Open AccessJournal Article
A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models
Reads0
Chats0
TLDR
In this paper, the authors describe the EM algorithm for finding the parameters of a mixture of Gaussian densities and a hidden Markov model (HMM) for both discrete and Gaussian mixture observation models.Abstract:
We describe the maximum-likelihood parameter estimation problem and how the ExpectationMaximization (EM) algorithm can be used for its solution. We first describe the abstract form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) finding the parameters of a hidden Markov model (HMM) (i.e., the Baum-Welch algorithm) for both discrete and Gaussian mixture observation models. We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical rigor.read more
Citations
More filters
Journal ArticleDOI
Machine learning
TL;DR: Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis.
Journal ArticleDOI
Simultaneous truth and performance level estimation (STAPLE): an algorithm for the validation of image segmentation
TL;DR: An expectation-maximization algorithm for simultaneous truth and performance level estimation (STAPLE), which considers a collection of segmentations and computes a probabilistic estimate of the true segmentation and a measure of the performance level represented by each segmentation.
Proceedings ArticleDOI
Clustering with Bregman Divergences
TL;DR: This paper proposes and analyzes parametric hard and soft clustering algorithms based on a large class of distortion functions known as Bregman divergences, and shows that there is a bijection between regular exponential families and a largeclass of BRegman diverGences, that is called regular Breg man divergence.
Journal ArticleDOI
Cooperative Localization in Wireless Networks
TL;DR: This paper describes several cooperative localization algorithms and quantify their performance, based on realistic UWB ranging models developed through an extensive measurement campaign using FCC-compliant UWB radios, and presents a powerful localization algorithm that is fully distributed, can cope with a wide variety of scenarios, and requires little communication overhead.
References
More filters
Proceedings Article
Regression with Input-dependent Noise: A Gaussian Process Treatment
TL;DR: This paper shows that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods and gives a posterior noise variance that well-approximates the true variance.
Journal ArticleDOI
Level-crossing problems for random processes
I. Blake,William C. Lindsey +1 more
TL;DR: A survey of known results on certain aspects of the level-crossing properties of random processes is presented and provides a basis for further study in the area.
Book
Continuous Univariate Distributions, Volume 2
TL;DR: In this paper, the authors present a continuous univariate distribution model for continuous distributions, which is a variant of the one presented in this paper, but with a slightly different distribution model.
Proceedings Article
Tangent Prop - A formalism for specifying selected invariances in an adaptive network
Patrice Y. Simard,Patrice Y. Simard,Bernard Victorri,Yann LeCun,John S. Denker,John S. Denker +5 more
TL;DR: A scheme is implemented that allows a network to learn the derivative of its outputs with respect to distortion operators of their choosing, which not only reduces the learning time and the amount of training data, but also provides a powerful language for specifying what generalizations the authors wish the network to perform.
Journal ArticleDOI
Radon-Nikodym Derivatives of Gaussian Measures
TL;DR: In this paper, the Radom-Nikodym derivative of the Radon-Niels (R-N) derivative of a Gaussian measure is derived for the case of the Gaussian process W(T + 1) - W(t).