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Factor analysis models explain dependence among observed variables by a smaller number of unobserved factors. A main challenge in confirmatory factor analysis is determining whether the factor loading matrix is identifiable from the…
This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a…
Defect lines in conformal field theory can be perturbed by chiral defect fields. If the unperturbed defects satisfy su(2)-type fusion rules, the operators associated to the perturbed defects are shown to obey functional relations known from…
A fine tuned hierarchy between a strongly coupled high energy compositeness scale and a much lower chiral symmetry breaking scale is a requisite ingredient in many models of dynamical electroweak symmetry breaking. Using a nonperturbative…
Survival analysis is an important problem in healthcare because it models the relationship between an individual's covariates and the onset time of an event of interest (e.g., death). It is important for survival models to be…
In this paper we formally analyse the use of sparse filtering algorithms to perform covariate shift adaptation. We provide a theoretical analysis of sparse filtering by evaluating the conditions required to perform covariate shift…
Confounding bias, missing data, and selection bias are three common obstacles to valid causal inference in the data sciences. Covariate adjustment is the most pervasive technique for recovering casual effects from confounding bias. In this…
We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and…
In causal matching designs, some control subjects are often left unmatched, and some covariates are often left unmodeled. This article introduces "rebar," a method using high-dimensional modeling to incorporate these commonly discarded data…
Where the response variable in a big data set is consistent with the variable of interest for small area estimation, the big data by itself can provide the estimates for small areas. These estimates are often subject to the coverage and…
Deep neural networks have been shown to learn and rely on spurious correlations present in the data that they are trained on. Reliance on such correlations can cause these networks to malfunction when deployed in the real world, where these…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Compositional data arise in many areas of research in the natural and biomedical sciences. One prominent example is in the study of the human gut microbiome, where one can measure the relative abundance of many distinct microorganisms in a…
Local variable selection aims to test for the effect of covariates on an outcome within specific regions. We outline a challenge that arises in the presence of non-linear effects and model misspecification. Specifically, for common…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
Accurately modeling the correlation structure of errors is critical for reliable uncertainty quantification in probabilistic time series forecasting. While recent deep learning models for multivariate time series have developed efficient…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background…
The correlated Wishart model provides a standard tool for the analysis of correlations in a rich variety of systems. Although much is known for complex correlation matrices, the empirically much more important real case still poses…
Asynchronous trading in high-frequency financial markets introduces significant biases into econometric analysis, distorting risk estimates and leading to suboptimal portfolio decisions. Existing synchronization methods, such as the…