Related papers: An Adaptive Test of Independence with Analytic Ker…
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches…
In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…
Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random…
Numerous studies have been devoted to the estimation and inference problems for functional linear models (FLM). However, few works focus on model checking problem that ensures the reliability of results. Limited tests in this area do not…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
In this paper, we investigate the adequacy testing problem of high-dimensional factor-augmented regression model. Existing test procedures perform not well under dense alternatives. To address this critical issue, we introduce a novel…
Given a database and a target attribute of interest, how can we tell whether there exists a functional, or approximately functional dependence of the target on any set of other attributes in the data? How can we reliably, without bias to…
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
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…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
We introduce a notion called entropic independence that is an entropic analog of spectral notions of high-dimensional expansion. Informally, entropic independence of a background distribution $\mu$ on $k$-sized subsets of a ground set of…
We propose a new adaptive hypothesis test for inequality (e.g., monotonicity, convexity) and equality (e.g., parametric, semiparametric) restrictions on a structural function in a nonparametric instrumental variables (NPIV) model. Our test…
We consider the problem of uniformity testing of Lipschitz continuous distributions with bounded support. The alternative hypothesis is a composite set of Lipschitz continuous distributions that are at least $\varepsilon$ away in $\ell_1$…