Related papers: Bayesian adaptation
Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance. We derive minimax optimal rules for confidence-rated prediction in this setting. By using PAC-Bayes analysis on…
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Independence-based (IB) assignments to Bayesian belief networks were originally proposed as abductive explanations. IB assignments assign fewer variables in abductive explanations than do schemes assigning values to all evidentially…
Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…
We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to…
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…
We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…
This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
Adaptation is used by biological sensory systems to respond to a wide range of environmental signals, by adapting their response properties to the statistics of the stimulus in order to maximize information transmission. We derive rules of…
We propose a fast and theoretically grounded method for Bayesian variable selection and model averaging in latent variable regression models. Our framework addresses three interrelated challenges: (i) intractable marginal likelihoods, (ii)…
It has become increasingly common to collect high-dimensional binary response data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…