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We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
Communication-avoiding algorithms allow redundant computations to minimize the number of inter-process communications. In this paper, we propose to exploit this redundancy for fault-tolerance purpose. We illustrate this idea with QR…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
In this article we perform an asymptotic analysis of Bayesian parallel kernel density estimators introduced by Neiswanger, Wang and Xing (2014). We derive the asymptotic expansion of the mean integrated squared error for the full data…
We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few non-zero binary digits.
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…
We apply a flexible numerical integrator to the simulation of adiabatic quantum computation with nonlinear paths. We find that a nonlinear path may significantly improve the performance of adiabatic algorithms versus the conventional…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…
The storage and computation requirements of Convolutional Neural Networks (CNNs) can be prohibitive for exploiting these models over low-power or embedded devices. This paper reduces the computational complexity of the CNNs by minimizing an…
We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graph ${\bf G}(N,p)$. For $N^{-1+o(1)}\leq p\leq 1/2$, we show that the non-trivial edge eigenvectors are asymptotically jointly normal.…
We propose a strategy for modeling the behavior of an adiabatic quantum computer described by an Ising Hamiltonian with $N$ sites and the coordination number $Z$. The method is based on the $1/Z$ expansion for the density matrix of the…
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming…
When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…
We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a…
This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability…
We present a quantitative basis-independent analysis of combinatory logic. Using a general argument regarding plane binary trees with labelled leaves, we generalise the results of David et al. and Bendkowski et al. to all Turing-complete…