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We introduce a new statistical quantity the energy to test whether two samples originate from the same distributions. The energy is a simple logarithmic function of the distances of the observations in the variate space. The distribution of…
For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…
Neuron-level firing data is believed to be governed by latent activation patterns during task completion. Analysing repeated trials of a task allows us to study these patterns, typically by averaging in-vivo neural spikes across trials.…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here,…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
Due to their parsimony, separable covariance models have been popular in modeling matrix-variate data. However, the inference from such a model may be misleading if the population covariance matrix $\Sigma$ is actually non-separable,…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Evaluating whether data streams are drawn from the same distribution is at the heart of various machine learning problems. This is particularly relevant for data generated by dynamical systems since such systems are essential for many…
Pearson's Chi-squared test, though widely used for detecting association between categorical variables, exhibits low statistical power in large sparse contingency tables. To address this limitation, two novel permutation tests have been…
We derive and study a significance test for determining if a panel of functional time series is separable. In the context of this paper, separability means that the covariance structure factors into the product of two functions, one…
The problem of sparse linear regression is relevant in the context of linear system identification from large datasets. When data are collected from real-world experiments, measurements are always affected by perturbations or low-precision…
The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…
The problem of testing equality of the entire second order structure of two independent functional linear processes is considered. A fully functional $L^2$-type test is developed which evaluates, over all frequencies, the Hilbert-Schmidt…