Related papers: Generalized Ziggurat Algorithm for Unimodal and Un…
Modern instruction-tuned large language models (LLMs) have made remarkable progress in code generation. However, these LLMs fine-tuned with standard supervised fine-tuning (SFT) sometimes generate plausible-looking but functionally…
Let $\mathbf{H}=(h_{ij})$ and $\mathbf{G}=(g_{ij})$ be two $m\times n$, $m\leq n$, random matrices, each with i.i.d complex zero-mean unit-variance Gaussian entries, with correlation between any two elements given by…
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb{P}(\sum_{i=1}^{N}{X_i} \leq \gamma)$, via importance sampling (IS). We…
Backpropagation is the pivotal algorithm underpinning the success of artificial neural networks, yet it has critical limitations such as biologically implausible backward locking and global error propagation. To circumvent these…
High energy physics has a constant demand for random number generators (RNGs) with high statistical quality. In this paper, we present ROOT's implementation of the RANLUX++ generator. We discuss the choice of relying only on standard C++…
In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true…
We consider a channel-independent decoder which is for i.i.d. random codes what the maximum mutual-information decoder is for constant composition codes. We show that this decoder results in exactly the same i.i.d. random coding error…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
A quantum random number generator (QRNG) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics. Most approaches to QRNG employ single-photon detection technologies and are limited in speed. Here, we…
The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. Our aim in this article is to develop software for this distribution for…
We investigate the possibility to detect primordial non-Gaussianity by analysing the bulk of the probability distribution function (PDF) of late-time cosmic density fluctuations. For this purpose we devise a new method to predict the impact…
In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each…
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
We study algorithms for online change-point detection (OCPD), where samples that are potentially heavy-tailed, are presented one at a time and a change in the underlying mean must be detected as early as possible. We present an algorithm…
We propose random hinge forests, a simple, efficient, and novel variant of decision forests. Importantly, random hinge forests can be readily incorporated as a general component within arbitrary computation graphs that are optimized…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
Genome wide association studies directly assay 10^6 single nucleotide polymorphisms (SNPs) across a study cohort. Probabilistic estimation of additional sites by genotype imputation can increase this set of variants by 10- to 40-fold. Even…
In this paper, we propose a numerical method to uniformly handle the random genetic drift model for pure drift with or without natural selection and mutation. For pure drift and natural selection case, the Dirac $\delta$ singularity will…