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We tackle the problem of multiscale regression for predictors that are spatially or temporally indexed, or with a pre-specified multiscale structure, with a Bayesian modular approach. The regression function at the finest scale is expressed…

This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest -- means, variances, and other moments of the random…

Explainable boosting machines (EBMs) are popular "glass-box" models that learn a set of univariate functions using boosting trees. These achieve explainability through visualizations of each feature's effect. However, unlike linear model…

We introduce a new shrinkage variable selection operator for linear models which we term the \emph{adaptive ridge selector} (ARiS). This approach is inspired by the \emph{relevance vector machine} (RVM), which uses a Bayesian hierarchical…

This work studies an information-theoretic performance limit of an integrated sensing and communication (ISAC) system where the goal of sensing is to estimate a random continuous state. Considering the mean-squared error (MSE) for…

This paper focuses on linear regression models with non-conjugate sparsity-inducing regularizers such as lasso and group lasso. Although the empirical Bayes approach enables us to estimate the regularization parameter, little is known on…

It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. We show how, in a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure…

Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator…

In real-world sampling of k-space data, one generally makes a stochastic error not only in the value of the sample but in the effective position of the drawn sample. We refer to the latter as imprecise sampling and apply this concept to the…

We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference in Bayesian statistical models represented by probabilistic programs. Given a model and a sample-approximated…

We consider a Bayesian approach to model selection in Gaussian linear regression, where the number of predictors might be much larger than the number of observations. From a frequentist view, the proposed procedure results in the penalized…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

In recent years, Ising prior with the network information for the "in" or "out" binary random variable in Bayesian variable selections has received more and more attentions. In this paper, we discover that even without the informative prior…

We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…

Inverse reinforcement learning (IRL) attempts to infer human rewards or preferences from observed behavior. Since human planning systematically deviates from rationality, several approaches have been tried to account for specific human…

Bayesian additive regression trees (BART) are popular Bayesian ensemble models used in regression and classification analysis. Under this modeling framework, the regression function is approximated by an ensemble of decision trees,…

Data-driven individualized decision making has recently received increasing research interests. Most existing methods rely on the assumption of no unmeasured confounding, which unfortunately cannot be ensured in practice especially in…

Regression calibration as developed by Rosner, Spiegelman and Willet is used to correct the bias in effect estimates due to measurement error in continuous exposures. The method involves two models: a measurement error model (MEM) relating…

Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…