DeepAI
Log In Sign Up

Estimation of high dimensional Gamma convolutions through random projections

03/25/2022
by   Oskar Laverny, et al.
0

Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them appealing to the practitioner. However, fitting such distributions when the dimension gets high is a challenge. We propose stochastic estimation procedures based on the approximation of a Laguerre integrated square error via (shifted) cumulants approximation, evaluated on random projections of the dataset. Through the analysis of our loss via tools from Grassmannian cubatures, sparse optimization on measures and Wasserstein gradient flows, we show the convergence of the stochastic gradient descent to a proper estimator of the high dimensional distribution. We propose several examples on both low and high-dimensional settings.

READ FULL TEXT
03/04/2021

Estimation of multivariate generalized gamma convolutions through Laguerre expansions

The generalized gamma convolutions class of distributions appeared in Th...
06/29/2021

Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections

The Sliced-Wasserstein distance (SW) is being increasingly used in machi...
10/13/2021

Seismic Tomography with Random Batch Gradient Reconstruction

Seismic tomography solves high-dimensional optimization problems to imag...
10/24/2019

A slice tour for finding hollowness in high-dimensional data

Taking projections of high-dimensional data is a common analytical and v...
04/20/2016

Random Projection Estimation of Discrete-Choice Models with Large Choice Sets

We introduce sparse random projection, an important dimension-reduction ...
10/23/2022

Stochastic Mirror Descent for Large-Scale Sparse Recovery

In this paper we discuss an application of Stochastic Approximation to s...
02/10/2020

Super-efficiency of automatic differentiation for functions defined as a minimum

In min-min optimization or max-min optimization, one has to compute the ...