Related papers: The Multivariate Covering Lemma and its Converse
A $t-\a$ covering array is an $m\times n$ matrix, with entries from an alphabet of size $\alpha$, such that for any choice of $t$ rows, and any ordered string of $t$ letters of the alphabet, there exists a column such that the "values" of…
Compositional data (i.e., data comprising random variables that sum up to a constant) arises in many applications including microbiome studies, chemical ecology, political science, and experimental designs. Yet when compositional data serve…
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…
Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible.…
Covariate shift, a widely used assumption in tackling {\it distributional shift} (when training and test distributions differ), focuses on scenarios where the distribution of the labels conditioned on the feature vector is the same, but the…
We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…
A single-letter lower bound on the sum rate of multiple description coding with tree-structured distortion constraints is established by generalizing Ozarow's celebrated converse argument through the introduction of auxiliary random…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
We present connections between the recent literature on multigroup fairness for prediction algorithms and classical results in computational complexity. Multiaccurate predictors are correct in expectation on each member of an arbitrary…
A distribution matcher (DM) encodes a binary input data sequence into a sequence of symbols (codeword) with desired target probability distribution. The set of the output codewords constitutes a codebook (or code) of a DM.…
The Littlewood Conjecture in Diophantine approximation can be thought of as a problem about covering the plane by a union of hyperbolas centered at rational points. In this paper we consider the problem of translating the center of each…
In traditional Distributional Semantic Models (DSMs) the multiple senses of a polysemous word are conflated into a single vector space representation. In this work, we propose a DSM that learns multiple distributional representations of a…
In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…
A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of…
Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of…
Although it is widely accepted that `no-broadcasting' -- the nonclonability of quantum information -- is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet…
Colexification refers to the phenomenon of multiple meanings sharing one word in a language. Cross-linguistic lexification patterns have been shown to be largely predictable, as similar concepts are often colexified. We test a recent claim…
We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…
This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution…