Results 1 - 10 of 1,211,252

Maximum likelihood from incomplete data via the EM algorithm

by A. P. Dempster, N. M. Laird, D. B. Rubin - JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B , 1977
"... A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situat ..."
Abstract - Cited by 11972 (17 self) - Add to MetaCart
situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.

An analysis of transformations

by G. E. P. Box, D. R. Cox - Journal of the Royal Statistical Society. Series B (Methodological , 1964
"... In the analysis of data it is often assumed that observations y,, y,,...,y, are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal, homoscedasti ..."
Abstract - Cited by 1067 (3 self) - Add to MetaCart
In the analysis of data it is often assumed that observations y,, y,,...,y, are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters 0. In this paper we make the less restrictive assumption that such a normal

Probabilistic Principal Component Analysis

by Michael E. Tipping, Chris M. Bishop - JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B , 1999
"... Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of paramet ..."
Abstract - Cited by 709 (5 self) - Add to MetaCart
Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation

Mixtures of Probabilistic Principal Component Analysers

by Michael E. Tipping, Christopher M. Bishop , 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
Abstract - Cited by 532 (6 self) - Add to MetaCart
maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context

Compositional Model Checking

by E. M. Clarke, D. E. Long, K. L. Mcmillan , 1999
"... We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approac ..."
Abstract - Cited by 3252 (70 self) - Add to MetaCart
We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type

Fast and robust fixed-point algorithms for independent component analysis

by Aapo Hyvärinen - IEEE TRANS. NEURAL NETW , 1999
"... Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s informat ..."
Abstract - Cited by 884 (34 self) - Add to MetaCart
Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon’s

Estimation of probabilities from sparse data for the language model component of a speech recognizer

by Slava M. Katz - IEEE Transactions on Acoustics, Speech and Signal Processing , 1987
"... Abstract-The description of a novel type of rn-gram language model is given. The model offers, via a nonlinear recursive procedure, a com-putation and space efficient solution to the problem of estimating prob-abilities from sparse data. This solution compares favorably to other proposed methods. Wh ..."
Abstract - Cited by 799 (2 self) - Add to MetaCart
Abstract-The description of a novel type of rn-gram language model is given. The model offers, via a nonlinear recursive procedure, a com-putation and space efficient solution to the problem of estimating prob-abilities from sparse data. This solution compares favorably to other proposed methods

Bandera: Extracting Finite-state Models from Java Source Code

by James C. Corbett, Matthew B. Dwyer, John Hatcliff, Shawn Laubach, Corina S. Pasareanu, Hongjun Zheng - IN PROCEEDINGS OF THE 22ND INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING , 2000
"... Finite-state verification techniques, such as model checking, have shown promise as a cost-effective means for finding defects in hardware designs. To date, the application of these techniques to software has been hindered by several obstacles. Chief among these is the problem of constructing a fini ..."
Abstract - Cited by 654 (33 self) - Add to MetaCart
), and difficult to optimize (which is necessary to combat the exponential complexity of verification algorithms). In this paper, we describe an integrated collection of program analysis and transformation components, called Bandera, that enables the automatic extraction of safe, compact finite-state models from

Survey on Independent Component Analysis

by Aapo Hyvärinen - NEURAL COMPUTING SURVEYS , 1999
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
Abstract - Cited by 2309 (104 self) - Add to MetaCart
of the original data. Well-known linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes

Transform Analysis and Asset Pricing for Affine Jump-Diffusions

by Darrell Duffie, Jun Pan, Kenneth Singleton - Econometrica , 2000
"... In the setting of ‘‘affine’ ’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applicat ..."
Abstract - Cited by 710 (38 self) - Add to MetaCart
In the setting of ‘‘affine’ ’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example
Results 1 - 10 of 1,211,252