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We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…
Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically,…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many…
Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This paper discusses a theoretical…
Rank aggregation systems collect ordinal preferences from individuals to produce a global ranking that represents the social preference. Rank-breaking is a common practice to reduce the computational complexity of learning the global…
In this paper we investigate how a typical, large-dimensional representation looks for a complex Lie algebra. In particular, we study the family $\mathfrak{sl}_{r+1}(\mathbb{C})$ of Lie algebras for $r \geq 2$ and derive asymptotic…
In a novel approach to the multiple testing problem, Efron (2004; 2007) formulated estimators of the distribution of test statistics or nominal p-values under a null distribution suitable for modeling the data of thousands of unaffected…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
Let $f(x)$ be an irreducible polynomial with integer coefficients of degree at least two. Hooley proved that the roots of the congruence equation $f(x)\equiv 0\mod n$ is uniformly distributed. as a parallel of Hooley's theorem under ideal…
We associate a real distribution to any complex Lie algebroid that we call distribution of real elements and a new invariant that we call real rank, given by the pointwise rank of this distribution. When the real rank is constant, we obtain…
We extend the algorithms of Robinson, Smyth, and McKee--Smyth to enumerate all real-rooted integer polynomials of a fixed degree, where the first few (at least three) leading coefficients are specified. Additionally, we introduce new linear…
The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…
Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…