, language has been modeled with manually-constructed grammars that describe which strings are grammatical and which are not; however, with the recent availability of massive amounts of on-line text, statistically-trained models are an attractive alternative. These models are generally probabilistic, yielding a score reflecting sentence frequency instead of a binary grammaticality judgement. Probabilistic models of language are a fundamental tool in speech recognition for resolving acoustically ambiguous utterances. For example, we prefer the transcription forbear to four bear as the former string is far more frequent in English text. Probabilistic models also have application in optical character recognition, handwriting recognition, spelling correction, part-of-speech tagging, and machine translation. In this thesis, we investigate three problems involving the probabilistic modeling of languag...

Some models of textual corpora employ text generation methods involving n-gram statistics, while others use latent topic variables inferred using the “bag-of-words ” assumption, in which word order is ignored. Previously, these methods have not been combined. In this work, I explore a hierarchical generative probabilistic model that incorporates both n-gram statistics and latent topic variables by extending a unigram topic model to include properties of a hierarchical Dirichlet bigram language model. The model hyperparameters are inferred using a Gibbs EM algorithm. On two data sets, each of 150 documents, the new model exhibits better predictive accuracy than either a hierarchical Dirichlet bigram language model or a unigram topic model. Additionally, the inferred topics are less dominated by function words than are topics discovered using unigram statistics, potentially making them more meaningful. 1.