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A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models

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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.

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Citations
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Modelling riverflow in the Volta Basin of West Africa : a data-driven framework

B.A. Amisigo
TL;DR: In this article, a riverflow modelling framework was developed for monthly riverflow prediction in the 400,000 km2 Volta Basin of West Africa using a spatio-temporal linear dynamic model employing the Kalman smoother and the Expectation-Maximisation (EM) algorithm.
Journal ArticleDOI

On Adjusted Viterbi Training

TL;DR: This work proves the asymptotic fixed point property of VA for general hidden Markov models for applications where EM is replaced by Viterbi training, or extraction (VT), also known as the Baum–Viterbi algorithm.
Proceedings ArticleDOI

Visible Surface Reconstruction from Normals with Discontinuity Consideration

TL;DR: An optimization algorithm which alternately optimizes until convergence the surface integrabilities and discontinuities inherent in the normal field, in order to derive a segmented surface description of the visible scene without noticeable distortion is presented.
Proceedings ArticleDOI

Learning communities: connectivity and dynamics of interacting agents

TL;DR: The goal is real-time learning and modification of social network relationships by applying statistical machine learning techniques to data obtained from unobtrusive wearable sensors.
Patent

Method of detecting activity with a motion sensor, and corresponding device and computer program

TL;DR: In this paper, a method for detecting the activity (A) of a physical system having a motion sensor comprises the following steps: extracting (100) a sequence (M) of measurements provided by the motion sensor, deducing (102) therefrom an observation sequence (O) calculated using the sequence of measurements (M); determining (104) the activity of the physical system in the form of a sequence of states corresponding to the observation sequence, using a statistical model of components of the observed sequence in view of a plurality of possible predetermined states in which the physical systems may be located
References
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TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.