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Suppose that two large, multi-dimensional data sets are each noisy measurements of the same underlying random process, and principle components analysis is performed separately on the data sets to reduce their dimensionality. In some…
We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…
Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…
Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most…
We consider a spatial functional linear regression, where a scalar response is related to a square integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to…
Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point…
Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal…
This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression,…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
When randomized ensemble methods such as bagging and random forests are implemented, a basic question arises: Is the ensemble large enough? In particular, the practitioner desires a rigorous guarantee that a given ensemble will perform…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
In our previous work, we designed a systematic policy to prioritize sampling locations to lead significant accuracy improvement in spatial interpolation by using the prediction uncertainty of Gaussian Process Regression (GPR) as "attraction…
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…
We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…
This paper studies estimation of panel cointegration models with cross-sectional dependence generated by unobserved global stochastic trends. The standard least squares estimator is, in general, inconsistent owing to the spuriousness…
A new method for estimation of intragranular strain fields in polycrystalline materials based on scanning three-dimensional X-ray diffraction data (scanning-3DXRD) is presented and evaluated. Given an apriori known anisotropic compliance,…