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…
Let $X$ be an integrable real random variable with mean zero and two-sided sub-Gaussian tail $\mathbb{P}(|X|>t)\le 2e^{-t^{2}/2}$ for all $t\ge 0$. We determine the smallest constant $c_\star$ such that $X$ is dominated in convex order by…
Markov Chain Monte Carlo (MCMC) is a flexible approach to approximate sampling from intractable probability distributions, with a rich theoretical foundation and comprising a wealth of exemplar algorithms. While the qualitative correctness…
We study the Multiple-try Metropolis algorithm using the framework of Poincar\'e inequalities. We describe the Multiple-try Metropolis as an auxiliary variable implementation of a resampling approximation to an ideal Metropolis--Hastings…
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…
Using the framework of weak Poincar\'e inequalities, we provide a general comparison between Hybrid and Ideal Slice Sampling in terms of their corresponding Dirichlet forms. In particular, under suitable assumptions Hybrid Slice Sampling…
We present a new method for proving the norm concentration inequality of sub-Gaussian variables. Our proof is based on an averaged version of the moment generating function, termed the averaged moment generating function. Our method applies…
Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…
Piecewise-Deterministic Markov Processes (PDMPs) hold significant promise for sampling from complex probability distributions. However, their practical implementation is hindered by the need to compute model-specific bounds. Conversely,…
We derive the first explicit bounds for the spectral gap of a random walk Metropolis algorithm on $R^d$ for any value of the proposal variance, which when scaled appropriately recovers the correct $d^{-1}$ dependence on dimension for…
We investigate the use of a certain class of functional inequalities known as weak Poincar\'e inequalities to bound convergence of Markov chains to equilibrium. We show that this enables the straightforward and transparent derivation of…
We investigate the application of Weak Poincar\'e Inequalities (WPI) to Markov chains to study their rates of convergence and to derive complexity bounds. At a theoretical level we investigate the necessity of the existence of WPIs to…
Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes…
We develop a theory of weak Poincar\'e inequalities to characterize convergence rates of ergodic Markov chains. Motivated by the application of Markov chains in the context of algorithms, we develop a relevant set of tools which enable the…
Markov chain Monte Carlo (MCMC) is a key algorithm in computational statistics, and as datasets grow larger and models grow more complex, many popular MCMC algorithms become too computationally expensive to be practical. Recent progress has…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…