Related papers: On the Probability Distribution of Superimposed Ra…
We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…
Probability distribution modeling is the basis for most competitive methods for lossless coding of screen content. One such state-of-the-art method is known as soft context formation (SCF). For each pixel to be encoded, a probability…
Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random…
Quantitative research relies heavily on coding, and coding errors are relatively common even in published research. In this paper, we examine whether individuals are more or less likely to check their code depending on the results they…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical…
We study the probability distribution of the number of common zeros of a system of $m$ random $n$-variate polynomials over a finite commutative ring $R$. We compute the expected number of common zeros of a system of polynomials over $R$.…
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size $m$. In particular, the size of the sample is allowed to be…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
This paper presents a new supervised representation learning framework, namely structured probabilistic coding (SPC), to learn compact and informative representations from input related to the target task. SPC is an encoder-only…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…