Related papers: A Bayesian Stochastic Approximation Method
In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and…
Gaussian process (GP) based Bayesian optimization (BO) is a powerful method for optimizing black-box functions efficiently. The practical performance and theoretical guarantees of this approach depend on having the correct GP hyperparameter…
We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…
High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by…
Stochastic approximation Monte Carlo (SAMC) has recently been proposed by Liang, Liu and Carroll [J. Amer. Statist. Assoc. 102 (2007) 305--320] as a general simulation and optimization algorithm. In this paper, we propose to improve its…
The paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic H\"older class estimator. Next applying…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…
Ordinal categorical data are routinely encountered in many practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the…
We consider Bayesian linear regression with sparsity-inducing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically…
Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy…
We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…
In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in…
Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…