Related papers: Variable-Length Intrinsic Randomness Allowing Posi…

We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…

In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…

The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the `most representative' or `most relevant' variables. However,…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…

We suggest generalized robustness for quantifying nonlocality and derive its equivalence to the maximum violation ratio of Bell inequalities defined as vectors with non-negative elements. We investigate its properties by comparing it with…

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were…

We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in…

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. The control…

Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g.,…

Given two vectors in Euclidean space, how unlikely is it that a random vector has a larger inner product with the shorter vector than with the longer one? When the random vector has independent, identically distributed components, we…

In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…

We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This distance, inspired by optimal transport, facilitates stability results; one can quantify how seriously issues like sampling bias,…

The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This…

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs…

This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…

We establish the first known upper bound on the exact and Wyner's common information of $n$ continuous random variables in terms of the dual total correlation between them (which is a generalization of mutual information). In particular, we…

Let $(\{1,2,\ldots,n\},d)$ be a metric space. We analyze the expected value and the variance of $\sum_{i=1}^{\lfloor n/2\rfloor}\,d({\boldsymbol{\pi}}(2i-1),{\boldsymbol{\pi}}(2i))$ for a uniformly random permutation ${\boldsymbol{\pi}}$ of…