Related papers: On integer partitions and the Wilcoxon rank-sum st…

We study global inference for regression coefficients in high-dimensional linear models under potentially heavy-tailed errors. While sum-type tests are powerful for dense alternatives and max-type tests excel for sparse alternatives,…

We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to…

For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…

The Lloyd Theorem of (Sol\'e, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, NRT metric, mixed Hamming metric, and for the sum-rank…

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form…

In computable analysis testing a real number for being zero is a fundamental example of a non-computable task. This causes problems for division: We cannot ensure that the number we want to divide by is not zero. In many cases, any real…

We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…

The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…

This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes…

We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…

Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is…

We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting that have constant failure rate. In spite of the minimal algebraic structure, there is a…

This paper develops a general framework for conducting inference on the rank of an unknown matrix $\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\mathrm H_0: \mathrm{rank}(\Pi_0)\le r$. The problem is of first…

An important issue raised by Efron in the context of large-scale multiple comparisons is that in many applications the usual assumption that the null distribution is known is incorrect, and seemingly negligible differences in the null may…

For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a…

We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…

The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra. Conventional algorithms for its computation typically rely on matrix-adjoint products, making them sensitive to errors arising from…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction…