Related papers: A Generalized Poor-Verdu Error Bound for Multihypo…

Given an observed random variable, consider the problem of recovering its distribution among a family of candidate ones. The two-point inequality, Fano's lemma and more recently an inequality due to Venkataramanan and Johnson (2018) allow…

We prove the first margin-based generalization bound for voting classifiers, that is asymptotically tight in the tradeoff between the size of the hypothesis set, the margin, the fraction of training points with the given margin, the number…

We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…

In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…

Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…

This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…

This paper focuses on the analysis of average Gaussian error probabilities in certain fading channels, i.e. we are interested in E[Q((p {\gamma})^(1/2))] where Q(.) is the Gaussian Q-function, p is a positive real number and {\gamma} is a…

The $\gamma$-FDP and $k$-FWER multiple testing error metrics, which are tail probabilities of the respective error statistics, have become popular recently as less-stringent alternatives to the FDR and FWER. We propose general and flexible…

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

The reliability function of memoryless channels with noiseless feedback and variable-length coding has been found to be a linear function of the average rate in the classic work of Burnashev. In this work we consider unifilar channels with…

We consider the problem of modulation and estimation of a random parameter $U$ to be conveyed across a discrete memoryless channel. Upper and lower bounds are derived for the best achievable exponential decay rate of a general moment of the…

A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…

Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…

We consider a linear multi-hop network composed of multi-state discrete-time memoryless channels over each hop, with orthogonal time-sharing across hops under a half-duplex relaying protocol. We analyze the probability of error and…

We extend a low-rate improvement of the random coding bound on the reliability of a classical discrete memoryless channel to its quantum counterpart. The key observation that we make is that the problem of bounding below the error exponent…

In this paper we obtain a lower bound of exponent of average probability of error for classical quantum multiple access channel, which implies that for all rate pairs in the capacity region is achievable by a code with exponential…

This paper employs the add-and-subtract technique of the auxiliary receiver approach to establish a new upper bound for the distributed hypothesis testing problem. This new bound has fewer assumptions than the upper bound proposed by Rahman…

This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper…

We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…

Given finite-dimensional random vectors $Y$, $X$, and $Z$ that form a Markov chain in that order (i.e., $Y \to X \to Z$), we derive upper bounds on the excess minimum risk using generalized information divergence measures. Here, $Y$ is a…