Related papers: The expected bit complexity of the von Neumann rej…
In relative entropy coding, a sender aims to design a stochastic code such that, on input $X \sim P_X$, the receiver can generate a sample $Y \sim P_{Y \mid X}$. It is a standard result that (1) this requires at least $I(X; Y)$ bits, (2)…
This article introduces new algorithms for the uniform random generation of labelled planar graphs. Its principles rely on Boltzmann samplers, as recently developed by Duchon, Flajolet, Louchard, and Schaeffer. It combines the Boltzmann…
We show how to generate random derangements efficiently by two different techniques: random restricted transpositions and sequential importance sampling. The algorithm employing restricted transpositions can also be used to generate random…
We consider a multi-stage distributed detection scenario, where $n$ sensors and a fusion center (FC) are deployed to accomplish a binary hypothesis test. At each time stage, local sensors generate binary messages, assumed to be spatially…
In his seminal 1923 work, Neyman studied the variance estimation problem for the difference-in-means estimator of the average treatment effect in completely randomized experiments. He proposed a variance estimator that is conservative in…
The toss of a coin is usually regarded as the epitome of randomness, and has been used for ages as a means to resolve disputes in a simple, fair way. Perhaps as ancient as consulting objects such as coins and dice is the art of maliciously…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
We consider a problem of replication of random vectors by ordinary integrals in the setting when a underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral…
In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. This algorithm is very similar to the standard method for generating a random permutation, but is less well…
To improve accuracy and speed of regressions and classifications, we present a data-based prediction method, Random Bits Regression (RBR). This method first generates a large number of random binary intermediate/derived features based on…
Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and have recently emerged using optics based physical systems. Here we examine the inverse problem…
We investigate the problem of regression where one is allowed to abstain from predicting. We refer to this framework as regression with reject option as an extension of classification with reject option. In this context, we focus on the…
We continue the study of restricted Monte Carlo algorithms in a general setting. Here we show a lower bound for minimal errors in the setting with finite restriction in terms of deterministic minimal errors. This generalizes a result of…
In this article, we propose a new counter-based implementation of John von Neumann's middle-square random number generator (RNG). Several rounds of squaring are applied to a counter to produce a random output. We discovered that four rounds…
We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training objective function. Our algorithm is…
We study in limit law the complexity of some anticipated rejection random sampling algorithms. We express this complexity in terms of a probabilistic process, the threshold sum process. We show that, under the right conditions, the…
Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…
Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
Sampling from circular distributions is a fundamental task in directional statistics. A key challenge in acceptance-rejection methods lies in selecting an efficient envelope density, as poor choices can lead to low acceptance rates and…