Related papers: Range (R\'enyi) Entropy Queries and Partitioning

We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…

Semisupervised text classification has become a major focus of research over the past few years. Hitherto, most of the research has been based on supervised learning, but its main drawback is the unavailability of labeled data samples in…

We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a…

Sample selection improves the efficiency and effectiveness of machine learning models by providing informative and representative samples. Typically, samples can be modeled as a sample graph, where nodes are samples and edges represent…

The efficient generation of random quantum states is a long-standing challenge, motivated by their diverse applications in quantum information processing tasks. In this work, we identify entanglement as the key resource that enables local…

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…

We leverage the Gibbs inequality and its natural generalization to R\'enyi entropies to derive closed-form parametric expressions of the optimal lower bounds of $\rho$th-order guessing entropy (guessing moment) of a secret taking values on…

We develop a unified framework for computing R\'enyi and entanglement entropies of arbitrary spacetime intervals in time-dependent states of $(1+1)$-dimensional conformal field theories. By combining the spacetime density matrix formalism…

Predictive modeling in archaeology is essential for the understanding of people's behavior in the past and for guiding heritage conservation. However, spatial sampling bias caused by uneven research effort can severely limit model…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

In the remote state estimation problem, an observer tries to reconstruct the state of a dynamical system at a remote location, where no direct sensor measurements are available. The observer only has access to information sent through a…

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…

This paper studies the problem of estimating the differential entropy $h(S+Z)$, where $S$ and $Z$ are independent $d$-dimensional random variables with $Z\sim\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$. The distribution of $S$ is unknown, but $n$…

In this article we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy approach. Unlike standard procedures that require equating at zero the score function of the maximum-likelihood…

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

Policy search methods are crucial in reinforcement learning, offering a framework to address continuous state-action and partially observable problems. However, the complexity of exploring vast policy spaces can lead to significant…

In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum…

We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…

The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…

We show how entanglement entropies allow for the estimation of quasi-long-range order in one dimensional systems whose low-energy physics is well captured by the Tomonaga-Luttinger liquid universality class. First, we check our procedure in…