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We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we…
In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta>0$) by replacing the entries equal to one by…
We consider the ensemble of $N\times N$ ($N\gg 1$) symmetric random matrices with the bimodal independent distribution of matrix elements: each element could be either "1" with the probability $p$, or "0" otherwise. We pay attention to the…
The class of norm-dependent Random Matrix Ensembles is studied in the presence of an external field. The probability density in those ensembles depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact…
For many practical, high-risk applications, it is essential to quantify uncertainty in a model's predictions to avoid costly mistakes. While predictive uncertainty is widely studied for neural networks, the topic seems to be under-explored…
A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…
Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two…
We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the…
We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary…
Machine learning-based Deepfake detection models have achieved impressive results on benchmark datasets, yet their performance often deteriorates significantly when evaluated on out-of-distribution data. In this work, we investigate an…
Ensembles improve prediction performance and allow uncertainty quantification by aggregating predictions from multiple models. In deep ensembling, the individual models are usually black box neural networks, or recently, partially…
Despite deep neural network (DNN)'s impressive prediction performance in various domains, it is well known now that a set of DNN models trained with the same model specification and the same data can produce very different prediction…
The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work \cite{EYY} under certain conditions on the probability distributions of the matrix elements. A major class of…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute…
We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…
Ensemble models can be used to estimate prediction uncertainties in machine learning models. However, an ensemble of N models is approximately N times more computationally demanding compared to a single model when it is used for inference.…