Related papers: Variable Selection Consistency of Gaussian Process…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
There has been an intense development on the estimation of a sparse regression coefficient vector in statistics, machine learning and related fields. In this paper, we focus on the Bayesian approach to this problem, where sparsity is…
Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive…
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new…
We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and…
Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…
We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
This paper studies large sample properties of a Bayesian approach to inference about slope parameters $\gamma$ in linear regression models with a structural break. In contrast to the conventional approach to inference about $\gamma$ that…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results addressing these problems over a fixed…
In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist.…
The Na\"ive Mean Field (NMF) approximation is widely employed in modern Machine Learning due to the huge computational gains it bestows on the statistician. Despite its popularity in practice, theoretical guarantees for high-dimensional…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary gaussian noise having unknown correlation function. A general model selection procedure on the basis of…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…