Efficient Algorithms for Estimating the Parameters of Mixed Linear Regression Models

05/12/2021
by   Babak Barazandeh, et al.
0

Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM) algorithm is a widely-used algorithm for maximum likelihood estimation of MLR parameters. However, when noise is non-Gaussian, the steps of EM algorithm may not have closed-form update rules, which makes EM algorithm impractical. In this work, we study the maximum likelihood estimation of the parameters of MLR model when the additive noise has non-Gaussian distribution. In particular, we consider the case that noise has Laplacian distribution and we first show that unlike the the Gaussian case, the resulting sub-problems of EM algorithm in this case does not have closed-form update rule, thus preventing us from using EM in this case. To overcome this issue, we propose a new algorithm based on combining the alternating direction method of multipliers (ADMM) with EM algorithm idea. Our numerical experiments show that our method outperforms the EM algorithm in statistical accuracy and computational time in non-Gaussian noise case.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/24/2018

On the Behavior of the Expectation-Maximization Algorithm for Mixture Models

Finite mixture models are among the most popular statistical models used...
research
10/15/2019

Alternatives of the EM Algorithm for Estimating the Parameters of the Student-t Distribution

In this paper, we consider maximum likelihood estimation of the degree o...
research
11/21/2017

On the EM-Tau algorithm: a new EM-style algorithm with partial E-steps

The EM algorithm is one of many important tools in the field of statisti...
research
06/11/2018

Confidence ellipsoids for regression coefficients by observations from a mixture

Confidence ellipsoids for linear regression coefficients are constructed...
research
11/12/2018

Statistical Inference for Stable Distribution Using EM algorithm

The class of α-stable distributions with a wide range of applications in...
research
05/12/2011

Closed-form EM for Sparse Coding and its Application to Source Separation

We define and discuss the first sparse coding algorithm based on closed-...
research
01/03/2022

Multiview point cloud registration with anisotropic and space-varying localization noise

In this paper, we address the problem of registering multiple point clou...

Please sign up or login with your details

Forgot password? Click here to reset