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We consider the sequential sampling of species, where observed samples are classified into the species they belong to. We are particularly interested in studying some quantities describing the sampling process when there is a new species…
In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy.
A new, iterative algorithm is presented to calculate the Embedded Element Pattern (EEP) tranformation from a set of patterns computed for a uniform antenna port loading (scaled identinty matrix) to a set of those computed for a non-uniform…
It is common to assess the "memory strength" of a stationary process looking at how fast the normalized log-determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization…
Entropy production (EP) is a central measure in nonequilibrium thermodynamics, as it can quantify the irreversibility of a process as well as its energy dissipation in special cases. Using the time-reversal asymmetry in a system's path…
Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
A novel method for correlation analysis using scale-dependent Renyi entropies is described. The method involves calculating the entropy of a data distribution as an explicit function of the scale of a d-dimensional partition of d-cubes,…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
Representation learning is a fundamental building block for analyzing entities in a database. While the existing embedding learning methods are effective in various data mining problems, their applicability is often limited because these…
Noncommutative topological entropy estimates are obtained for polynomial gauge invariant endomorphisms of Cuntz algebras, generalising known results for the canonical shift endomorphisms. Exact values for the entropy are computed for a…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
Probabilistic embeddings have several advantages over deterministic embeddings as they map each data point to a distribution, which better describes the uncertainty and complexity of data. Many works focus on adjusting the distribution…
Do word embeddings converge to learn similar things over different initializations? How repeatable are experiments with word embeddings? Are all word embedding techniques equally reliable? In this paper we propose evaluating methods for…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…
A generalized Mott relation of metal melting entropy is derived by means of non-extensive solid and liquid quantum entropy that we calculate from grand partition functions of localized ordered quantum solid and of disordered quantum…
Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…
Open quantum systems are governed by both unitary and non-unitary dynamics, with dissipation arising from the latter. Traditional quantum divergence measures, such as quantum relative entropy, fail to account for the non-unitary oriented…
Mixture distributions are a workhorse model for multimodal data in information theory, signal processing, and machine learning. Yet even when each component density is simple, the differential entropy of the mixture is notoriously hard to…