Weighted Vendi score

What it takes and gives

Runs with

Python 3.10 or later

Entry points

weighted_vendi_score, vendi_from_features

Known answers

13 cases its tests reproduce

Limits and scope

Limits

Dense eigendecomposition by Jacobi rotations: intended for at most a few hundred members. Eigenvalues at or below 1e-12 are treated as zero, which matters for orders below 1. The score depends entirely on the chosen kernel; it says nothing about quality, coverage of a target distribution or usefulness of the members.

Guarantees

n mutually orthogonal members with equal weights score n; identical members score 1. Splitting a member into identical clones whose weights sum to its weight leaves the score unchanged. The score lies between 1 and the number of members with positive weight and does not increase with the order q.

Assumes

The similarity matrix is a valid kernel: symmetric, positive semidefinite, with k(x, x) = 1. Weights express how much each row counts; rows with weight 0 do not affect the score.

Where it is shown

• Statistics for comparing resultsDeterministic skills

Related components

• Brier score decomposition and expected calibration error
• Split conformal prediction intervals
• Anytime-valid confidence sequence for a bounded mean
• Probabilistic and deflated Sharpe ratio
• Ledoit-Wolf covariance shrinkage
• Maximum mean discrepancy with an RBF kernel