Statistical Inference in Evolutionary Models of DNA Sequences via the EM Algorithm

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Asger Hobolth ◽  
Jens Ledet Jensen
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Statistical Inference ◽  
Dna Sequences ◽  
Expectation Maximization ◽  
Continuous Time ◽  
Information Matrix ◽  
Evolutionary Models ◽  
Likelihood Estimator ◽  
The Em Algorithm

We describe statistical inference in continuous time Markov processes of DNA sequences related by a phylogenetic tree. The maximum likelihood estimator can be found by the expectation maximization (EM) algorithm and an expression for the information matrix is also derived. We provide explicit analytical solutions for the EM algorithm and information matrix.

scholarly journals Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 373
Author(s):  
Branislav Panić ◽  
Jernej Klemenc ◽  
Marko Nagode
Keyword(s):  
Em Algorithm ◽  
Density Estimation ◽  
Mixture Model ◽  
Expectation Maximization ◽  
State Of The Art ◽  
R Package ◽  
Likelihood Estimator ◽  
Local Optima ◽  
The Em Algorithm ◽  
Initialization Algorithm

A commonly used tool for estimating the parameters of a mixture model is the Expectation–Maximization (EM) algorithm, which is an iterative procedure that can serve as a maximum-likelihood estimator. The EM algorithm has well-documented drawbacks, such as the need for good initial values and the possibility of being trapped in local optima. Nevertheless, because of its appealing properties, EM plays an important role in estimating the parameters of mixture models. To overcome these initialization problems with EM, in this paper, we propose the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as a more effective initialization algorithm. Three different strategies are derived for dealing with the unknown number of components in the mixture model. These strategies are thoroughly tested on artificial datasets, density–estimation datasets and image–segmentation problems and compared with state-of-the-art initialization methods for the EM. Our proposal shows promising results in terms of clustering and density-estimation performance as well as in terms of computational efficiency. All the improvements are implemented in the rebmix R package.

scholarly journals Fisher information and statistical inference for phase-type distributions

2011 ◽  
Vol 48 (A) ◽  
pp. 277-293 ◽  
Author(s):  
Mogens Bladt ◽  
Luz Judith R. Esparza ◽  
Bo Friis Nielsen
Keyword(s):  
Em Algorithm ◽  
Statistical Inference ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Likelihood Function ◽  
Information Matrix ◽  
The Em Algorithm ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Newton Raphson

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton–Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton–Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

SMEM Algorithm Is Not Fully Compatible with Maximum-Likelihood Framework

2002 ◽  
Vol 14 (6) ◽  
pp. 1261-1266 ◽  
Author(s):  
Akihiro Minagawa ◽  
Norio Tagawa ◽  
Toshiyuki Tanaka
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Mixture Models ◽  
Expectation Maximization ◽  
Evaluation Method ◽  
Local Optimum ◽  
The Em Algorithm ◽  
Optimum Property ◽  
Split And Merge ◽  
Searching Method

The expectation-maximization (EM) algorithm with split-and-merge operations (SMEM algorithm) proposed by Ueda, Nakano, Ghahramani, and Hinton (2000) is a nonlocal searching method, applicable to mixture models, for relaxing the local optimum property of the EM algorithm. In this article, we point out that the SMEM algorithm uses the acceptance-rejection evaluation method, which may pick up a distribution with smaller likelihood, and demonstrate that an increase in likelihood can then be guaranteed only by comparing log likelihoods.

scholarly journals Fisher information and statistical inference for phase-type distributions

2011 ◽  
Vol 48 (A) ◽  
pp. 277-293
Author(s):  
Mogens Bladt ◽  
Luz Judith R. Esparza ◽  
Bo Friis Nielsen
Keyword(s):  
Em Algorithm ◽  
Statistical Inference ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Likelihood Function ◽  
Information Matrix ◽  
The Em Algorithm ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Newton Raphson

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton–Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton–Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

Maximum-likelihood estimation in linkage heterogeneity models including additional information via the EM algorithm

1995 ◽  
Vol 12 (5) ◽  
pp. 515-527 ◽  
Author(s):  
Jeanine J. Houwing-Duistermaat ◽  
Lodewijk A. Sandkuijl ◽  
Arthur A. B. Bergen ◽  
Hans C. van Houwelingen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Likelihood Estimation ◽  
Additional Information ◽  
The Em Algorithm

scholarly journals Direct fast estimator for recombination frequency in the F2 cross

2021 ◽  
Author(s):  
Mathias Lorieux
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Maximum Likelihood Estimator ◽  
Recombination Frequency ◽  
Short Note ◽  
Simulation Studies ◽  
Likelihood Estimator ◽  
Simple Estimate ◽  
Efficient Simulation

AbstractIn this short note, a new unbiased maximum-likelihood estimator is proposed for the recombination frequency in the F2 cross. The estimator is much faster to calculate than its EM algorithm equivalent, yet as efficient. Simulation studies are carried to illustrate the gain over another simple estimate proposed by Benito & Gallego (2004).

scholarly journals Unsupervised Learning in RSS-Based DFLT Using an EM Algorithm

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5549
Author(s):  
Ossi Kaltiokallio ◽  
Roland Hostettler ◽  
Hüseyin Yiğitler ◽  
Mikko Valkama
Keyword(s):  
Em Algorithm ◽  
Expectation Maximization ◽  
Tracking System ◽  
Model Parameters ◽  
Calibration Data ◽  
Tracking Accuracy ◽  
Time Period ◽  
The Em Algorithm ◽  
Device Free ◽  
Localization And Tracking

Received signal strength (RSS) changes of static wireless nodes can be used for device-free localization and tracking (DFLT). Most RSS-based DFLT systems require access to calibration data, either RSS measurements from a time period when the area was not occupied by people, or measurements while a person stands in known locations. Such calibration periods can be very expensive in terms of time and effort, making system deployment and maintenance challenging. This paper develops an Expectation-Maximization (EM) algorithm based on Gaussian smoothing for estimating the unknown RSS model parameters, liberating the system from supervised training and calibration periods. To fully use the EM algorithm’s potential, a novel localization-and-tracking system is presented to estimate a target’s arbitrary trajectory. To demonstrate the effectiveness of the proposed approach, it is shown that: (i) the system requires no calibration period; (ii) the EM algorithm improves the accuracy of existing DFLT methods; (iii) it is computationally very efficient; and (iv) the system outperforms a state-of-the-art adaptive DFLT system in terms of tracking accuracy.

scholarly journals Models and Algorithms for Tracking Target with Coordinated Turn Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghui Yuan ◽  
Feng Lian ◽  
Chongzhao Han
Keyword(s):  
Em Algorithm ◽  
Expectation Maximization ◽  
Multiple Models ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Motion Model ◽  
Single Model ◽  
Kinematic Constraint ◽  
The Em Algorithm ◽  
Turn Rate

Tracking target with coordinated turn (CT) motion is highly dependent on the models and algorithms. First, the widely used models are compared in this paper—coordinated turn (CT) model with known turn rate, augmented coordinated turn (ACT) model with Cartesian velocity, ACT model with polar velocity, CT model using a kinematic constraint, and maneuver centered circular motion model. Then, in the single model tracking framework, the tracking algorithms for the last four models are compared and the suggestions on the choice of models for different practical target tracking problems are given. Finally, in the multiple models (MM) framework, the algorithm based on expectation maximization (EM) algorithm is derived, including both the batch form and the recursive form. Compared with the widely used interacting multiple model (IMM) algorithm, the EM algorithm shows its effectiveness.

Sign in / Sign up

Export Citation Format

Share Document