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
Proceedings ArticleDOI
Multiresolution reflectance filtering
TL;DR: This work presents a multiresolution reflectance framework based on microfacet normal distributions within a pixel over different scales that can rapidly and accurately incorporate fine reflectance detail that is customarily disregarded inMultiresolution rendering methods.
Journal ArticleDOI
A Filter Model Based on Hidden Generalized Mixture Transition Distribution Model for Intrusion Detection System in Vehicle Ad Hoc Networks
TL;DR: A novel filter model based on a hidden generalized mixture transition distribution model (HgMTD) in VANETs is proposed, called FM-HGMTD, which can quickly filter the messages from neighboring vehicles so as to reduce the overhead and detection time.
Journal ArticleDOI
Three-dimensional reconstruction of the statistics of heterogeneous objects from a collection of one projection image of each object.
TL;DR: An estimation problem for statistical reconstruction of heterogeneous three-dimensional objects from two-dimensional tomographic data (single-particle cryoelectron microscope images) is posed as the problem of estimating class probabilities, means, and covariances for a Gaussian mixture where both the mean and covariance are stochastically structured.
Journal ArticleDOI
Metastable Decomposition of High-Dimensional Meteorological Data with Gaps
TL;DR: In this paper, the authors presented an extension of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series, which is based on a combination of ensembles of hidden Markov models (HMMs) with state-specific principal component analysis (PCA) in extended space.
Journal ArticleDOI
Trajectory learning and reproduction for differential drive mobile robots based on GMM/HMM and dynamic time warping using learning from demonstration framework
TL;DR: New Learning from Demonstration-based algorithm that generalizes and extracts relevant features of desired motion trajectories for differential drive mobile robots is presented, which results in high quality reproductions of the motion.
References
More filters
Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
The Nature of Statistical Learning Theory
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
Statistical learning theory
TL;DR: Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
Book
The Fractal Geometry of Nature
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.