Scalable Bayesian Learning with posteriors (2406.00104v2)

Abstract: Although theoretically compelling, Bayesian learning with modern machine learning models is computationally challenging since it requires approximating a high dimensional posterior distribution. In this work, we (i) introduce posteriors, an easily extensible PyTorch library hosting general-purpose implementations making Bayesian learning accessible and scalable to large data and parameter regimes; (ii) present a tempered framing of stochastic gradient Markov chain Monte Carlo, as implemented in posteriors, that transitions seamlessly into optimization and unveils a minor modification to deep ensembles to ensure they are asymptotically unbiased for the Bayesian posterior, and (iii) demonstrate and compare the utility of Bayesian approximations through experiments including an investigation into the cold posterior effect and applications with LLMs.

• The paper introduces a PyTorch library, 'posteriors', that makes Bayesian learning scalable for large datasets and high-dimensional parameters.
• It presents a tempered SGMCMC framework that bridges optimization and unbiased posterior sampling in deep ensembles.
• Experimental results validate improved generalization, uncertainty quantification, and effective handling of the cold posterior effect.

Scalable Bayesian Learning with Posteriors

The paper "Scalable Bayesian Learning with Posteriors" addresses the challenges and methodologies of implementing Bayesian learning in modern machine learning models. The authors introduce several innovations to make Bayesian learning feasible and effective at scale, particularly in contexts with large datasets and high-dimensional parameter spaces.

At the core of this work is the introduction of a PyTorch library, "posteriors," designed to facilitate scalable Bayesian learning. This library offers general-purpose implementations that support large data and parameter regimes, helping to overcome the computational challenges traditionally associated with Bayesian methods.

Key Contributions

1. Posteriors Library: The authors present a PyTorch library called "posteriors," which allows users to perform scalable Bayesian learning. The library hosts a variety of implementations, allowing for extensibility and making Bayesian methods accessible to broader machine learning communities.
2. Tempered Stochastic Gradient MCMC: The paper introduces a tempered framing of Stochastic Gradient Markov Chain Monte Carlo (SGMCMC) that transitions into optimization. This framework reveals a minor modification to deep ensembles, ensuring they are asymptotically unbiased with respect to the Bayesian posterior.
3. Experimental Validation: Through various experimental setups, the paper demonstrates the utility of Bayesian approximations. This includes an exploration of the cold posterior effect and applications to LLMs.

Methodological Insights

The authors discuss several prominent Bayesian learning methods tailored for large-scale problems, all implemented in the posteriors library:

• Laplace Approximation: This method approximates the posterior distribution as a Gaussian centered at the maximum a posteriori (MAP) estimate, with a covariance derived from the Fisher information matrix.
• Variational Inference (VI): VI provides a framework for approximating complex posterior distributions via optimization. A Gaussian approximation is typically utilized, and the optimization seeks to minimize the Kullback-Leibler divergence.
• Stochastic Gradient MCMC (SGMCMC): SGMCMC forms a Monte Carlo approximation of the posterior by evolving stochastic differential equations, benefiting from the scalable computational capabilities of minibatching.

Practical and Theoretical Implications

• Improved Generalization: By leveraging posterior distributions rather than point estimates, Bayesian methods in machine learning enhance generalization and robustness, particularly for out-of-distribution predictions.
• Online Learning: Bayesian frameworks support continuous learning from data streams without substantial retraining, helping mitigate issues like catastrophic forgetting.
• Uncertainty Quantification: Precisely decomposing predictive uncertainty into aleatoric and epistemic components is crucial for understanding model behavior and reliability, making Bayesian approaches valuable for high-stakes applications.

Experimental Results

The experiments highlight the efficacy of Bayesian models, showcasing improved performance over traditional optimization, particularly in capturing uncertainties and adapting to new data. Furthermore, the paper observes the so-called cold posterior effect, particularly prominent in Gaussian approximations, which appears less so in methods like SGMCMC.

Future Directions

The framework and library introduced in this paper open avenues for extensive research into optimization and sampling methods. Posteriors' architecture, which integrates functional programming paradigms, suggests potential for development in second-order optimization techniques and advanced discretization methods.

In summary, this paper delivers a substantial contribution to the field of scalable Bayesian learning through both theoretical insights and practical tools. It provides a robust foundation for further exploration and application in various domains within AI and machine learning.