Related papers: On dimension reduction in conditional dependence m…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
Randomized experiments on a network often involve interference between connected units; i.e., a situation in which an individual's treatment can affect the response of another individual. Current approaches to deal with interference, in…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is…
Causal effect moderation investigates how the effect of interventions (or treatments) on outcome variables changes based on observed characteristics of individuals, known as potential effect moderators. With advances in data collection,…
Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…
Conditional independence plays a foundational role in database theory, probability theory, information theory, and graphical models. In databases, conditional independence appears in database normalization and is known as the (embedded)…
Assuming some regression model, it is common to study the conditional distribution of survival given covariates. Here, we consider the impact of further conditioning, specifically conditioning on a marginal survival function, known or…
We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…
Unsupervised domain adaptation studies how to transfer a learner from a labeled source domain to an unlabeled target domain with different distributions. Existing methods mainly focus on matching the marginal distributions of the source and…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
We propose a semiparametric model to study the effect of covariates on the distribution of a censored event time while making minimal assumptions about the censoring mechanism. The result is a partially identified model, in the sense that…
We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
A common concern when trying to draw causal inferences from observational data is that the measured covariates are insufficiently rich to account for all sources of confounding. In practice, many of the covariates may only be proxies of the…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
Testing the simplifying assumption in high-dimensional vine copulas is a difficult task. Tests must be based on estimated observations and check constraints on high-dimensional distributions. So far, corresponding tests have been limited to…
Modern recording techniques enable neuroscientists to simultaneously study neural activity across large populations of neurons, with capturing predictor-dependent correlations being a fundamental challenge in neuroscience. Moreover, the…