DeepAI

# On the Compressibility of Affinely Singular Random Vectors

There are several ways to measure the compressibility of a random measure; they include the general rate-distortion curve, as well as more specific notions such as Renyi information dimension (RID), and dimensional-rate bias (DRB). The RID parameter indicates the concentration of the measure around lower-dimensional subsets of the space while the DRB parameter specifies the compressibility of the distribution over these lower-dimensional subsets. While the evaluation of such compressibility parameters is well-studied for continuous and discrete measures (e.g., the DRB is closely related to the entropy and differential entropy in discrete and continuous cases, respectively), the case of discrete-continuous measures is quite subtle. In this paper, we focus on a class of multi-dimensional random measures that have singularities on affine lower-dimensional subsets. These cases are of interest when working with linear transformation of component-wise independent discrete-continuous random variables. Here, we evaluate the RID and DRB for such probability measures. We further provide an upper-bound for the RID of multi-dimensional random measures that are obtained by Lipschitz functions of component-wise independent discrete-continuous random variables (x). The upper-bound is shown to be achievable when the Lipschitz function is A x, where A satisfies (A) = (A)+1 (e.g., Vandermonde matrices). The above results in the case of discrete-domain moving-average processes with non-Gaussian excitation noise allow us to evaluate the block-average RID and to find a relationship between this parameter and other existing compressibility measures.

• 3 publications
• 32 publications
• 21 publications
04/29/2019

### Cramér-Rao-type Bound and Stam's Inequality for Discrete Random Variables

The variance and the entropy power of a continuous random variable are b...
12/03/2020

### Modeling Count Data via Copulas

Copula models have been widely used to model the dependence between cont...
07/09/2020

### On Optimal Uniform Concentration Inequalities for Discrete Entropies in the High-dimensional Setting

We prove an exponential decay concentration inequality to bound the tail...
05/10/2021

### Large deviation principles induced by the Stiefel manifold, and random multi-dimensional projections

Given an n-dimensional random vector X^(n) , for k < n, consider its k-d...
03/19/2021

### Stochastic comparisons, differential entropy and varentropy for distributions induced by probability density functions

Stimulated by the need of describing useful notions related to informati...
04/24/2018

### Rate-Distortion Theory for General Sets and Measures

This paper is concerned with a rate-distortion theory for sequences of i...
12/21/2022

### Typicality for stratified measures

Stratified measures on Euclidean space are defined here as convex combin...