Related papers: Algorithmic randomness for Doob's martingale conve…
Determinantal Point Processes (DPPs) are a family of probabilistic models that have a repulsive behavior, and lend themselves naturally to many tasks in machine learning where returning a diverse set of objects is important. While there are…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model…
Confidence sequences, anytime p-values (called p-processes in this paper), and e-processes all enable sequential inference for composite and nonparametric classes of distributions at arbitrary stopping times. Examining the literature, one…
Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are…
Mostof the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong…
A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of…
In this paper we are concerned with backward stochastic differential equations with random default time and their applications to default risk. The equations are driven by Brownian motion as well as a mutually independent martingale…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
Randomness in the sense of Martin-L\"of can be defined in terms of lower semicomputable supermartingales. We show that such a supermartingale cannot be replaced by a pair of supermartingales that bet only on the even bits (the first one)…
Algorithmic \emph{replicability} has recently been introduced to address the need for reproducible experiments in machine learning. A \emph{replicable online learning} algorithm is one that takes the same sequence of decisions across…
In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the Schr\"oder and the B\"ottcher case. These results are…
Importance sampling algorithms for heavy-tailed random walks are considered. Using a specification with algorithms based on mixtures of the original distribution with some other distribution, sufficient conditions for obtaining bounded…
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…
We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients through sampling from the variational distribution. This algorithm divides the problem of…
We propose an adaptive independent Metropolis--Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis--Hastings algorithm.…
We say that a random integer variable $X$ is monotone if the modulus of the characteristic function of $X$ is decreasing on $[0,\pi]$. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random…
This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and…