Related papers: Some Comments on the Strong Simplex Conjecture
In this paper, the authors report a way to use concepts from statistical learning to gain an advantage in terms of error exponents while communicating over a discrete memoryless channel. The study utilizes the simulation capability of the…
We consider a statistical problem of detection of a signal with unknown energy in a multi-channel system, observed in a Gaussian noise. We assume that the signal can appear in the $k$-th channel with a known small prior probability…
Over repeat presentations of the same stimulus, sensory neurons show variable responses. This "noise" is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
We present an algorithm for strongly refuting smoothed instances of all Boolean CSPs. The smoothed model is a hybrid between worst and average-case input models, where the input is an arbitrary instance of the CSP with only the negation…
The present manuscript studies signal detection by likelihood ratio tests in a number of spiked random matrix models, including but not limited to Gaussian mixtures and spiked Wishart covariance matrices. We work directly with multi-spiked…
The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with…
Small chemical sensors are subjected to adsorption-desorption fluctuations which usually considered as noise contaminating useful signal. Based on temporal properties of this noise, it is shown that it can be made useful if proper…
Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that,…
Stochastic resonance describes the utility of noise in improving the detectability of weak signals in certain types of systems. It has been observed widely in natural and engineered settings, but its utility in image classification with…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
We report on a particular example of noise and data representation interacting to introduce systematic error. Many instruments collect integer digitized values and appy nonlinear coding, in particular square-root coding, to compress the…
We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information.…
Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for a long-standing conjecture on optimality of Gaussian encondings for the ultimate communication rate of generalized heterodyne…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
We exhibit a linear threshold function in 5 variables with strictly smaller noise stability (for small values of the correlation parameter) than the majority function on 5 variables, thereby providing a counterexample to the "Majority is…
In this paper, we derive several criteria for (weak) synchronization by noise without the global swift transitivity property. Our sufficient conditions for (weak) synchronization are necessary and can be applied to scenarios involving…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
Models that learn spurious correlations from training data often fail when deployed in new environments. While many methods aim to learn invariant representations to address this, they often underperform standard empirical risk minimization…
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to…