Related papers: Distance and Kernel-Based Measures for Global and …
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
The predominant method for evaluating the quality of causal models is to measure the graphical accuracy of the learned model structure. We present an alternative method for evaluating causal models that directly measures the accuracy of…
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…
Kernel-based testing has revolutionized the field of non-parametric tests through the embedding of distributions in an RKHS. This strategy has proven to be powerful and flexible, yet its applicability has been limited to the standard…
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…
Sampling in control applications is increasingly done non-equidistantly in time. This includes applications in motion control, networked control, resource-aware control, and event-based control. Some of these applications, like the ones…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
We introduce a broadly applicable statistical procedure for testing which parametric distribution family generated a random sample of data. The method, termed the Difference in Differential Entropy (DDE) test, provides a unified framework…
We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of…
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…
Nonparametric detection of existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a…
Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity…
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic…
In this paper, we address the problem of two-sample testing in the presence of missing data under a variety of missingness mechanisms. Our focus is on the well-known energy distance-based two-sample test. In addition to the standard…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…