Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular weak tail domination implies strong tail domination. In particular positive answer to Oleszkiewicz question would follow from the so-called Bernoulli conjecture. Introduction. This note is motivated by the following...

A fast and robust type of unsupervised multispectral texture segmentation method with unknown number of classes is presented. Single decorrelated monospectral texture factors are represented by four local autoregressive random field models recursively evaluated for each pixel and for each spectral band. The segmentation algorithm is based on the underlying Gaussian mixture model and starts with...

We study the recovery of Hermitian low rank matrices X ∈ Cn×n from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form ajaj for some measurement vectors a1, . . . , am, i.e., the measurements are given by yj = tr(Xaja ∗ j ). The case where the matrix X = xx ∗ to...

The mean return time of a discrete Markov chain to a point x is the reciprocal of the invariant probability π(x). We revisit this classical theme to investigate certain exit times for stochastic difference equations of autoregressive type. More specifically, we will discuss the asymptotics, as ε→ 0, of the first time τ that the n-dimensional process Yt = f(Yt−1) + εξt, t = 1, 2, . . . (where ξ1...

It is well known that even slight changes in nonuniform illumination lead to a large image variability and are crucial for many visual tasks. This paper presents a new ICA related probabilistic model where the number of sources exceeds the number of sensors to perform an image segmentation and illumination removal, simultaneously. We model illumination and reflectance in log space by a generali...

Let x1, . . . xn be independent normally distributed vectors on Rd. We determine the distribution function of the minimum norm of the 2n vectors ±x1 ± x2 · · · ± xn.

R. R. Nandy, D. Cordes University of Washington, Seattle, Wa, United States Synopsis The multiple comparison problem has always been a challenging one in fMRI due to the complex nature of spatial dependence among neighboring voxels. A popular conservative solution is the Bonferroni correction which works well when the hypotheses are independent but turns out to be too conservative for fMRI anal...

The “carries” when n random numbers are added base b form a Markov chain with an “amazing” transition matrix determined by Holte [24]. This same Markov chain occurs in following the number of descents or rising sequences when n cards are repeatedly riffle shuffled. We give generating and symmetric function proofs and determine the rate of convergence of this Markov chain to stationarity. Simila...

w e ppose a new algorithm for enhancing noisy speech which have been degraded by statistically independent additive noise. The al p rithm is based upon modeling the clean speech as a hidden Markov process with mixtures of Gaussian autoregressive (AR) output processes, and the noise process as a sequence of stationary, statistically independent, Gaussian AR vectors. The parameter sets of the mod...

This paper addresses the problem of designing binary codes for high-dimensional data such that vectors that are similar in the original space map to similar binary strings. We introduce a simple distribution-free encoding scheme based on random projections, such that the expected Hamming distance between the binary codes of two vectors is related to the value of a shift-invariant kernel (e.g., ...