# Compressibility Analysis of Asymptotically Mean Stationary Processes

arXiv: https://arxiv.org/abs/2107.03975 · HTML: https://mlsanity.com/paper/2107.03975/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Understanding Encoder-Decoder Structures in Machine Learning Using Information Measures](https://mlsanity.com/paper/2405.20452/) (2024)

## Abstract (arXiv)

This work provides new results for the analysis of random sequences in terms of ℓp-compressibility. The results characterize the degree in which a random sequence can be approximated by its best k-sparse version under different rates of significant coefficients (compressibility analysis). In particular, the notion of strong ℓp-characterization is introduced to denote a random sequence that has a well-defined asymptotic limit (sample-wise) of its best k-term approximation error when a fixed rate of significant coefficients is considered (fixed-rate analysis). The main theorem of this work shows that the rich family of asymptotically mean stationary (AMS) processes has a strong ℓp-characterization. Furthermore, we present results that characterize and analyze the ℓp-approximation error function for this family of processes. Adding ergodicity in the analysis of AMS processes, we introduce a theorem demonstrating that the approximation error function is constant and determined in closed-form by the stationary mean of the process. Our results and analyses contribute to the theory and understanding of discrete-time sparse processes and, on the technical side, confirm how instrumental the point-wise ergodic theorem is to determine the compressibility expression of discrete-time processes even when stationarity and ergodicity assumptions are relaxed.