Related papers: A Null Model for Mapper Subtype Claims

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in…

We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…

Tensor-valued data are being encountered increasingly more commonly, in the biological, natural as well as the social sciences. The learning of the unknown model parameter vector given such data, involves covariance modelling of such data,…

We extend Gaussian networks - directed acyclic graphs that encode probabilistic relationships between variables - to its vector form. Vector Gaussian continuous networks consist of composite nodes representing multivariates, that take…

Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for…

Assessing the statistical significance of network patterns is crucial for understanding whether such patterns indicate the presence of interesting network phenomena, or whether they simply result from less interesting processes, such as…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Random graph models with community structure have been studied extensively in the literature. For both the problems of detecting and recovering community structure, an interesting landscape of statistical and computational phase transitions…

Permutation invariant Gaussian matrix models were recently developed for applications in computational linguistics. A 5-parameter family of models was solved. In this paper, we use a representation theoretic approach to solve the general…

Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation. Unlike earlier covariance-based approaches for…

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…

Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…

This study addresses the issue of graph generation with generative models. In particular, we are concerned with graph community augmentation problem, which refers to the problem of generating unseen or unfamiliar graphs with a new community…

The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…

We present the path-sum formulation for exact statistical inference of marginals on Gaussian graphical models of arbitrary topology. The path-sum formulation gives the covariance between each pair of variables as a branched continued…

The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow…

The two-sample test is a fundamental problem in statistics with a wide range of applications. In the realm of high-dimensional data, nonparametric methods have gained prominence due to their flexibility and minimal distributional…