Related papers: Information Theory with Kernel Methods
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
It is often said that control and estimation problems are in duality. Recently, in (Aubin-Frankowski,2021), we found new reproducing kernels in Linear-Quadratic optimal control by focusing on the Hilbert space of controlled trajectories,…
Motivated by the engineering applications of uncertainty quantification, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science,…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
Commonly observed patterns typically follow a few distinct families of probability distributions. Over one hundred years ago, Karl Pearson provided a systematic derivation and classification of the common continuous distributions. His…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
Relations among von Neumann entropies of different parts of an $N$-partite quantum system have direct impact on our understanding of diverse situations ranging from spin systems to quantum coding theory and black holes. Best formulated in…
In this work we use the extremization method of various information-theoretic measures (Fisher information, Shannon entropy, Tsallis entropy) for $d$-dimensional quantum systems, which complementary describe the spreading of the quantum…
Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows…
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…