An adaptive statistical languagemodel is described, which successfullyintegrates long distancelinguistic information with other knowledge sources. Most existing statistical language models exploit only the immediate history of a text. To extract information from further back in the document's history, we propose and use trigger pairs as the basic information bearing elements. This allows the model to adapt its expectations to the topic of discourse. Next, statistical evidence from multiple sources must be combined. Traditionally, linear interpolation and its variants have been used, but these are shown here to be seriously deficient. Instead, we apply the principle of Maximum Entropy (ME). Each information source gives rise to a set of constraints, to be imposed on the combined estimate. The intersection of these constraints is the set of probability functions which are consistent with all the information sources. The function with the highest entropy within that set is the ME solution...

We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = (x i1 ; x i2 ; : : : ; x im ) t denote the performance of the stock market on day i ; where x ij is the factor by which the j-th stock increases on day i : Let b i = (b i1 ; b i2 ; : : : ; b im ) t ; b ij 0; P j b ij = 1 ; denote the proportion b ij of wealth invested in the j-th stock on day i : Then S n = Q n i=1 b t i x i is the factor by which wealth is increased in n trading days. Consider as a goal the wealth S n = max b Q n i=1 b t x i that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that S n exceeds the best stock, the Dow Jones average, and the value line index at time n: In fact, S n usually exceeds these quantities by an exponential factor. Let x 1 ; x 2 ; : : : ; be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence ...

Statistical Language Models estimate the distribution of various natural language phenomena for the purpose of speech recognition and other language technologies. Since the first significant model was proposed in 1980, many attempts have been made to improve the state of the art. We review them here, point to a few promising directions, and argue for a Bayesian approach to integration of linguistic theories with data. 1. OUTLINE Statistical language modeling (SLM) is the attempt to capture regularities of natural language for the purpose of improving the performance of various natural language applications. By and large, statistical language modeling amounts to estimating the probability distribution of various linguistic units, such as words, sentences, and whole documents. Statistical language modeling is crucial for a large variety of language technology applications. These include speech recognition (where SLM got its start), machine translation, document classification and routing, optical character recognition, information retrieval, handwriting recognition, spelling correction, and many more. In machine translation, for example, purely statistical approaches have been introduced in [1]. But even researchers using rule-based approaches have found it beneficial to introduce some elements of SLM and statistical estimation [2]. In information retrieval, a language modeling approach was recently proposed by [3], and a statistical/information theoretical approach was developed by [4]. SLM employs statistical estimation techniques using language training data, that is, text. Because of the categorical nature of language, and the large vocabularies people naturally use, statistical techniques must estimate a large number of parameters, and consequently depend critically on the availability of large amounts of training data.

This paper consists of an overview on universal prediction from an information-theoretic perspective. Special attention is given to the notion of probability assignment under the selfinformation loss function, which is directly related to the theory of universal data compression.

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...

We present the design of a linguistic postprocessor for character recognizers. The central module of our system is a trainable variable memory length Markov model (VLMM) which predicts the next character given a variable length window of past characters. The overall system is composed of several finite state automata, including the main VLMM and a proper noun VLMM. The best model reported in the literature (Brown et al 1992) achieves 1.75 bits per character on the Brown corpus. On that same corpus, our model, trained on 10 times less data, reaches 2.19 bits per character and is 200 times smaller (_ 160,000 parameters). The model was designed for handwriting recognition applications but can be used for other OCR problems and speech recognition.

This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a “decomposed” CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems.

this paper is to show that the difference between the best machine models and human models is smaller than might be indicated by these results. This follows from a number of observations: firsfly, the original human experiments used only 27 character English (letters plus space) against full 128 character ASCII text for most computer experiznents; secondly, using large amounts of priming text substantially improves PPM's performance; and thirdly, the PPM algorithm can k,e modified to perform better for English text. The result of this is machine performance down to 1.46 bpc

We define predictive information Ipred(T) as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times T: Ipred(T) can remain finite, grow logarithmically, or grow as a fractional power law. If the time series allows us to learn a model with a finite number of parameters, then Ipred(T) grows logarithmically with a coefficient that counts the dimensionality of the model space. In contrast, power-law growth is associated, for example, with the learning of infinite parameter (or nonparametric) models such as continuous functions with smoothness constraints. There are connections between the predictive information and measures of complexity that have been defined both in learning theory and the analysis of physical systems through statistical mechanics and dynamical systems theory. Furthermore, in the same way that entropy provides the unique measure of available information consistent with some simple and plausible conditions, we argue that the divergent part of Ipred(T) provides the unique measure for the complexity of dynamics underlying a time series. Finally, we discuss how these ideas may be useful in problems in physics, statistics, and biology.

A computational theory of the visual recognition of words of text is developed. The theory, based on previous studies of how people read, includes three stages: hypothesis generation, hypothesis testing, and global contextual analysis. Hypothesis generation uses gross visual features, such as those that could be extracted from the peripheral presentation of a word, to provide expectations about word identity. Hypothesis testing integrates the information determined by hypothesis generation with more detailed features that are extracted from the word image. Global contextual analysis provides syntactic and semantic information that influences hypothesis testing. Algorithmic realization of the computational theory also consists of three stages. Hypothesis generation is implemented by extracting simple features from an input word and using those features to find a set of dictionary words with those features in common. Hypothesis testing uses this set of words to drive further selective image analysis that matches the input to one of the members of this set. This is done with a tree of feature tests that can be executed in several different ways to recognize an input word. Global contextual analysis is implemented with a process that uses knowledge of typical word-class transitions to improve the performance of the hypothesis testing stage. This is executable in parallel with hypothesis testing. This methodology is in sharp contrast to conventional machine reading algorithms which usually segment a word into characters and recognize the individual characters. Thus, a word decision is arrived at as a composite of character decisions. The algorithm presented here avoids the segmentation stage and does not require an exhaustive analysis of each character and thus is a character recognition algorithm. Statistical projections show the viability of all three stages of the proposed approach. Experiments with images of text show that the methodology performs well in difficult situations, such as touching and overlapping characters.