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score-covariance-estimate

Score and compare covariance estimates with precise's assessor panel. Use when you need to judge an estimate out-of-sample or rank competing estimators — and especially in high dimensions, where the plain held-out likelihood is misleading.

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microprediction/precise
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Score / rank covariance estimates

from precise import all_assessors, assessor_from_name

for A in all_assessors():
    s = A().score(cov, X_test=X_test, true_cov=Sigma_true)   # higher = better
  • cov is the estimate to judge; X_test is held-out data (rows = observations); true_cov is the population covariance (only available in simulation).
  • Each assessor exposes needs_data and needs_truth; pass what it needs. Truth-free assessors work on real data, truth-requiring ones (e.g. FrobeniusToTruth) only in simulation.
  • All assessors follow higher = better, so you can rank or argmax directly.

The one rule that matters in high dimensions

Do not rank estimators by the held-out Gaussian log-likelihood when p is comparable to n. The likelihood is dominated by the smallest, unidentifiable eigenvalues of the estimate; empirically it ranks estimators below chance in that regime. Instead use inversion-free or block judges:

Regime / goalUse
low dimension, well-conditionedLogLikelihood (it is optimal here)
high dimension (p/n near 1 or larger)BlockPseudoLikelihood, SchurLikelihood, VariogramScore, FrobeniusToTruth (sim only)
economic / portfolio relevanceGMVVariance (out-of-sample minimum-variance variance)
forecasting a variance from a noisy proxya QLIKE / Bregman-consistent loss, not RMSE on the proxy — RMSE on a noisy variance proxy can rank inconsistently

SchurLikelihood(gamma=...) is a tunable bridge: gamma=1 is the full likelihood (fragile in high-d), gamma=0 the robust block-diagonal one, interior values better-conditioned than either.

Don't over-read the numbers

  • Rankings are ensemble-sensitive: a result on one data-generating process need not transfer. If the conclusion matters, sweep several generators and report per-regime (see the assess-covariance-method skill).
  • A lower point error (RMSE) is not a tradable or actionable signal by itself.
  • If you attach significance to a ranking, the loss differentials are usually dependent (overlapping windows, correlated assets); naive standard errors overstate significance — see the inference section of the assess-covariance-method skill.

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