[Paper Review] Optimized Hidden Markov Model based on Constrained Particle Swarm Optimization

Chang Liu, Yacine Ouzrout+2 more|arXiv (Cornell University)|Nov 7, 2018

Web Data Mining and Analysis13 references4 citations

TL;DR

This paper proposes a Particle Swarm Optimization-based Hidden Markov Model (PSOHMM) that overcomes the local optima limitation of the traditional Baum-Welch algorithm by integrating constrained PSO to optimize HMM parameters. By introducing re-normalization and re-mapping mechanisms, PSOHMM enforces statistical constraints while achieving faster convergence and superior solution quality compared to BWHMM.

ABSTRACT

As one of Bayesian analysis tools, Hidden Markov Model (HMM) has been used to in extensive applications. Most HMMs are solved by Baum-Welch algorithm (BWHMM) to predict the model parameters, which is difficult to find global optimal solutions. This paper proposes an optimized Hidden Markov Model with Particle Swarm Optimization (PSO) algorithm and so is called PSOHMM. In order to overcome the statistical constraints in HMM, the paper develops re-normalization and re-mapping mechanisms to ensure the constraints in HMM. The experiments have shown that PSOHMM can search better solution than BWHMM, and has faster convergence speed.

Motivation & Objective

• To address the limitation of the Baum-Welch algorithm in finding global optima for HMM parameter estimation.
• To develop a novel optimization framework that integrates particle swarm optimization with statistical constraints inherent in HMMs.
• To improve convergence speed and solution quality in HMM parameter learning through metaheuristic optimization.
• To ensure that optimized HMM parameters remain valid by enforcing stochastic constraints via re-mapping and re-normalization.

Proposed method

• Employ particle swarm optimization (PSO) to search for optimal HMM parameters, replacing the iterative expectation-maximization approach of Baum-Welch.
• Introduce a re-mapping mechanism to project particle positions into the valid probability simplex space required by HMM transition and emission probabilities.
• Apply a re-normalization technique to correct any constraint violations in transition and emission matrices after each PSO iteration.
• Constrain the search space using boundary conditions and penalty functions to maintain stochastic validity of HMM parameters.
• Use a fitness function based on log-likelihood of observed sequences to guide PSO particle updates.
• Integrate constraint handling directly into the PSO algorithm to maintain feasibility throughout optimization.

Experimental results

Research questions

• RQ1 Can particle swarm optimization effectively optimize HMM parameters while respecting the statistical constraints of probability distributions?
• RQ2 Does PSOHMM converge faster and achieve better log-likelihood scores than the standard Baum-Welch algorithm?
• RQ3 How effective are re-mapping and re-normalization in preserving the validity of HMM parameters during PSO optimization?
• RQ4 Can PSOHMM avoid local optima more effectively than Baum-Welch in complex sequence modeling tasks?

Key findings

• PSOHMM achieves better solution quality than BWHMM, as evidenced by higher log-likelihood scores on test sequences.
• PSOHMM demonstrates faster convergence speed compared to the iterative Baum-Welch algorithm.
• The re-mapping and re-normalization mechanisms successfully maintain the stochastic constraints of HMM parameters throughout optimization.
• The proposed constraint-handling techniques prevent invalid probability matrices, ensuring the validity of the optimized HMM.
• Empirical results confirm that PSOHMM outperforms BWHMM in both convergence speed and final solution quality.
• The integration of PSO with HMM parameter learning provides a robust alternative to traditional EM-based methods.