Related papers: On randomized step sizes in Metropolis-Hastings al…
We consider the minimization of a sum of an expectation-valued coordinate-wise $L_i$-smooth nonconvex function and a nonsmooth block-separable convex regularizer. We propose an asynchronous variance-reduced algorithm, where in each…
The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…
Although the Metropolis algorithm is simple to implement, it often has difficulties exploring multimodal distributions. We propose the repelling-attracting Metropolis (RAM) algorithm that maintains the simple-to-implement nature of the…
Doubly intractable models are encountered in a number of fields, e.g. social networks, ecology and epidemiology. Inference for such models requires the evaluation of a likelihood function, whose normalising factor depends on the model…
We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov…
The Metropolis-Hastings algorithm is a cornerstone of Markov Chain Monte Carlo methods, underpinning a wide range of applications in computational physics, Bayesian inference, and machine learning. Quantum variants of Metropolis-Hastings…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
In continual learning, a learner has to keep learning from the data over its whole life time. A key issue is to decide what knowledge to keep and what knowledge to let go. In a neural network, this can be implemented by using a step-size…
We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a…
The choice of the stepsize in first-order convex optimization is typically based on the smoothness constant and plays a crucial role in the performance of algorithms. Recently, there has been a resurgent interest in introducing adaptive…
Integer linear programming (ILP) remains computationally challenging due to its NP-complete nature despite its central role in scheduling, logistics, and design optimization. We introduce a fully quantum Metropolis-Hastings algorithm for…
One main limitation of the existing optimal scaling results for Metropolis--Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis…
Markov chain Monte Carlo methods have become popular in statistics as versatile techniques to sample from complicated probability distributions. In this work, we propose a method to parameterize and train transition kernels of Markov chains…
We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…
We analyze the learning properties of the stochastic gradient method when multiple passes over the data and mini-batches are allowed. We study how regularization properties are controlled by the step-size, the number of passes and the…
Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…
The Random Walk Metropolis (RWM) algorithm is a Metropolis- Hastings MCMC algorithm designed to sample from a given target distribution \pi with Lebesgue density on R^N. RWM constructs a Markov chain by randomly proposing a new position…
In this article we propose multiplication based random walk Metropolis Hastings (MH) algorithm on the real line. We call it the random dive MH (RDMH) algorithm. This algorithm, even if simple to apply, was not studied earlier in Markov…