Related papers: Optimal upper bounds on expected kth record values…
In this paper, our aim is to analyse the generalization capabilities of first-order methods for statistical learning in multiple, different yet related, scenarios including supervised learning, transfer learning, robust learning and…
We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…
In this note, we show that the relative entropy of an empirical distribution of $n$ samples drawn from a set of size $k$ with respect to the true underlying distribution is exponentially concentrated around its expectation, with central…
We provide estimates on the fat-shattering dimension of aggregation rules of real-valued function classes. The latter consists of all ways of choosing $k$ functions, one from each of the $k$ classes, and computing a pointwise function of…
In this work, we develop upper bounds for key rates for device-independent quantum key distribution (DI-QKD) protocols and devices. We study the reduced cc-squashed entanglement and show that it is a convex functional. As a result, we show…
This paper develops an optimal Chernoff type bound for the probabilities of large deviations of sums $\sum_{k=1}^n f (X_k)$ where $f$ is a real-valued function and $(X_k)_{k \in \mathbb{Z}_{\ge 0}}$ is a finite state Markov chain with an…
This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
The information spectrum approach gives general formulae for optimal rates of codes in many areas of information theory. In this paper the quantum spectral divergence rates are defined and properties of the rates are derived. The entropic…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper proposes an easy-to-compute upper bound for the overlap index between two probability distributions without requiring any knowledge of the distribution models. The computation of our bound is time-efficient and memory-efficient…
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…
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…
We consider the problem of randomly choosing the sensors of a linear time-invariant dynamical system subject to process and measurement noise. We sample the sensors independently and from the same distribution. We measure the performance of…