Related papers: An Information-Theoretic View of Stochastic Locali…
We offer a new approach to the information decomposition problem in information theory: given a 'target' random variable co-distributed with multiple 'source' variables, how can we decompose the mutual information into a sum of non-negative…
We prove that finite multivariate Erlang mixture densities with a common rate parameter are dense in the class of probability densities on $\mathbb{R}_{+}^{d}$ that belong to $L^{p}$, for every dimension $d\in\mathbb{N}$ and every $1\le…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition of stochastic channels is defined by marginalization. Last year at ACT, the notion of 'copy-composition' was…
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…
If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to…
The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the…
Stochastic ordering among distributions has been considered in a variety of scenarios. Economic studies often involve research about the ordering of investment strategies or social welfare. However, as noted in the literature, stochastic…
The use of coarse graining to connect physical and information theoretic entropies has recently been given a precise formulation in terms of ``observational entropy'', describing entropy for observers with respect to a measurement. Here we…
This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no…
The number partitioning problem is a classic problem of combinatorial optimization in which a set of $n$ numbers is partitioned into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the…
Electron localization is the tendency of an electron in a many-body system to exclude other electrons from its vicinity. Using a new natural measure of localization based on the exact manyelectron wavefunction, we find that localization can…
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…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which,…
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.…
Indentation test is used with growing popularity for the characterization of various materials on different scales. Developed methods are combining the test with computer simulation and inverse analyses to assess material parameters…