相关论文: Gaussian model selection with an unknown variance

Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

Penalized regression has become a standard tool for model building across a wide range of application domains. Common practice is to tune the amount of penalization to tradeoff bias and variance or to optimize some other measure of…

Most classification models can be considered as the process of matching templates. However, when intra-class uncertainty/variability is not considered, especially for datasets containing unbalanced classes, this may lead to classification…

We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…

Estimating the causal effect of a treatment or health policy with observational data can be challenging due to an imbalance of and a lack of overlap between treated and control covariate distributions. In the presence of limited overlap,…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…

In the context of high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where the penalty…

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…

We consider a simulation-based Ranking and Selection (R&S) problem with input uncertainty, where unknown input distributions can be estimated using input data arriving in batches of varying sizes over time. Each time a batch arrives,…

We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be…

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact…

We present a deterministic method to compute the Gaussian average of neural networks used in regression and classification. Our method is based on an equivalence between training with a particular regularized loss, and the expected values…

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…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric causal framework for identification and learning with…

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or…