Related papers: Problems of robustness for universal coding scheme…
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\sigma$-models. We find that the algorithm in which we update the embedded Ising model \`a la Swendsen-Wang has critical slowing-down as $z_\chi \approx 1$. If instead…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
Universally achievable error exponents pertaining to certain families of channels (most notably, discrete memoryless channels (DMC's)), and various ensembles of random codes, are studied by combining the competitive minimax approach,…
Distributional assumptions have been shown to be necessary for the robust learnability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019). In this paper, we study…
We study the long-term behavior of the iteration of a random map consisting of Lipschitz transformations on a compact metric space, independently and randomly selected according to a fixed probability measure. Such a random map is said to…
Self-testing is a phenomenon where the use of specific quantum states or measurements can be inferred solely from the correlations they generate. We introduce a universal method for conducting robustness analysis in the self-testing of…
We introduce a universal quantization scheme based on random coding, and we analyze its performance. This scheme consists of a source-independent random codebook (typically_mismatched_ to the source distribution), followed by optimal…
We present a framework facilitating the implementation and comparison of text compression algorithms. We evaluate its features by a case study on two novel compression algorithms based on the Lempel-Ziv compression schemes that perform well…
This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
Algorithmic robust statistics has traditionally focused on the contamination model where a small fraction of the samples are arbitrarily corrupted. We consider a recent contamination model that combines two kinds of corruptions: (i) small…
We continue the study of statistical/computational tradeoffs in learning robust classifiers, following the recent work of Bubeck, Lee, Price and Razenshteyn who showed examples of classification tasks where (a) an efficient robust…
The genetic code has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimisation problem as a Quadratic…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing…
We analyze the robustness of optimally controlled evolution equations with respect to spatially localized perturbations. We prove that if the involved operators are domain-uniformly stabilizable and detectable, then these localized…
When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is…
We address the problem of computing reliable policies in reinforcement learning problems with limited data. In particular, we compute policies that achieve good returns with high confidence when deployed. This objective, known as the…
It is well known that lossless compression of a discrete memoryless source with near-uniform encoder output is possible at a rate above its entropy if and only if the encoder is randomized. This work focuses on deriving conditions for…
We provide a novel achievability proof of the Slepian-Wolf theorem for i.i.d. sources over finite alphabets. We demonstrate that random codes that are linear over the real field achieve the classical Slepian-Wolf rate-region. For finite…