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In this paper we investigate the asymptotic distribution of likelihood ratio tests in models with several groups, when the number of groups converges with the dimension and sample size to infinity. We derive central limit theorems for the…
Density-based clustering methods often surpass centroid-based counterparts, when addressing data with noise or arbitrary data distributions common in real-world problems. In this study, we reveal a key property intrinsic to density-based…
In the computational study of political redistricting, feasibility necessitates the use of a discretization of regions such as states, counties, and towns. In nearly all cases, researchers use a dual graph, whose vertices represent small…
Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single…
Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that…
Clustering algorithms start with a fixed divergence, which captures the possibly asymmetric distance between a sample and a centroid. In the mixture model setting, the sample distribution plays the same role. When all attributes have the…
Denote by $A$ the adjacency matrix of an Erdos-Renyi graph with bounded average degree. We consider the problem of maximizing $\langle A-E\{A\},X\rangle$ over the set of positive semidefinite matrices $X$ with diagonal entries $X_{ii}=1$.…
We show that scale-adjusted versions of the centroid-based classifier enjoys optimal properties when used to discriminate between two very high-dimensional populations where the principal differences are in location. The scale adjustment…
Credal partitions in the framework of belief functions can give us a better understanding of the analyzed data set. In order to find credal community structure in graph data sets, in this paper, we propose a novel evidential community…
Compressive sensing (CS) has attracted significant attention in parameter estimation tasks, where parametric dictionaries (PDs) collect signal observations for a sampling of the parameter space and yield sparse representations for signals…
Approximate spectral clustering (ASC) was developed to overcome heavy computational demands of spectral clustering (SC). It maintains SC ability in predicting non-convex clusters. Since it involves a preprocessing step, ASC defines new…
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…
This paper introduces two new families of non-parametric tests of goodness-of-fit on the compact classical groups. One of them is a family of tests for the eigenvalue distribution induced by the uniform distribution, which is consistent…
This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of…
Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…
In nonadaptive combinatorial group testing (CGT), it is desirable to identify a small set of up to $d$ defectives from a large population of $n$ items with as few tests (i.e. large rate) and efficient identifying algorithm as possible. In…
Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…
We propose a non-parametric method to cluster mixed data containing both continuous and discrete random variables. The product space of continuous and categorical sample spaces is approximated locally by analyzing neighborhoods with cluster…
In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence…