Related papers: Pseudorandomness, symmetry, smoothing: I

In this article, we investigate posterior convergence in nonparametric regression models where the unknown regression function is modeled by some appropriate stochastic process. In this regard, we consider two setups. The first setup is…

In hypothesis testing problems the property of strict unbiasedness describes whether a test is able to discriminate, in the sense of a difference in power, between any distribution in the null hypothesis space and any distribution in the…

Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…

Learning algorithms that divide the data into batches are prevalent in many machine-learning applications, typically offering useful trade-offs between computational efficiency and performance. In this paper, we examine the benefits of…

Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models.…

The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a…

Following Fisher, it is widely believed that randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed." In particular, it is said to control for known and unknown…

By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolutely continuous univariate distributions. Instead of trying…

We prove new probabilistic upper bounds on generalization error of complex classifiers that are combinations of simple classifiers. Such combinations could be implemented by neural networks or by voting methods of combining the classifiers,…

We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the…

Diffusion models that can generate high-quality data from randomly sampled Gaussian noises have become the mainstream generative method in both academia and industry. Are randomly sampled Gaussian noises equally good for diffusion models?…

Randomized rumor spreading is a classical protocol to disseminate information across a network. At SODA 2008, a quasirandom version of this protocol was proposed and competitive bounds for its run-time were proven. This prompts the…

We prove that every randomized Boolean function admits a supersimulator: a randomized polynomial-size circuit whose output on random inputs cannot be efficiently distinguished from reality with constant advantage, even by polynomially…

A boson sampling device is a specialised quantum computer that solves a problem which is strongly believed to be computationally hard for classical computers. Recently a number of small-scale implementations have been reported, all based on…

Boosting and other ensemble methods combine a large number of weak classifiers through weighted voting to produce stronger predictive models. To explain the successful performance of boosting algorithms, Schapire et al. (1998) showed that…

Distributed computing models typically assume reliable communication between processors. While such assumptions often hold for engineered networks, e.g., due to underlying error correction protocols, their relevance to biological systems,…

We consider the Bayesian analysis of a few complex, high-dimensional models and show that intuitive priors, which are not tailored to the fine details of the model and the estimated parameters, produce estimators which perform poorly in…

This paper studies binary classification in robust one-bit compressed sensing with adversarial errors. It is assumed that the model is overparameterized and that the parameter of interest is effectively sparse. AdaBoost is considered, and,…