Related papers: On the Classification and Algorithmic Analysis of …
Generalized Cullen Numbers are positive integers of the form $C_b(n):=nb^n+1$. In this work we generalize some known divisibility properties of Cullen Numbers and present two primality tests for this family of integers. The first test is…
In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
Multiple Instance Learning (MIL) is a weakly-supervised problem in which one label is assigned to the whole bag of instances. An important class of MIL models is instance-based, where we first classify instances and then aggregate those…
In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resort to trial division by a few initial prime numbers, since such a division take less time. How far we should go with such a division is…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Negative Binomial regression is a staple in Operations Management empirical research. Most of its analytical aspects are considered either self-evident, or minutiae that are better left to specialised textbooks. But what if the evidence…
We introduce CriticSMC, a new algorithm for planning as inference built from a composition of sequential Monte Carlo with learned Soft-Q function heuristic factors. These heuristic factors, obtained from parametric approximations of the…
We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…
Fix coprime natural numbers $a,q$. Assuming the Prime $k$-tuple Conjecture, we show that there exist arbitrarily long arithmetic progressions of Carmichael numbers, each of which lies in the reduced residue class $a$ mod $q$ and is a…
A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further. Both the formalism and proof are presented in a much more…
In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results. The results have been classified (and referred to) as…
At present one can not find a single counterexample to even a simplest version of Frobenius primality test. The assessment of probability of the mistake, presented in [I.B. Damgard and G.S.Frandsen, Journal of Cryptology, 2006] is strongly…
Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…
Positivity is one of the three conditions for causal inference from observational data. The standard way to validate positivity is to analyze the distribution of propensity. However, to democratize the ability to do causal inference by…
Random Number Generators play a critical role in a number of important applications. In practice, statistical testing is employed to gather evidence that a generator indeed produces numbers that appear to be random. In this paper, we…
We determine the number of statistically significant factors in a forecast model using a random matrices test. The applied forecast model is of the type of Reduced Rank Regression (RRR), in particular, we chose a flavor which can be seen as…