Related papers: On The Memory Complexity of Uniformity Testing

Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error…

In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…

In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…

We consider a broad class of permutation invariant statistical problems by extending the standard decision theoretic definition to allow also selective inference tasks, where the target is specified only after seeing the data. For any such…

In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $n$ items among which $k$ are defective, the…

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

We consider the best-choice problem for independent (not necessarily iid) observations $X_1, \cdots, X_n$ with the aim of selecting the sample minimum. We show that in this full generality the monotone case of optimal stopping holds and the…

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…

We study pure exploration with infinitely many bandit arms generated i.i.d. from an unknown distribution. Our goal is to efficiently select a single high quality arm whose average reward is, with probability $1-\delta$, within $\varepsilon$…

Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…

Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…

We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…

The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…

The problem of distributed testing against independence with variable-length coding is considered when the \emph{average} and not the \emph{maximum} communication load is constrained as in previous works. The paper characterizes the optimum…

This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we…

We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…

The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing…