Related papers: Testing relevant difference in high-dimensional li…
We consider testing the significance of a subset of covariates in a nonparametric regression. These covariates can be continuous and/or discrete. We propose a new kernel-based test that smoothes only over the covariates appearing under the…
This paper investigates testing for deviation of a high-dimensional mean vector $\boldsymbol{\mu}$. In contrast to the standard one-sample significance test of the form: $H_0^\texttt{e} : \boldsymbol{\mu} = \boldsymbol{\mu}_0$ versus…
Transfer learning across heterogeneous data distributions (a.k.a. domains) and distinct tasks is a more general and challenging problem than conventional transfer learning, where either domains or tasks are assumed to be the same. While…
In this article, we propose a class of $L_q$-norm based U-statistics for a family of global testing problems related to high-dimensional data. This includes testing of mean vector and its spatial sign, simultaneous testing of linear model…
In networks of independent entities that face similar predictive tasks, transfer machine learning enables to re-use and improve neural nets using distributed data sets without the exposure of raw data. As the number of data sets in business…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
The problem of learning one task using samples from another task is central to transfer learning. In this paper, we focus on answering the following question: when does combining the samples from two related tasks perform better than…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
Domain adaptation (DA) aims to transfer knowledge learned from a labeled source domain to an unlabeled or a less labeled but related target domain. Ideally, the source and target distributions should be aligned to each other equally to…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
We propose a new measure of variable importance in high-dimensional regression based on the change in the LASSO solution path when one covariate is left out. The proposed procedure provides a novel way to calculate variable importance and…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
This paper focuses on the problem of testing the null hypothesis that the regression functions of several populations are equal under a general nonparametric homoscedastic regression model. It is well known that linear kernel regression…
Motivated by the problem of detecting a change in the evolution of a network, we consider the preferential attachment random graph model with a time-dependent attachment function. Our goal is to detect whether the attachment mechanism…
We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…
Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs are graphs, sets, and point clouds. Recent work on graph…
It is well known that nonparametric regression estimation and inference procedures are subject to the curse of dimensionality. Moreover, model interpretability usually decreases with the data dimension. Therefore, model-free variable…
Development of comprehensive prediction models are often of great interest in many disciplines of science, but datasets with information on all desired features often have small sample sizes. We describe a transfer learning approach for…
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more…