Combining Monte Carlo and mean-field-like methods for inference in hidden Markov random fields

Area of Science:

• Statistics
• Machine Learning
• Computer Vision

Background:

• Exact inference is often intractable with missing data, especially with complex interactions.
• Existing approximation methods include simulation-based and deterministic variational methods.
• Variational methods are fast but may lack theoretical rigor, while simulation methods are computationally expensive.

Purpose of the Study:

• To develop a new class of algorithms that merge the benefits of simulation and deterministic methods.
• To address challenges in approximate inference for hidden Markov random fields (HMRFs).
• To improve computational efficiency and accuracy in handling missing data.

Main Methods:

• Proposed algorithms are stochastic perturbations of variational expectation maximization (VEM) algorithms.
• Focus on a specific perturbation and prove its almost sure convergence.
• Applied to inference problems in hidden Markov random fields (HMRFs).

Main Results:

• The proposed algorithms demonstrate (almost sure) convergence to the same limit set as VEM.
• Experimental results on synthetic and real-world images show competitive or superior performance.
• The new methods achieve performance comparable to existing simulation-based and variational EM-like algorithms.

Conclusions:

• The novel hybrid algorithms effectively combine speed and theoretical guarantees for approximate inference.
• These methods offer a promising alternative for handling missing data in HMRFs.
• The approach shows practical utility in image analysis tasks.