Related papers: On high-dimensional modifications of some graph-ba…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…
In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…
In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…
Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…
We propose a two-sample test for covariance matrices in the high-dimensional regime, where the dimension diverges proportionally to the sample size. Our hybrid test combines a Frobenius-norm-based statistic as considered in Li and Chen…
This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…
Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular,…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…
Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance,…
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
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…
Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…
We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…