Related papers: Harmonic analysis of random number generators
This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…
Pseudo-random number generators (PRNGs) are widely used in modern computing and are expected to exhibit excellent statistical performance and repeatability. This study evaluates and compares modern PRNGs used in high performance computing…
The problem of making practical, useful goodness of fit tests in the Bayesian paradigm is largely open. We introduce a class of special cases (testing for uniformity: have the cards been shuffled enough; does my random generator work) and a…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows: 1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\prod_{i=1}^n…
Among the biggest challenges in property-based testing (PBT) is the constrained random generation problem: given a predicate on program values, randomly sample from the set of all values satisfying that predicate, and only those values.…
Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data. Recently, it has been…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
We present a new high-level synthesis methodology for using large language model tools to generate hardware designs. The methodology uses exclusively open-source tools excluding the large language model. As a case study, we use our…
Monte Carlo simulations are an important tool in statistical physics, complex systems science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
We consider the problem of sequential binary hypothesis testing with a distributed sensor network in a non-Gaussian noise environment. To this end, we present a general formulation of the Consensus + Innovations Sequential Probability Ratio…
Interacting urns with exponential reinforcement were introduced and studied in Launay (2011). As its parameter $\rho$ tends to $\iy$, this reinforcement mechanism converges to the "generalized" reinforcement, in which the probability of…
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate…
We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
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…
The paper addresses the problem of designing radar detectors more robust than Kelly's detector to possible mismatches of the assumed target signature, but with no performance degradation under matched conditions. The idea is to model the…