Related papers: Measuring Association on Topological Spaces Using …
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation…
The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…
In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Quantum measurements often exhibit non-classical features, such as contextuality, which generalizes Bell's non-locality and serves as a resource in various quantum computation models. Existing frameworks have rigorously captured these…
In statistics cumulants are defined to be functions that measure the linear independence of random variables. In the non-communicative case the Boolean cumulants can be described as functions that measure deviation of a map between algebras…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
This paper investigates the use of nonparametric kernel-regression to obtain a tasksimilarity aware meta-learning algorithm. Our hypothesis is that the use of tasksimilarity helps meta-learning when the available tasks are limited and may…
We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space of probability…
Dette, Siburg, and Stoimenov (2013) introduced a copula-based measure of dependence, which implies independence if it vanishes and is equal to 1 if one variable is a measurable function of the other. For continuous distributions, the…
We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and…
We extend the classical Mercer theorem to reproducing kernel Hilbert spaces whose elements are functions from a measurable space $X$into $\mathbb C^n$. Given a finite measure $\mu$ on $X$, we represent the reproducing kernel $K$ as…
We propose the use of non-parametric, graph-based tests to assess the distributional balance of covariates in observational studies with multi-valued treatments. Our tests utilize graph structures ranging from Hamiltonian paths that connect…
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…