Related papers: A generalization of the Von Neumann extractor
While variational dropout approaches have been shown to be effective for network sparsification, they are still suboptimal in the sense that they set the dropout rate for each neuron without consideration of the input data. With such…
The problem of random number generation from an uncorrelated random source (of unknown probability distribution) dates back to von Neumann's 1951 work. Elias (1972) generalized von Neumann's scheme and showed how to achieve optimal…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
Probabilistic artificial neural networks offer intriguing prospects for enabling the uncertainty of artificial intelligence methods to be described explicitly in their function; however, the development of techniques that quantify…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
We propose a novel modular debiasing technique applicable to any discrete random source, addressing the fundamental challenge of reliably extracting high-quality randomness from inherently imperfect physical processes. The method involves…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
The binary Euclidean algorithm is a modification of the classical Euclidean algorithm for computation of greatest common divisors which avoids ordinary integer division in favour of division by powers of two only. The expectation of the…
Recently, a classical algorithm for estimating the normalized Betti number of an arbitrary simplicial complex was proposed. Motivated by a quantum algorithm with a similar Monte Carlo structure and improved sample complexity, we give a more…
The von Neumann algorithm is a simple coordinate-descent algorithm to determine whether the origin belongs to a polytope generated by a finite set of points. When the origin is in the of the polytope, the algorithm generates a sequence of…
Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
Pruning the weights of randomly initialized neural networks plays an important role in the context of lottery ticket hypothesis. Ramanujan et al. (2020) empirically showed that only pruning the weights can achieve remarkable performance…
We describe a novel way to represent the probability distribution of a random binary string as a mixture having a maximally weighted component associated with independent (though not necessarily identically distributed) Bernoulli…
A method for generating random $U(1)$ variables with Boltzmann distribution is presented. It is based on the rejection method with transformation of variables. High efficiency is achieved for all range of temparatures or coupling…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
The paper considers implementations of some randomized algorithms in connection with obtaining a random $n^2 \times n^2$ Sudoku matrix with programming language C++. For this purpose we describes the set $\Pi_n$ of all $(2n) \times n$…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…