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The process of rank aggregation is intimately intertwined with the structure of skew-symmetric matrices. We apply recent advances in the theory and algorithms of matrix completion to skew-symmetric matrices. This combination of ideas…
Consider a random bipartite multigraph $G$ with $n$ left nodes and $m \geq n \geq 2$ right nodes. Each left node $x$ has $d_x \geq 1$ random right neighbors. The average left degree $\Delta$ is fixed, $\Delta \geq 2$. We ask whether for the…
Most implementations of sampling algorithms for continuous distributions use floating-point numbers, which introduce round-off errors and approximations. These errors can be difficult to analyze, and can cause security issues when used in…
In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null)…
The scan statistic is by far the most popular method for anomaly detection, being popular in syndromic surveillance, signal and image processing, and target detection based on sensor networks, among other applications. The use of the scan…
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…
Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Distributed systems have been widely used in practice to accomplish data analysis tasks of huge scales. In this work, we target on the estimation problem of generalized linear models on a distributed system with nonrandomly distributed…
We analytically derive the bit-string probability distributions of subsystems of random pure states and depolarized random states using the Dirichlet distribution. We identify the exact Beta distribution as the universal statistical law of…
In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…
The network data has attracted considerable attention in modern statistics. In research on complex network data, one key issue is finding its underlying connection structure given a network sample. The methods that have been proposed in…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Learning how to aggregate ranking lists has been an active research area for many years and its advances have played a vital role in many applications ranging from bioinformatics to internet commerce. The problem of discerning reliability…
We introduce two abstract theorems that reduce a variety of complex exponential distributional approximation problems to the construction of couplings. These are applied to obtain new rates of convergence with respect to the Wasserstein and…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…
We study global distribution of zeros for a wide range of ensembles of random polynomials. Two main directions are related to almost sure limits of the zero counting measures, and to quantitative results on the expected number of zeros in…