Related papers: Sparse Bayesian Partially Identified Models for Se…

In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…

Large-scale modern data often involves estimation and testing for high-dimensional unknown parameters. It is desirable to identify the sparse signals, ``the needles in the haystack'', with accuracy and false discovery control. However, the…

We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…

We consider the Sparse Principal Component Analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a Mixed Integer Program (MIP) and can be solved to global…

We consider a joint processing of $n$ independent sparse regression problems. Each is based on a sample $(y_{i1},x_{i1})...,(y_{im},x_{im})$ of $m$ \iid observations from $y_{i1}=x_{i1}\t\beta_i+\eps_{i1}$, $y_{i1}\in \R$, $x_{i 1}\in\R^p$,…

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to…

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…

We describe the Bedside Patient Rescue (BPR) project, the goal of which is risk prediction of adverse events for non-ICU patients using ~200 variables (vitals, lab results, assessments, ...). There are several missing predictor values for…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

We consider the problem of providing valid inference for a selected parameter in a sparse regression setting. It is well known that classical regression tools can be unreliable in this context due to the bias generated in the selection…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct…

This paper describes the use of flexible Bayesian regression models for estimating a partially identified probability function. Our approach permits efficient sensitivity analysis concerning the posterior impact of priors on the partially…

Sparse methods are the standard approach to obtain interpretable models with high prediction accuracy. Alternatively, algorithmic ensemble methods can achieve higher prediction accuracy at the cost of loss of interpretability. However, the…

We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than $\approx 1%$, of the variance of the target variables. To facilitate the prediction of the…

Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data. Specifically, PPI methods provide tighter confidence intervals by combining small amounts of human-labeled data with…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…