Related papers: Linear Regression, Covariate Selection and the Fai…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
This article discusses D-optimal Bayesian crossover designs for generalized linear models. Crossover trials with t treatments and p periods, for $t <= p$, are considered. The designs proposed in this paper minimize the log determinant of…
In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Evaluating the joint significance of covariates is of fundamental importance in a wide range of applications. To this end, p-values are frequently employed and produced by algorithms that are powered by classical large-sample asymptotic…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
We propose a Bayesian variable selection method in the framework of modal regression for heavy-tailed responses. An efficient expectation-maximization algorithm is employed to expedite parameter estimation. A test statistic is constructed…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
In the high-dimensional regression model a response variable is linearly related to $p$ covariates, but the sample size $n$ is smaller than $p$. We assume that only a small subset of covariates is `active' (i.e., the corresponding…
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…
We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and…
Biased sampling designs can be highly efficient when studying rare (binary) or low variability (continuous) endpoints. We consider longitudinal data settings in which the probability of being sampled depends on a repeatedly measured…
Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a…
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…