# A Density Evolution framework for Preferential Recovery of Covariance and Causal Graphs from Compressed Measurements

arXiv: https://arxiv.org/abs/2203.09636 · HTML: https://mlsanity.com/paper/2203.09636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Statistical physics of inference: Thresholds and algorithms](https://mlsanity.com/paper/1511.02476/) (2015)
- [Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity](https://mlsanity.com/paper/1703.01196/) (2017)

## Abstract (arXiv)

In this paper, we propose a general framework for designing sensing matrix boldsymbolA ∈ ℝd× p, for estimation of sparse covariance matrix from compressed measurements of the form boldsymboly = boldsymbolAboldsymbolx + boldsymboln, where boldsymboly, boldsymboln ∈ ℝd, and boldsymbolx ∈ ℝp. By viewing covariance recovery as inference over factor graphs via message passing algorithm, ideas from coding theory, such as textitDensity Evolution (DE), are leveraged to construct a framework for the design of the sensing matrix. The proposed framework can handle both (1) regular sensing, i.e., equal importance is given to all entries of the covariance, and (2) preferential sensing, i.e., higher importance is given to a part of the covariance matrix. Through experiments, we show that the sensing matrix designed via density evolution can match the state-of-the-art for covariance recovery in the regular sensing paradigm and attain improved performance in the preferential sensing regime. Additionally, we study the feasibility of causal graph structure recovery using the estimated covariance matrix obtained from the compressed measurements.