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The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…
Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…
Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for…
In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…
We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…
Estimation and inference of treatment effects under unconfounded treatment assignments often suffer from bias and the `curse of dimensionality' due to the nonparametric estimation of nuisance parameters for high-dimensional confounders.…
We consider the topic of multivariate regression on manifold-valued output, that is, for a multivariate observation, its output response lies on a manifold. Moreover, we propose a new regression model to deal with the presence of grossly…
Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…
The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor…
The package High-dimensional Metrics (\Rpackage{hdm}) is an evolving collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on providing confidence…
Cluster-weighted modeling (CWM) is a mixture approach for modeling the joint probability of a response variable and a set of explanatory variables. The parameters are estimated by means of the expectation-maximization algorithm according to…
Many important computer vision applications are naturally formulated as regression problems. Within medical imaging, accurate regression models have the potential to automate various tasks, helping to lower costs and improve patient…
Many pre-trained models (PTMs) are available in modern applications. Because different PTMs are often trained on different datasets, their performances can vary substantially for different new tasks, and the ranking of the candidates may…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of…
Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of…
We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well-known to suffer…
In chemical processing and bioprocessing, conventional online sensors are limited to measure only basic process variables like pressure and temperature, pH, dissolved O and CO$_2$ and viable cell density (VCD). The concentration of other…
Meta-regression models are commonly used to synthesize and compare effect sizes. Unfortunately, traditional meta-regression methods are ill-equipped to handle the complex and often unknown correlations among non-independent effect sizes.…
Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…