arxiv_ml 85% Match Research Paper Researchers in probabilistic modeling,Machine learning engineers 19 hours ago

A new class of Markov random fields enabling lightweight sampling

generative-ai › flow-models

📄 Abstract

Abstract: This work addresses the problem of efficient sampling of Markov random fields (MRF). The sampling of Potts or Ising MRF is most often based on Gibbs sampling, and is thus computationally expensive. We consider in this work how to circumvent this bottleneck through a link with Gaussian Markov Random fields. The latter can be sampled in several cost-effective ways, and we introduce a mapping from real-valued GMRF to discrete-valued MRF. The resulting new class of MRF benefits from a few theoretical properties that validate the new model. Numerical results show the drastic performance gain in terms of computational efficiency, as we sample at least 35x faster than Gibbs sampling using at least 37x less energy, all the while exhibiting empirical properties close to classical MRFs.

Key Contributions

This paper introduces a new class of Markov Random Fields (MRFs) by establishing a link with Gaussian Markov Random Fields (GMRFs). This novel approach enables significantly more efficient sampling compared to traditional Gibbs sampling, achieving at least 35x speedup and using 37x less energy, while maintaining empirical properties close to classical MRFs.

Business Value

Enables faster and more cost-effective inference in applications relying on MRFs, such as image processing, computer vision, and statistical physics simulations.

Paper Metadata

Innovation Type

Algorithmic

Deployment Feasibility

High, as it improves upon existing sampling methods without introducing new complex infrastructure.

Limitations Addressed

Computational expense and inefficiency of Gibbs sampling for MRFs.

Performance Gains

At least 35x faster sampling, at least 37x less energy.

Technical Tags

Markov Random FieldsGibbs SamplingGaussian Markov Random FieldsLightweight SamplingDiscrete MRFReal-valued GMRFComputational EfficiencyEnergy Minimization

Research Topics

Probabilistic Graphical ModelsSampling TechniquesModel EfficiencyStatistical Inference

Methods & Architectures

Mapping from GMRF to discrete MRFLightweight sampling Markov Random Fields (MRF)Gaussian Markov Random Fields (GMRF)

Applications & Tasks

Statistical Modeling Machine Learning Efficient SamplingComputational Bottleneck Sampling from MRFs

Related Fields

Statistical PhysicsComputer VisionMachine Learning Theory

Keywords

Markov Random FieldsGibbs SamplingGaussian Markov Random FieldsSamplingEfficiencyComputational CostProbabilistic ModelsStatistical InferenceDiscrete ModelsContinuous Models

Academic Context

#Probabilistic Graphical Models#Sampling Techniques#Model Efficiency#Statistical Inference

Commercial Potential

Competitive Edge

Offers a more efficient alternative to traditional Gibbs sampling for MRFs.

Resource Requirements

Compute Needs

Standard computational resources for statistical modeling.

Data Requirements

None explicitly mentioned, likely requires data suitable for MRF modeling.

Scalability

Improved sampling efficiency suggests better scalability for large models.

Production Readiness

Maturity Level

Research

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