Article
Version 1
Preserved in Portico This version is not peer-reviewed
Conditional Mixture Model and Its Application for Regression Model
Version 1
: Received: 24 October 2020 / Approved: 27 October 2020 / Online: 27 October 2020 (11:41:42 CET)
Version 2 : Received: 28 October 2020 / Approved: 28 October 2020 / Online: 28 October 2020 (11:18:04 CET)
Version 2 : Received: 28 October 2020 / Approved: 28 October 2020 / Online: 28 October 2020 (11:18:04 CET)
How to cite: Nguyen, L. Conditional Mixture Model and Its Application for Regression Model. Preprints 2020, 2020100550. https://doi.org/10.20944/preprints202010.0550.v1 Nguyen, L. Conditional Mixture Model and Its Application for Regression Model. Preprints 2020, 2020100550. https://doi.org/10.20944/preprints202010.0550.v1
Abstract
Expectation maximization (EM) algorithm is a powerful mathematical tool for estimating statistical parameter when data sample contains hidden part and observed part. EM is applied to learn finite mixture model in which the whole distribution of observed variable is finite sum of partial distributions. Coverage ratio of every partial distribution is specified by the probability of hidden variable. An application of mixture model is soft clustering in which cluster is modeled by hidden variable whereas each data point can be assigned to more than one cluster and degree of such assignment is represented by the probability of hidden variable. However, such probability in traditional mixture model is simplified as a parameter, which can cause loss of valuable information. Therefore, in this research I propose a so-called conditional mixture model (CMM) in which the probability of hidden variable is modeled as a full probabilistic density function (PDF) that owns individual parameter. CMM aims to improve power of mixture model. I also propose an application of CMM which is called adaptive regressive model (ARM). Traditional regression model is effective when data sample is scattered equally. If data points are grouped into clusters, regression model tries to learn a unified regression function which goes through all data points. Obviously, such unified function is not effective to evaluate response variable based on grouped data points. The concept “adaptive” of ARM means that ARM solves the ineffectiveness problem by selecting the best cluster of data points firstly and then evaluating response variable within such best cluster. In order words, ARM reduces estimation space of regression model so as to gain high accuracy in calculation.
Keywords
expectation maximization (EM) algorithm; finite mixture model; conditional mixture model; regression model; adaptive regressive model (ARM)
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment