Semisupervised learning of hidden Markov models via a homotopy method

Area of Science:

• Machine Learning
• Statistical Modeling
• Sequential Data Analysis

Background:

• Hidden Markov Models (HMMs) are widely used for sequential data analysis.
• Training HMM classifiers often involves balancing labeled and unlabeled data, controlled by an allocation parameter \lambda.
• Existing methods face challenges with local optima in supervised HMM learning (\lambda = 0).

Purpose of the Study:

• To develop a robust method for designing HMM classifiers using semisupervised learning.
• To address the issue of local optima in HMM parameter estimation.
• To provide a framework for selecting the optimal allocation parameter \lambda for semisupervised HMMs.

Main Methods:

• Application of a homotopy method to track solutions from supervised (\lambda = 0) to unsupervised (\lambda = 1) HMM learning.
• Development of a modified homotopy map specifically for HMMs to ensure a continuous path of solutions.
• Utilizing the tracked path for selecting \lambda and choosing among multiple supervised solutions.

Main Results:

• The proposed homotopy method successfully tracks solutions from \lambda = 0 to \lambda = 1 for HMMs.
• The method provides a means to select an appropriate \lambda for semisupervised HMM solutions.
• Demonstrated robustness and feasibility compared to the Expectation-Maximization (EM) algorithm for semisupervised HMM training.

Conclusions:

• The modified homotopy method offers a reliable approach for semisupervised HMM classifier design.
• This technique enhances the selection of \lambda and aids in overcoming local optima challenges.
• The method shows significant promise for analyzing both measured and synthetic sequential data.