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Incorporating information about the target distribution in proposal mechanisms generally produces efficient Markov chain Monte Carlo algorithms (or at least, algorithms that are more efficient than uninformed counterparts). For instance, it…

In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

The objective of unsupervised graph representation learning (GRL) is to learn a low-dimensional space of node embeddings that reflect the structure of a given unlabeled graph. Existing algorithms for this task rely on negative sampling…

Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…

We consider a variant of inexact Newton Method, called Newton-MR, in which the least-squares sub-problems are solved approximately using Minimum Residual method. By construction, Newton-MR can be readily applied for unconstrained…

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for…

Feature engineering plays an important role in the success of a machine learning model. Most of the effort in training a model goes into data preparation and choosing the right representation. In this paper, we propose a robust feature…

The Metropolis algorithm is one of the Markov chain Monte Carlo (MCMC) methods that realize sampling from the target probability distribution. In this paper, we are concerned with the sampling from the distribution in non-identifiable cases…

Node classification using Graph Neural Networks (GNNs) has been widely applied in various practical scenarios, such as predicting user interests and detecting communities in social networks. However, recent studies have shown that…

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…

We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization,…

We introduced the Hug and Hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels: Hug and Hop. Hug is a non-reversible kernel that…

Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

The present paper focuses on the problem of sampling from a given target distribution $\pi$ defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an…

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering insights toward a more comprehensive NN understanding. Exhaustive enumeration or traditional…

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…

There is emerging evidence that trust-region (TR) algorithms are very effective at solving derivative-free nonconvex stochastic optimization problems in which the objective function is a Monte Carlo (MC) estimate. A recent strand of…