Related papers: Maximum-of-Differences Test for Comparing Multivar…
In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the…
Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the…
In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…
The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the…
Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
The inaccuracy of neural network models on inputs that do not stem from the training data distribution is both problematic and at times unrecognized. Model uncertainty estimation can address this issue, where uncertainty estimates are often…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
Nonparametric two-sample tests such as the Maximum Mean Discrepancy (MMD) are often used to detect differences between two distributions in machine learning applications. However, the majority of existing literature assumes that error-free…
Maximum Mean Discrepancy (MMD) is widely used in a number of domain adaptation (DA) methods and shows its effectiveness in aligning data distributions across domains. However, in previous DA research, MMD-based DA methods focus mostly on…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…
This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study…
Comparing the top $k$ elements between two or more ranked results is a common task in many contexts and settings. A few measures have been proposed to compare top $k$ lists with attractive mathematical properties, but they face a number of…
This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion…
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…