Related papers: On randomness reduction in the Johnson-Lindenstrau…
Allen-Zhu, Gelashvili, Micali, and Shavit construct a sparse, sign-consistent Johnson-Lindenstrauss distribution, and prove that this distribution yields an essentially optimal dimension for the correct choice of sparsity. However, their…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
The paper is devoted to the study of a parametric deformation model of independent and identically random variables. Firstly, we construct an efficient and very easy to compute recursive estimate of the parameter. Our stochastic estimator…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
Randomness is one of the important key concepts of statistics. In epidemiology or medical science, we investigate our hypotheses and interpret results through this statistical randomness. We hypothesized by imposing some conditions to this…
In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel…
A randomized misfit approach is presented for the efficient solution of large-scale PDE-constrained inverse problems with high-dimensional data. The purpose of this paper is to offer a theory-based framework for random projections in this…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
Sums of of 1-dependent integer-valued random variables are approximated by compound Poisson, negative binomial and Binomial distributions and signed compound Poisson measures. Estimates are obtained for total variation and local metrics.…
This is an invitation to the probabilistic approach for constructing K\"ahler-Einstein metrics on complex projective algebraic manifolds X. The metrics in question emerge in the large N-limit from a canonical way of sampling N points on X,…
A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear…
This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate result in spite of its simple form.…
Balancing covariates is critical for credible and efficient randomized experiments. Rerandomization addresses this by repeatedly generating treatment assignments until covariate balance meets a prespecified threshold. By shrinking this…
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second.…