Related papers: Randomness extraction in computability theory

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

We present a rejection method based on recursive covering of the probability density function with equal tiles. The concept works for any probability density function that is pointwise computable or representable by tabular data. By the…

In 1952, von Neumann introduced the rejection method for random variate generation. We revisit this algorithm when we have a source of perfect bits at our disposal. In this random bit model, there are universal lower bounds for generating a…

Despite their growing capabilities, language models still frequently reproduce content from their training data, generate repetitive text, and favor common grammatical patterns and vocabulary. A possible cause is the decoding strategy: the…

We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute expected convergence rates with respect to any arbitrary a…

Fair Machine Learning endeavors to prevent unfairness arising in the context of machine learning applications embedded in society. Despite the variety of definitions of fairness and proposed "fair algorithms", there remain unresolved…

Rejection sampling is a popular method used to generate numbers that follow some given distribution. We study the use of this method to generate random numbers in the unit interval from increasing probability density functions. We focus on…

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…

This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…

Connections between relations in relation extraction, which we call class ties, are common. In distantly supervised scenario, one entity tuple may have multiple relation facts. Exploiting class ties between relations of one entity tuple…

We study the problem of extracting a prescribed number of random bits by reading the smallest possible number of symbols from non-ideal stochastic processes. The related interval algorithm proposed by Han and Hoshi has asymptotically…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical…

A device-independent randomness expansion protocol aims to take an initial random string and generate a longer one, where the security of the protocol does not rely on knowing the inner workings of the devices used to run it. In order to do…

The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…

The Poisson-sampling technique eliminates dependencies among symbol appearances in a random sequence. It has been used to simplify the analysis and strengthen the performance guarantees of randomized algorithms. Applying this method to…

In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…

In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

Long samples of text from neural language models can be of poor quality. Truncation sampling algorithms--like top-$p$ or top-$k$ -- address this by setting some words' probabilities to zero at each step. This work provides framing for the…