Related papers: A generalization of the Von Neumann extractor
Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…
We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a $0-1$…
We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
Sampling complex free energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a…
A universal generator for integer-valued square-integrable random variables is introduced. The generator relies on a rejection technique based on a generalization of the inversion formula for integer-valued random variables. The proposal…
Suppose that we are given an infinite binary sequence which is random for a Bernoulli measure of parameter $p$. By the law of large numbers, the frequency of zeros in the sequence tends to~$p$, and thus we can get better and better…
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges…
Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…
It is shown that a random binary process with impulse-like autocorrelation can be generated by randomizing the length of symbols occurring in a random Bernoulli process. Such randomization is achieved by random (or judiciously designed…
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…
Several approximate inference methods have been proposed for deep discrete latent variable models. However, non-parametric methods which have previously been successfully employed for classical sparse coding models have largely been…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
We study a general class of nonlinear iterative algorithms which includes power iteration, belief propagation and approximate message passing, and many forms of gradient descent. When the input is a random matrix with i.i.d. entries, we use…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…