相关论文: The expected bit complexity of the von Neumann rej…

The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…

We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…

We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$, where $n$ is…

We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea, which seems to be missing in the literature, is a simple scheme to…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman--Pearson…

In 1952, von Neumann gave a series of groundbreaking lectures that proved it was possible for circuits consisting of 3-input majority gates that have a sufficiently small independent probability $\delta > 0$ of malfunctioning to reliably…

The Monte Carlo algorithm is increasingly utilized, with its central step involving computer-based random sampling from stochastic models. While both Markov Chain Monte Carlo (MCMC) and Reject Monte Carlo serve as sampling methods, the…

When deploying classifiers in the real world, users expect them to respond to inputs appropriately. However, traditional classifiers are not equipped to handle inputs which lie far from the distribution they were trained on. Malicious…

If you cancel out the digit 6 from the ratio 16/64, you get the right answer by the wrong method. In 1979 R.P. Boas made an extensive study of such "anomalous cancellations" and generated many examples, in many bases. We continue his…

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…

Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…

Sequential techniques can enhance the efficiency of the approximate Bayesian computation algorithm, as in Sisson et al.'s (2007) partial rejection control version. While this method is based upon the theoretical works of Del Moral et al.…

We present a new family of model selection algorithms based on the resampling heuristics. It can be used in several frameworks, do not require any knowledge about the unknown law of the data, and may be seen as a generalization of local…

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…

We present a variational inference (VI) framework that unifies and leverages sequential Monte-Carlo (particle filtering) with \emph{approximate} rejection sampling to construct a flexible family of variational distributions. Furthermore, we…

Brakerski et. al [BCM+18] introduced the model of cryptographic testing of a single untrusted quantum device and gave a protocol for certifiable randomness generation. We use the leakage resilience properties of the Learning With Errors…

In classification with a reject option, the classifier is allowed in uncertain cases to abstain from prediction. The classical cost-based model of a reject option classifier requires the cost of rejection to be defined explicitly. An…

The adaptive rejection sampling (ARS) algorithm is a universal random generator for drawing samples efficiently from a univariate log-concave target probability density function (pdf). ARS generates independent samples from the target via…

We study convergence and convergence rates for resampling schemes. Our first main result is a general consistency theorem based on the notion of negative association, which is applied to establish the almost-sure weak convergence of…