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For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
In this article, we derive concentration inequalities for the cross-validation estimate of the generalization error for subagged estimators, both for classification and regressor. General loss functions and class of predictors with both…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
An additive noise channel is considered, in which the distribution of the noise is nonparametric and unknown. The problem of learning encoders and decoders based on noise samples is considered. For uncoded communication systems, the problem…
The reliability function of a channel is the maximum achievable exponential rate of decay of the error probability as a function of the transmission rate. In this work, we derive bounds on the reliability function of discrete memoryless…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to $n$ independent and identically distributed samples, denoted by…
We consider the problem of lower bounding the error probability under the invariant causal prediction (ICP) framework. To this end, we examine and draw connections between ICP and the zero-rate Gaussian multiple access channel by first…
New lower and upper bounds on the reliability function of typewriter channels are given. Our lower bounds improve upon the (multiletter) expurgated bound of Gallager, furnishing a new and simple counterexample to a conjecture made in 1967…
A channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson $\beta$ functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verd\'{u} (2014). The new bound…
Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…
A distributed binary hypothesis testing problem, in which multiple observers transmit their observations to a detector over noisy channels, is studied. Given its own side information, the goal of the detector is to decide between two…
In this paper, lower bounds on error probability in coding for discrete classical and classical-quantum channels are studied. The contribution of the paper goes in two main directions: i) extending classical bounds of Shannon, Gallager and…
New upper bounds on the relative entropy are derived as a function of the total variation distance. One bound refines an inequality by Verd\'{u} for general probability measures. A second bound improves the tightness of an inequality by…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
In this work, a new upper bound for average error probability of a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with given input and…
This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n +…