Sam Power

Rocco Caprio, Adrien Corenflos, Sam Power

We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results are general and sharp, allow for local convergence guarantees, hold for general smooth manifolds, and also in some non-smooth spaces. We consider applications to Bayesian Gaussian Mixture Models, and high-dimensional Bayesian Probit Regression, and Logistic Regression with Pólya-Gamma random variables (i.e. Jaakkola-Jordan's algorithm).

Bruno Mlodozeniec, Isaac Reid, Sam Power et al.

Randomness is an unavoidable part of training deep learning models, yet something that traditional training data attribution algorithms fail to rigorously account for. They ignore the fact that, due to stochasticity in the initialisation and batching, training on the same dataset can yield different models. In this paper, we address this shortcoming through introducing distributional training data attribution (d-TDA), the goal of which is to predict how the distribution of model outputs (over training runs) depends upon the dataset. Intriguingly, we find that influence functions (IFs), a popular data attribution tool, are 'secretly distributional': they emerge from our framework as the limit to unrolled differentiation, without requiring restrictive convexity assumptions. This provides a new perspective on the effectiveness of IFs in deep learning. We demonstrate the practical utility of d-TDA in experiments, including improving data pruning for vision transformers and identifying influential examples with diffusion models.

Christophe Andrieu, Anthony Lee, Sam Power et al.

We investigate the use of a certain class of functional inequalities known as weak Poincaré inequalities to bound convergence of Markov chains to equilibrium. We show that this enables the straightforward and transparent derivation of subgeometric convergence bounds for methods such as the Independent Metropolis--Hastings sampler and pseudo-marginal methods for intractable likelihoods, the latter being subgeometric in many practical settings. These results rely on novel quantitative comparison theorems between Markov chains. Associated proofs are simpler than those relying on drift/minorization conditions and the tools developed allow us to recover and further extend known results as particular cases. We are then able to provide new insights into the practical use of pseudo-marginal algorithms, analyse the effect of averaging in Approximate Bayesian Computation (ABC) and the use of products of independent averages, and also to study the case of lognormal weights relevant to particle marginal Metropolis--Hastings (PMMH).