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The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Optimization of high-dimensional black-box functions is an extremely challenging problem. While Bayesian optimization has emerged as a popular approach for optimizing black-box functions, its applicability has been limited to…
Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probability that the output belongs to a specific region remains…
Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…
Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…
This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…
Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…
We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
The set of nonnegative integer lattice points in a polytope, also known as the fiber of a linear map, makes an appearance in several applications including optimization and statistics. We address the problem of sampling from this set using…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
In deep active learning, it is especially important to choose multiple examples to markup at each step to work efficiently, especially on large datasets. At the same time, existing solutions to this problem in the Bayesian setup, such as…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…