Related papers: Mode Poset Probability Polytopes
The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…
The Probability Ranking Principle states that the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key point…
Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$,…
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
In this paper, we propose a statistical test to determine whether a given word is used as a polysemic word or not. The statistic of the word in this test roughly corresponds to the fluctuation in the senses of the neighboring words a nd the…
Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores…
We study approximations of smooth convex bodies by random ball-polytopes. We examine the following probability model: let $K\subset{\bf R}^d$ be a convex body such that $K$ slides freely in a ball of radius $R>0$ and has $C^2$ smooth…
The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. This task has been approached in the statistical literature from different perspectives,…
We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
We introduce a new `geometric realization' of an (abstract) simplicial complex, inspired by probability theory. This space (and its completion) is a metric space, which has the right (weak) homotopy type, and which can be compared with the…
We define an n-dimensional polytope Pi_n(x), depending on parameters x_i>0, whose combinatorial properties are closely connected with empirical distributions, plane trees, plane partitions, parking functions, and the associahedron. In…
Consider $n$ iid real-valued random vectors of size $k$ having iid coordinates with a general distribution function $F$. A vector is a maximum if and only if there is no other vector in the sample which weakly dominates it in all…
The modes of a statistical population are high frequency points around which most of the probability mass is accumulated. For the particular case of circular densities, we address the problem of testing if, given an observed sample of a…
First order stochastic dominance and monotone likelihood ratio are two partial orders on the $n$-probability simplex that play an important role in the establishment of structural results for MDPs and POMDPs. We study the strength of those…
Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…
We study two types of probability measures on the set of integer partitions of $n$ with at most $m$ parts. The first one chooses the random partition with a chance related to its largest part only. We then obtain the limiting distributions…
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…