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Markov random fields (MRFs) are difficult to evaluate as generative models because computing the test log-probabilities requires the intractable partition function. Annealed importance sampling (AIS) is widely used to estimate MRF partition…
Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…
Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle…
Kernel methods have revolutionized the fields of pattern recognition and machine learning. Their success, however, critically depends on the choice of kernel parameters. Using Gaussian process (GP) classification as a working example, this…
Kernel matrices (e.g. Gram or similarity matrices) are essential for many state-of-the-art approaches to classification, clustering, and dimensionality reduction. For large datasets, the cost of forming and factoring such kernel matrices…
Sampling from multimodal distributions is a central challenge in Bayesian inference and machine learning. In light of hardness results for sampling -- classical MCMC methods, even with tempering, can suffer from exponential mixing times --…
Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
Performing exact Bayesian inference for complex models is computationally intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are expensive for large datasets and…
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…
This paper deals with the Monte-Carlo methods for evaluating expectations of functionals of solutions to McKean-Vlasov Stochastic Differential Equations (MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is approximated…
We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of…
Partially observable Markov decision processes (POMDPs) are a general mathematical model for sequential decision-making in stochastic environments under state uncertainty. POMDPs are often solved \textit{online}, which enables the algorithm…
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…
Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…
We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
Instance selection (IS) addresses the critical challenge of reducing dataset size while keeping informative characteristics, becoming increasingly important as datasets grow to millions of instances. Current IS methods often struggle with…
Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability.…