Learning Energy-based Model via Dual-MCMC Teaching (2312.02469v1)

Abstract: This paper studies the fundamental learning problem of the energy-based model (EBM). Learning the EBM can be achieved using the maximum likelihood estimation (MLE), which typically involves the Markov Chain Monte Carlo (MCMC) sampling, such as the Langevin dynamics. However, the noise-initialized Langevin dynamics can be challenging in practice and hard to mix. This motivates the exploration of joint training with the generator model where the generator model serves as a complementary model to bypass MCMC sampling. However, such a method can be less accurate than the MCMC and result in biased EBM learning. While the generator can also serve as an initializer model for better MCMC sampling, its learning can be biased since it only matches the EBM and has no access to empirical training examples. Such biased generator learning may limit the potential of learning the EBM. To address this issue, we present a joint learning framework that interweaves the maximum likelihood learning algorithm for both the EBM and the complementary generator model. In particular, the generator model is learned by MLE to match both the EBM and the empirical data distribution, making it a more informative initializer for MCMC sampling of EBM. Learning generator with observed examples typically requires inference of the generator posterior. To ensure accurate and efficient inference, we adopt the MCMC posterior sampling and introduce a complementary inference model to initialize such latent MCMC sampling. We show that three separate models can be seamlessly integrated into our joint framework through two (dual-) MCMC teaching, enabling effective and efficient EBM learning.

• The paper introduces a novel dual-MCMC teaching approach that jointly refines energy-based models and complementary generators using MCMC-revised samples.
• It alternates maximum likelihood estimation with generator-guided MCMC sampling to overcome inefficient mixing and convergence issues.
• Extensive experiments show superior performance in realistic image synthesis compared to GANs and score-based models.

Learning Scheme for Energy-Based Models

Introduction

Energy-Based Models (EBMs) have emerged as powerful tools for capturing complex data distributions. These models use a neural network to parameterize an energy function that assigns low energy levels to likely data points and high energy levels to unlikely data points. While conventionally trained by maximum likelihood estimation (MLE), they generally rely on noise-initialized Markov Chain Monte Carlo (MCMC) sampling, which suffers from inefficiency.

To tackle this, a complementary generator model is typically employed as an informative initializer to help guide the sampling process. However, relying solely on generator samples as a replacement for MCMC has been shown to be less accurate. Addressing this, the paper introduces a novel dual-MCMC teaching learning scheme to efficiently integrate an EBM with complementary models. The joint learning framework ensures the EBM and generator model match both the EBM distribution and empirical data.

EBM Generation and MCMC Challenges

In essence, sampling from an EBM requires iterative updates that converge towards the target distribution when starting from an initial distribution. The conventional approach, which initializes from a non-informative noise source, often leads to inefficient mixing and convergence issues.

Recent advancements have explored using a generator, usually guided by a noise-initialized latent variable model, to kickstart the MCMC sampling process. Yet, the generator model's training does not traditionally incorporate empirical data examples, leading to potentially biased learning, which in turn can suboptimally influence EBM learning. Hence, a more effective EBM and complementary generator model learning method must be sought.

Dual-MCMC Teaching: A Novel Framework

The proposed framework modifies the MCMC sampling process using the generator model. The generator is not only trained to match the EBM but also the empirical data distribution, providing a robust initializer for subsequent MCMC sampling. This is achieved by alternating MLE with MCMC posterior sampling, integrating a generator-guided MCMC process, and supplementing with an inference model to start the latent MCMC sampling more informatively. Together, these form the dual-MCMC method employed for EBM learning.

This method aims to simultaneously align the generator with both EBM-derived and empirical data, allowing for the refinement of both models. Significantly, by employing MCMC-revised samples, the framework teaches complementary models to better initialize MCMC sampling and absorption of revisions.

Experiments and Contributions

The effectiveness of the proposed approach is backed by extensive experiments that demonstrate its superior performance in generating realistic image synthesis when benchmarked against standard data sets. The method is seen to outperform other learning schemes for EBMs, even comparison against generative adversarial networks, and score-based models. Further, analyses into the complementary models prove their capability to match MCMC-revised samples effectively, indicating their successful integration into the learning process.

In essence, the contributions of this work sum up as an innovative learning scheme that synchronizes the EBM with its accompanying models, a dual-MCMC teaching approach that promotes precise sampling and inference, and proof of the superior performance of the EBM so derived through empirical experimentation.

In conclusion, this novel joint learning framework successfully addresses biases and inefficiencies of previous methods, achieving a seamless integration of EBMs with generator models for effective and efficient data representation learning.