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A Parametric Texture Model based on Joint Statistics of Complex Wavelet Coefficients
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2000
"... We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We de ..."
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Cited by 386 (13 self)
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We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.
Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems
 Proceedings of the IEEE
, 1998
"... this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, ph ..."
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Cited by 294 (17 self)
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this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the illdefined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.
A Maximum Entropy Approach to Adaptive Statistical Language Modeling
 Computer, Speech and Language
, 1996
"... 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 h ..."
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Cited by 280 (12 self)
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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...
A Gaussian prior for smoothing maximum entropy models
, 1999
"... 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 ..."
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Cited by 246 (2 self)
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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 ngram language models. Because of the mature body of research in ngram model smoothing and the close connection between maximum entropy and conventional ngram models, this domain is wellsuited 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 than all other algorithms under consideration. This general and efficient method involves using a Gaussian prior on the parameters of the model and selecting maximum a posteriori instead of maximum likelihood parameter values. We contrast this method with previous ngram smoothing methods to explain its superior performance.
Maximum Entropy Models for Natural Language Ambiguity Resolution
, 1998
"... The best aspect of a research environment, in my opinion, is the abundance of bright people with whom you argue, discuss, and nurture your ideas. I thank all of the people at Penn and elsewhere who have given me the feedback that has helped me to separate the good ideas from the bad ideas. I hope th ..."
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Cited by 227 (1 self)
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The best aspect of a research environment, in my opinion, is the abundance of bright people with whom you argue, discuss, and nurture your ideas. I thank all of the people at Penn and elsewhere who have given me the feedback that has helped me to separate the good ideas from the bad ideas. I hope that Ihave kept the good ideas in this thesis, and left the bad ideas out! Iwould like toacknowledge the following people for their contribution to my education: I thank my advisor Mitch Marcus, who gave me the intellectual freedom to pursue what I believed to be the best way to approach natural language processing, and also gave me direction when necessary. I also thank Mitch for many fascinating conversations, both personal and professional, over the last four years at Penn. I thank all of my thesis committee members: John La erty from Carnegie Mellon University, Aravind Joshi, Lyle Ungar, and Mark Liberman, for their extremely valuable suggestions and comments about my thesis research. I thank Mike Collins, Jason Eisner, and Dan Melamed, with whom I've had many stimulating and impromptu discussions in the LINC lab. Iowe them much gratitude for their valuable feedback onnumerous rough drafts of papers and thesis chapters.
Filters, Random Fields and Maximum Entropy . . .
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1998
"... This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of vi ..."
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Cited by 225 (17 self)
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This article presents a statistical theory for texture modeling. This theory combines filtering theory and Markov random field modeling through the maximum entropy principle, and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Our theory characterizes the ensemble of images I with the same texture appearance by a probability distribution f (I) on a random field, and the objective of texture modeling is to make inference about f (I), given a set of observed texture examples. In our theory, texture modeling consists of two steps. (1) A set of filters is selected from a general filter bank to capture features of the texture, these filters are applied to observed texture images, and the histograms of the filtered images are extracted. These histograms are estimates of the marginal distributions of f (I). This step is called feature extraction. (2) The maximum entropy principle is employed to derive a distribution p(I), which is restricted to have the same marginal distributions as those in (1). This p(I) is considered as an estimate of f (I). This step is called feature fusion. A stepwise algorithm is proposed to choose filters from a general filter bank. The resulting model, called FRAME (Filters, Random fields And Maximum Entropy), is a Markov random field (MRF) model, but with a much enriched vocabulary and hence much stronger descriptive ability than the previous MRF models used for texture modeling. Gibbs sampler is adopted to synthesize texture images by drawing typical samples from p(I), thus the model is verified by seeing whether the synthesized texture images have similar visual appearances
Minimax Entropy Principle and Its Application to Texture Modeling
, 1997
"... This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a ..."
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Cited by 220 (47 self)
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This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a certain set of feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce these feature statistics. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed, in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The model complexity is restricted because of the sample variation in the observed feature statistics. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (Filter, Random field, And Minimax Entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. Relationship between our theory and the mechanisms of neural computation is also discussed.
Prior Probabilities
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determ ..."
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Cited by 219 (4 self)
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e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp
Two decades of statistical language modeling: Where do we go from here
 Proceedings of the IEEE
, 2000
"... 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 ..."
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Cited by 192 (1 self)
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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 rulebased 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.
Learning to Parse Natural Language with Maximum Entropy Models
, 1999
"... This paper presents a machine learning system for parsing natural language that learns from manually parsed example sentences, and parses unseen data at stateoftheart accuracies. Its machine learning technology, based on the maximum entropy framework, is highly reusable and not specific to the pa ..."
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Cited by 189 (0 self)
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This paper presents a machine learning system for parsing natural language that learns from manually parsed example sentences, and parses unseen data at stateoftheart accuracies. Its machine learning technology, based on the maximum entropy framework, is highly reusable and not specific to the parsing problem, while the linguistic hints that it uses to learn can be specified concisely. It therefore requires a minimal amount of human effort and linguistic knowledge for its construction. In practice, the running time of the parser on a test sentence is linear with respect to the sentence length. We also demonstrate that the parser can train from other domains without modification to the modeling framework or the linguistic hints it uses to learn. Furthermore, this paper shows that research into rescoring the top 20 parses returned by the parser might yield accuracies dramatically higher than the stateoftheart.