Related papers: Fast Bayesian Feature Selection for High Dimension…

Identifying small subsets of features that are relevant for prediction and/or classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult,…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection…

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…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…

Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…

Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking…

The problem of selecting the most useful features from a great many (eg, thousands) of candidates arises in many areas of modern sciences. An interesting problem from genomic research is that, from thousands of genes that are active…

Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…

In this paper, we propose a probabilistic model for computing an interpolative decomposition (ID) in which each column of the observed matrix has its own priority or importance, so that the end result of the decomposition finds a set of…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…

Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…