相关论文: A remark on unified error exponents: Hypothesis te…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
With time, machine learning models have increased in their scope, functionality and size. Consequently, the increased functionality and size of such models requires high-end hardware to both train and provide inference after the fact. This…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…
We propose a new type of effective densities via the potential distribution theorem. These densities are for the sake of enabling the mapping of the free energy of a uniform fluid onto that of a nonuniform fluid. The potential distribution…
The concentration of measure phenomena were discovered as the mathematical background of statistical mechanics at the end of the XIX - beginning of the XX century and were then explored in mathematics of the XX-XXI centuries. At the…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…
A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a…
Let $X_1,X_2, \ldots $ be independent random uniform points in a bounded domain $A \subset \mathbb{R}^d$ with smooth boundary. Define the coverage threshold $R_n$ to be the smallest $r$ such that $A$ is covered by the balls of radius $r$…
Classifications organize entities into categories that identify similarities within a category and discern dissimilarities among categories, and they powerfully classify information in support of analysis. We propose a new classification…
The min-entropy is a widely used metric to quantify the randomness of generated random numbers in cryptographic applications; it measures the difficulty of guessing the most likely output. An important min-entropy estimator is the…
Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…
We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…
A detection system with a single sensor and $\mathsf{K}$ detectors is considered, where each of the terminals observes a memoryless source sequence and the sensor sends a common message to all the detectors. The communication of this…
A subset $B$ of the ring $\mathbb{Z}_n$ is referred to as a $\ell$-covering set if $\{ ab \pmod n | 0\leq a \leq \ell, b\in B\} = \mathbb{Z}_n$. We show that there exists a $\ell$-covering set of $\mathbb{Z}_n$ of size $O(\frac{n}{\ell}\log…
We revisit the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
We consider the problem of covering multiple submodular constraints. Given a finite ground set $N$, a cost function $c: N \rightarrow \mathbb{R}_+$, $r$ monotone submodular functions $f_1,f_2,\ldots,f_r$ over $N$ and requirements…
This paper demonstrates how new principles of compressed sensing, namely asymptotic incoherence, asymptotic sparsity and multilevel sampling, can be utilised to better understand underlying phenomena in practical compressed sensing and…
We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…