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Graph Estimation with Joint Additive Models.

Arend Voorman¹, Ali Shojaie¹, Daniela Witten¹

¹Department of Biostatistics, University of Washington, Seattle, Washington, 98195-7232, U.S.A.

|July 12, 2014

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This study introduces a new semi-parametric method for estimating conditional independence graphs, improving accuracy when relationships are non-linear. The graph estimation with joint additive models (GEJAM) approach offers a robust alternative to traditional methods.

Area of Science:

Statistics
Machine Learning
Bioinformatics

Background:

Estimating conditional independence graphs is crucial in high-dimensional data analysis.
Traditional methods often assume multivariate Gaussian distributions or linear relationships, limiting accuracy when these assumptions are violated.

Purpose of the Study:

To develop a semi-parametric method for robust conditional independence graph estimation.
To address limitations of existing methods when dealing with non-linear relationships among variables.

Main Methods:

Proposed a novel method: graph estimation with joint additive models (GEJAM).
Developed an efficient algorithm for GEJAM computation and proved its consistency.
Extended the method for directed graphs with known causal ordering.

Keywords:

Conditional independence Graphical model Lasso Non-Gaussianity Nonlinearity Sparse additive model Sparsity

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Main Results:

GEJAM outperforms existing methods in scenarios with non-linear feature relationships.
Performance is comparable to traditional methods when conditional means are linear.
Demonstrated effectiveness on a cell-signaling dataset.

Conclusions:

GEJAM provides a flexible and accurate approach for conditional independence graph estimation.
The method is particularly advantageous for biological and other complex datasets with potential non-linear dependencies.