Library / Code module

Ledoit-Wolf covariance shrinkage

ledoit_wolf_shrinkage

Shrink a sample covariance toward a scaled identity with the Ledoit-Wolf intensity, giving a well-conditioned, positive definite estimate even when there are fewer observations than variables. Use it before inverting a covariance of metrics, features or embeddings estimated from few runs.

Files, names only

ATTRIBUTION.md 3.9 KB
LICENSE 1.0 KB
README.md 2.6 KB
atom_cli.py 3.0 KB
component.json 8.6 KB
ledoit_wolf_shrinkage.py 3.5 KB
numerics.py 28.0 KB
schema_lite.py 8.9 KB
test_ledoit_wolf_shrinkage.py 4.3 KB
test_package.py 12.0 KB

Full files in your harness.

What it takes and gives

Runs with: Python 3.10 or later
Entry points: ledoit_wolf, shrink
Known answers: 6 cases its tests reproduce

Cases it covers

not left singular: With 3 observations of 5 variables the sample covariance is singular; using it unshrunk makes its inverse undefined.

Limits and scope

Limits: Single target (scaled identity); other targets such as constant correlation or a diagonal are not included. The intensity is an estimate of the loss-minimizing value with an asymptotic guarantee, not the oracle intensity for a given small sample. Dense p by p matrices: meant for p up to a few hundred.
Guarantees: shrinkage = min(bbar^2, d^2) / d^2 lies in [0, 1]; it is 0 when the sample covariance is already a multiple of the identity. With shrinkage > 0 and a positive target scale the estimate is positive definite, even when p > n. Scaling the data by c scales the estimate by c^2 and leaves the shrinkage unchanged; rotating the data rotates the estimate.
Assumes: Observations are independent and identically distributed with finite fourth moments (the setting of the consistency result). The sample covariance divides by n, as in the Ledoit-Wolf derivation.

Details

Kind: Code module
Licence: MIT
Declared effects: runs commands
Source: github.com/alisonjieli-png/loop-engine/tools/creative_originals/evaluation_atoms/items/ledoit_wolf_shrinkage
Size: 10 files, 75.8 KB
Identity: library.supply.creative_originals.e9e146ec1aab31bae287f33c.20713d30419828ad
Version: 20713d30419828ada9081ec467da388c866dd61a6a271d428f96902441f9e41d

The version is the SHA-256 of the item your harness downloads; every file in it names its own checksum.

Where it is shown

Statistics for comparing resultsDeterministic skills

Related components

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