Related papers: On Enumerating Distributions for Associated Vector…
Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Categorical compositional distributional model of Coecke et al. (2010) suggests a way to combine grammatical composition of the formal, type logical models with the corpus based, empirical word representations of distributional semantics.…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
Distributional semantic models provide vector representations for words by gathering co-occurrence frequencies from corpora of text. Compositional distributional models extend these from words to phrases and sentences. In categorical…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
The efficiency of graph-based semi-supervised algorithms depends on the graph of instances on which they are applied. The instances are often in a vectorial form before a graph linking them is built. The construction of the graph relies on…
We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus…
We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while…
We consider families of finite quantum graphs of increasing size and we are interested in how eigenfunctions are distributed over the graph. As a measure for the distribution of an eigenfunction on a graph we introduce the entropy, it has…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\tr\rho_A^n$. We study the…
In this paper we derived a variational principle for the specific entropy on the context of symbolic dynamics of compact metric space alphabets and use this result to obtain the uniqueness of the equilibrium states associated to a Walters…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation…
This article presents the calculation of the entropy of a system with Zipfian distribution and shows that a communication system tends to present an exponent value close to one, but still greater than one, so that it might maximize entropy…