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Approximating discrete probability distributions with dependence trees

by C. K. Chow, C. N. Liu - IEEE TRANSACTIONS ON INFORMATION THEORY , 1968
"... A method is presented to approximate optimally an n-dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of n-1 first order dependence relationship among the n variables ..."
Abstract - Cited by 881 (0 self) - Add to MetaCart
variables. It is shown that the procedure derived in this paper yields an approximation of a minimum difference in information. It is further shown that when this procedure is applied to empirical observations from an unknown distribution of tree dependence, the procedure is the maximum-likelihood estimate

Learning generative visual models from few training examples: an incremental Bayesian approach tested on 101 object categories

by Li Fei-fei , 2004
"... Abstract — Current computational approaches to learning visual object categories require thousands of training images, are slow, cannot learn in an incremental manner and cannot incorporate prior information into the learning process. In addition, no algorithm presented in the literature has been te ..."
Abstract - Cited by 784 (16 self) - Add to MetaCart
are learnt incrementally in a Bayesian manner. Our incremental algorithm is compared experimentally to an earlier batch Bayesian algorithm, as well as to one based on maximum-likelihood. The incremental and batch versions have comparable classification performance on small training sets, but incremental

Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods

by John C. Platt - ADVANCES IN LARGE MARGIN CLASSIFIERS , 1999
"... The output of a classifier should be a calibrated posterior probability to enable post-processing. Standard SVMs do not provide such probabilities. One method to create probabilities is to directly train a kernel classifier with a logit link function and a regularized maximum likelihood score. Howev ..."
Abstract - Cited by 1051 (0 self) - Add to MetaCart
sigmoid versus a kernel method trained with a regularized likelihood error function. These methods are tested on three data-mining-style data sets. The SVM+sigmoid yields probabilities of comparable quality to the regularized maximum likelihood kernel method, while still retaining the sparseness

Quantal Response Equilibria For Normal Form Games

by Richard D. McKelvey, Thomas R. Palfrey - NORMAL FORM GAMES, GAMES AND ECONOMIC BEHAVIOR , 1995
"... We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish e ..."
Abstract - Cited by 647 (28 self) - Add to MetaCart
existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum

Maximum entropy markov models for information extraction and segmentation

by Andrew McCallum, Dayne Freitag, Fernando Pereira , 2000
"... Hidden Markov models (HMMs) are a powerful probabilistic tool for modeling sequential data, and have been applied with success to many text-related tasks, such as part-of-speech tagging, text segmentation and information extraction. In these cases, the observations are usually modeled as multinomial ..."
Abstract - Cited by 561 (18 self) - Add to MetaCart
as multinomial distributions over a discrete vocabulary, and the HMM parameters are set to maximize the likelihood of the observations. This paper presents a new Markovian sequence model, closely related to HMMs, that allows observations to be represented as arbitrary overlapping features (such as word

Power-law distributions in empirical data

by Aaron Clauset, Cosma Rohilla Shalizi, M. E. J. Newman - ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111 , 2009
"... Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
Abstract - Cited by 607 (7 self) - Add to MetaCart
estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law distribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We

Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation

by Yee Hwa Yang, Sandrine Dudoit, Percy Luu, Vivian Peng , 2002
"... There are many sources of systematic variation in cDNA microarray experiments which affect the measured gene expression levels (e.g. differences in labeling efficiency between the two fluorescent dyes). The term normalization refers to the process of removing such variation. A constant adjustment is ..."
Abstract - Cited by 718 (9 self) - Add to MetaCart
) is introduced to aid in intensity-dependent normalization. Lastly, to allow for comparisons of expression levels across slides, a robust method based on maximum likelihood estimation is proposed to adjust for scale differences among slides.

Regularized discriminant analysis

by Jerome H. Friedman - J. Amer. Statist. Assoc , 1989
"... Linear and quadratic discriminant analysis are considered in the small sample high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which are customize ..."
Abstract - Cited by 468 (2 self) - Add to MetaCart
Linear and quadratic discriminant analysis are considered in the small sample high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which

A maximum likelihood stereo algorithm

by Ingemar J. Cox, Sunita L. Hingorani, Satish B. Rao, Bruce M. Maggs - Computer Vision and Image Understanding , 1996
"... A stereo algorithm is presented that optimizes a maximum likelihood cost function. The maximum likelihood cost function assumes that corresponding features in the left and right images are Normally distributed about a common true value and consists of a weighted squared error term if two features ar ..."
Abstract - Cited by 234 (2 self) - Add to MetaCart
A stereo algorithm is presented that optimizes a maximum likelihood cost function. The maximum likelihood cost function assumes that corresponding features in the left and right images are Normally distributed about a common true value and consists of a weighted squared error term if two features

Maximum-Likelihood Models for Combined Analyses of Multiple Sequence Data

by Ziheng Yang - J. Mol. Evol , 1996
"... Models of nucleotide substitution were constructed for combined analyses of heterogeneous sequence data (such as those of multiple genes) from the same set of species. The models account for different aspects of the heterogeneity in the evolutionary process of different genes, such as differences in ..."
Abstract - Cited by 132 (16 self) - Add to MetaCart
in nucleotide frequencies, in substitution rate bias (for example, the transition /transversion rate bias), and in the extent of rate variation across sites. Model parameters were estimated by maximum likelihood and the likelihood ratio test was used to test hypotheses concerning sequence evolution
Results 11 - 20 of 3,463