Related papers: Generalized Rank Dirichlet Distributions
We construct a new distribution for the simplex using the Kumaraswamy distribution and an ordered stick-breaking process. We explore and develop the theoretical properties of this new distribution and prove that it exhibits symmetry under…
This paper is devoted to reduce the conservatism of distributionally robust optimization with moments information. Since the optimal solution of distributionally robust optimization is required to be feasible for all uncertain distributions…
We consider a well known model of random directed acyclic graphs of order $n$, obtained by recursively adding vertices, where each new vertex has a fixed outdegree $d\ge2$ and the endpoints of the $d$ edges from it are chosen uniformly at…
Counts in cells are used to analyse the higher order properties of the statistics of the EDSGC survey. The probability distribution is obtained from an equal area projection source catalog with infinite oversampling over the range…
Given a probability distribution $\mu$ in $\mathbb{R}^d$ represented by data, we study in this paper the generative modeling of the corresponding conditional probability distributions on the level-sets of a collective variable…
Let $G_1,\dots,G_m$ be independent copies of the standard gaussian random vector in $\mathbb{R}^d$. We show that there is an absolute constant $c$ such that for any $A \subset S^{d-1}$, with probability at least $1-2\exp(-c\Delta m)$, for…
Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati (2016). This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as…
Finding the mode of a high dimensional probability distribution $D$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $D$ is…
The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
This paper proposes two distributed random reshuffling methods, namely Gradient Tracking with Random Reshuffling (GT-RR) and Exact Diffusion with Random Reshuffling (ED-RR), to solve the distributed optimization problem over a connected…
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…
In this work, we present and study a generalized family of differentiable renderers. We discuss from scratch which components are necessary for differentiable rendering and formalize the requirements for each component. We instantiate our…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…
We analyze the convergence rate of the random reshuffling (RR) method, which is a randomized first-order incremental algorithm for minimizing a finite sum of convex component functions. RR proceeds in cycles, picking a uniformly random…
Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide…
We show how generalized parton distributions (GPDs) can be determined in the case where hadrons are described in terms of their partonic degrees of freedom through solutions of dynamical equations. We demonstrate our approach on the example…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…