Related papers: Uniform decomposition of probability measures: qua…
This paper continues work begun in \cite{M1}, in which we introduced a theory of Gowers uniformity norms for singular measures on $\mathbb{R}^d$. There, given a $d$-dimensional measure $\mu$, we introduced a $(k+1)d$-dimensional measure…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
We consider the approximation of a convolution of possibly different probability measures by (compound) Poisson distributions and also by related signed measures of higher order. We present new total variation bounds having a better…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
In this paper, we develop an approach for the exact determination of the minimum sample size for the estimation of a Poisson parameter with prescribed margin of error and confidence level. The exact computation is made possible by reducing…
We investigated the asymptotics of high-rate constrained quantization errors for a compactly supported probability measure P on Euclidean spaces whose quantizers are confined to a closed set S. The key tool is the metric projection of K…
This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…
Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for $n$-point subsets of $\ell_p$, for $p >…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…
This paper deals with studying vague convergence of random measures of the form $\mu_{n}=\sum_{i=1}^{n} p_{i,n} \delta_{\theta_i}$, where $(\theta_i)_{1\le i \le n}$ is a sequence of independent and identically distributed random variables…
We consider a sequence of identically independently distributed random samples from an absolutely continuous probability measure in one dimension with unbounded density. We establish a new rate of convergence of the $\infty-$Wasserstein…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
We introduce notions of dimension of an infinite group, or more generally, a metric space, defined using percolation. Roughly speaking, the percolation dimension $pdim(G)$ of a group $G$ is the fastest rate of decay of a symmetric…
Mutually Unbiased bases has various application in quantum information procession and coding theory. There can be maximum d + 1 MUBs in C^d and d/2 +1 MUBs in R^d. But , over R^d MUBs are known to be non existent when d is odd and for most…