Related papers: The Bayesian Analysis of Complex, High-Dimensional…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
Variants of fluctuation theorems recently discovered in the statistical mechanics of non-equilibrium processes may be used for the efficient determination of high-dimensional integrals as typically occurring in Bayesian data analysis. In…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…
Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…
Simultaneously achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Non-local priors (NLPs) possess appealing properties for high-dimensional model choice, but their use for estimation has not…
The usefulness of Bayesian models for density and cluster estimation is well established across multiple literatures. However, there is still a known tension between the use of simpler, more interpretable models and more flexible, complex…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Deep neural networks have been successful in diverse discriminative classification tasks, although, they are poorly calibrated often assigning high probability to misclassified predictions. Potential consequences could lead to…