Maximum Entropy Conditional Probability Modeling For Survival Analysis

Open Access
Author:
Duan, Wenxiao
Graduate Program:
Electrical Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
April 01, 2014
Committee Members:
  • David Jonathan Miller, Thesis Advisor
  • William Kenneth Jenkins, Thesis Advisor
Keywords:
  • Maximum Entropy
  • Survival Analysis
  • SNP
  • Gradient Ascent
Abstract:
In this thesis, we try to solve the survival analysis problem by building a maximum entropy model. The main idea extending maximum entropy conditional probability modeling (MECPM) from categorical class variable to ordinal class variable is to impose constraints consistent with an ordinal class variable. For learning parameters of each candidate constraint, we employ gradient ascent to maximize log-likelihood of model with candidate constraint. We narrow down the scope of candidates at a specified order by measuring kullback distance, and a greedy interaction growing search method is invoked to generate the candidate pool of constraints. For comparing and selecting constraints and constraint order, we employ BIC. Censoring issue is involved in our data. We take censored data into account when counting for probability ground truth and calculating estimated probability distribution, in order to properly exploit information in censored observations. A new log-likelihood function is proposed considering censored subjects.