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We introduce a Bayesian framework for mixed-type multivariate regression using continuous shrinkage priors. Our framework enables joint analysis of mixed continuous and discrete outcomes and facilitates variable selection from the $p$…
We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…
Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report…
A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its…
Considered here are robust subgroup-classifier learning and testing in change-plane regressions with heavy-tailed errors, which can identify subgroups as a basis for making optimal recommendations for individualized treatment. A new…
Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
Heavy-tailed stochastic gradient noise, commonly observed in transformer models, can destabilize the optimization process. Recent works mainly focus on developing and understanding approaches to address heavy-tailed noise in the centralized…
Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…
We address the problem of dynamic variable selection in time series regression with unknown residual variances, where the set of active predictors is allowed to evolve over time. To capture time-varying variable selection uncertainty, we…
Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with…
We introduce a new method of Bayesian wavelet shrinkage for reconstructing a signal when we observe a noisy version. Rather than making the common assumption that the wavelet coefficients of the signal are independent, we allow for the…
In this paper, we consider Bayesian variable selection problem of linear regression model with global-local shrinkage priors on the regression coefficients. We propose a variable selection procedure that select a variable if the ratio of…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Financial time series often exhibit skewness and heavy tails, making it essential to use models that incorporate these characteristics to ensure greater reliability in the results. Furthermore, allowing temporal variation in the skewness…
Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at…
We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…