Related papers: Construction of Benford Random Variables: Generato…
In the context of software testing, generating complex data inputs is frequently performed using a grammar-based specification. For combinatorial reasons, an exhaustive generation of the data -- of a given size -- is practically impossible,…
We study the natural question of constructing pseudorandom generators (PRGs) for low-degree polynomial threshold functions (PTFs). We give a PRG with seed-length log n/eps^{O(d)} fooling degree d PTFs with error at most eps. Previously, no…
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…
Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…
Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $2^n$, equals 1 not 10% or 11% of the time, as one would expect if all digits were equally likely, but about 30% of the time. This…
Benford's law describes a common phenomenon among many naturally occurring data sets and distributions in which the leading digits of the data are distributed with the probability of a first digit of $d$ base $B$ being…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or…
We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and…
Under ideal conditions, the probability density function (PDF) of a random variable, such as a sensor measurement, would be well known and amenable to computation and communication tasks. However, this is often not the case, so the user…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Distance distributions are a key building block in stochastic geometry modelling of wireless networks and in many other fields in mathematics and science. In this paper, we propose a novel framework for analytically computing the closed…
Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…
While the problem of estimating a probability density function (pdf) from its observations is classical, the estimation under additional shape constraints is both important and challenging. We introduce an efficient, geometric approach for…
We develop uniformly fast random variate generators for the Pearson IV distribution that can be used over the entire range of both shape parameters and highlight some applications in a Bayesian setting.
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…