Related papers: Chain rules for one-shot entropic quantities via o…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation…
We develop an information-theoretic framework for bounding the supremum of stochastic processes, offering a simpler and sharper alternative to classical chaining and slicing arguments for generalization bounds. The key idea is a lifting…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
Data mining techniques offer great opportunities for developing ethics lines, tools for communication, participation and innovation whose main aim is to ensure improvements and compliance with the values, conduct and commitments making up…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
We introduce two new concepts designed for the study of empirical processes. First, we introduce a new Orlicz norm which we call the Bernstein-Orlicz norm. This new norm interpolates sub-Gaussian and sub-exponential tail behavior. In…
We derive upper and lower bounds on the overall compression ratio of the 1978 Lempel-Ziv (LZ78) algorithm, applied independently to $k$-blocks of a finite individual sequence. Both bounds are given in terms of normalized empirical entropies…
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…
We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a…
A general approach is established for deriving one-shot performance bounds for information-theoretic problems on general alphabets beyond countable alphabets. It is mainly based on the quantization idea and a novel form of "likelihood…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
We propose a new approach to apply the chaining technique in conjunction with information-theoretic measures to bound the generalization error of machine learning algorithms. Different from the deterministic chaining approach based on…
We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential…
We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched R\'{e}nyi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version,…
In Hall's reformulation of the uncertainty principle, the entropic uncertainty relation occupies a core position and provides the first nontrivial bound for the information exclusion principle. Based upon recent developments on the…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…