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Gaussian Huber contamination model for covariance estimation
Definition
Let , , and let be a real positive semidefinite covariance matrix. For any Borel probability law on , define where is the finite-dimensional Gaussian law from Multivariate normal law, including singular covariance. A sample in this model consists of independent observations with common law . The target is the covariance of the uncontaminated Gaussian component, not the covariance of the mixture.
This is the covariance specialization of the Huber model in Huber contamination model. It is distinct from a clean heavy-tail moment model and from adversarial sample replacement.
Depends on
Used by
- A bounded covariance class forces a capped lower rate Counterexample
- A covariance matrix with one correlated block Example
- Dense Gaussian Huber covariance model Example
- Huber covariance modulus lower bound for unrestricted matrix-valued actions Lemma
- Operator error bound for the Gaussian Huber matrix-depth estimator Lemma
- The Gaussian Huber covariance mixture is a probability law Lemma
- The Huber covariance contamination modulus has a quadratic lower bound Lemma
- The scaled Gaussian covariance has matrix depth at least one half Lemma
- Dense Gaussian Huber covariance: high-probability upper and capped lower bounds Theorem
- Single-block sparse Gaussian Huber covariance: high-probability upper and low-ratio lower bounds Theorem
Dependency tree · two levels
28 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Mengjie Chen, Chao Gao and Zhao Ren, Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model, §2 (standard reference, not scraped)