Related papers: Metric Distributional Discrepancy in Metric Space
Machine learning models are increasingly used in practice. However, many machine learning methods are sensitive to test or operational data that is dissimilar to training data. Out-of-distribution (OOD) data is known to increase the…
Large-scale hypothesis testing has become a ubiquitous problem in high-dimensional statistical inference, with broad applications in various scienfitic disciplines. One relevant application is constituted by imaging mass spectrometry (IMS)…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…
The Nested Dirichlet Distribution (NDD) provides a flexible alternative to the Dirichlet distribution for modeling compositional data, relaxing constraints on component variances and correlations through a hierarchical tree structure. While…
Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure…
(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…
We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…
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…
Current advances in next generation sequencing techniques have allowed researchers to conduct comprehensive research on microbiome and human diseases, with recent studies identifying associations between human microbiome and health outcomes…
A new robust pairwise statistic, the pairwise median scaled difference (MSD), is proposed for the detection of anomalous location/uncertainty pairs in heteroscedastic interlaboratory study data with associated uncertainties. The…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
The capability of reliably detecting out-of-distribution samples is one of the key factors in deploying a good classifier, as the test distribution always does not match with the training distribution in most real-world applications. In…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
Randomness or mutual independence is an important underlying assumption for most widely used statistical methods for circular data. Verifying this assumption is essential to ensure the validity and reliability of the resulting inferences.…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
Learning to disentangle and represent factors of variation in data is an important problem in AI. While many advances have been made to learn these representations, it is still unclear how to quantify disentanglement. While several metrics…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$…
The standardized mean difference (SMD) is a widely used measure of effect size, particularly common in psychology, clinical trials, and meta-analysis involving continuous outcomes. Traditionally, under the equal variance assumption, the SMD…