Robust Latent Variable Graphical Models: Exact Recovery and Fundamental Limits
We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix, a structure that arises when latent-variable marginalization is combined with conditioning on linear measurements. The proposed convex estimator replaces the sample covariance by the centered Gaussian measure-transformed (MT) covariance, which preserves the signed graph of the sparse component under the nominal model, and penalizes the low-rank component by the nuclear norm of a congruence transform, an atomic norm that encodes structural side information. Our main result is a primal--dual witness theorem: under restricted invertibility and ...
| Authors | Chuansen Peng, Xiaojing Shen |
|---|---|
| Primary category | stat.ML |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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