Massively Parallel Expectation Maximization For Approximate Posteriors

Bayesian inference for hierarchical models can be very challenging. MCMC methods have difficulty scaling to large models with many observations and latent variables. While variational inference (VI) and reweighted wake-sleep (RWS) can be more scalable, they are gradient-based methods and so often require many iterations to converge. Our key insight was that modern massively parallel importance weighting methods (Bowyer et al., 2024) give fast and accurate posterior moment estimates, and we can use these moment estimates to rapidly learn an approximate posterior. Specifically, we propose using expectation maximization to fit the approximate posterior, which we call QEM. The expectation step involves computing the posterior moments using high-quality massively parallel estimates from Bowyer et al. (2024). The maximization step involves fitting the approximate posterior using these moments, which can be done straightforwardly for simple approximate posteriors such as Gaussian, Gamma, Beta, Dirichlet, Binomial, Multinomial, Categorical, etc. (or combinations thereof). We show that QEM is faster than state-of-the-art, massively parallel variants of RWS and VI, and is invariant to reparameterizations of the model that dramatically slow down gradient based methods.

Position: Don't use the CLT in LLM evals with fewer than a few hundred datapoints

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .