# Markov Boundary Discovery with Ridge Regularized Linear Models

arXiv: https://arxiv.org/abs/1509.03935 · HTML: https://mlsanity.com/paper/1509.03935/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2015.

## Built on by (most cited first, 4 of 4)

- [Model Agnostic Sample Reweighting for Out-of-Distribution Learning](https://mlsanity.com/paper/2301.09819/) (2023)
- [A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalization](https://mlsanity.com/paper/2111.02355/) (2021)
- [Uncovering Meanings of Embeddings via Partial Orthogonality](https://mlsanity.com/paper/2310.17611/) (2023)
- [Markov Blanket Discovery using Minimum Message Length](https://mlsanity.com/paper/2107.08140/) (2021)

## Abstract (arXiv)

Ridge regularized linear models (RRLMs), such as ridge regression and the SVM, are a popular group of methods that are used in conjunction with coefficient hypothesis testing to discover explanatory variables with a significant multivariate association to a response. However, many investigators are reluctant to draw causal interpretations of the selected variables due to the incomplete knowledge of the capabilities of RRLMs in causal inference. Under reasonable assumptions, we show that a modified form of RRLMs can get very close to identifying a subset of the Markov boundary by providing a worst-case bound on the space of possible solutions. The results hold for any convex loss, even when the underlying functional relationship is nonlinear, and the solution is not unique. Our approach combines ideas in Markov boundary and sufficient dimension reduction theory. Experimental results show that the modified RRLMs are competitive against state-of-the-art algorithms in discovering part of the Markov boundary from gene expression data.