lenskit.metrics.ranking

LensKit ranking (and list) metrics.

Classes

RankingMetricBase	Base class for most ranking metrics, implementing an n parameter for
DCG	Compute the _unnormalized_ discounted cumulative gain [JarvelinKekalainen02].
NDCG	Compute the normalized discounted cumulative gain [JarvelinKekalainen02].
Entropy	Evaluate diversity using Shannon entropy over item categories.
RankBiasedEntropy	Evaluate diversity using rank-biased Shannon entropy over item categories.
ExposureGini	Measure exposure distribution of recommendations with the Gini coefficient.
ListGini	Measure item diversity of recommendations with the Gini coefficient.
Hit	Compute whether or not a list is a hit; any list with at least one
ILS	Evaluate recommendation diversity using intra-list similarity (ILS).
LogRBP	Evaluate recommendations with the natural logarithm of rank-biased precision,
AveragePrecision	Compute Average Precision (AP) for a single user's recommendations. This is
MeanPopRank	Compute the _obscurity_ (mean popularity rank) of the recommendations.
Precision	Compute recommendation precision. This is computed as:
Recall	Compute recommendation recall. This is computed as:
RBP	Evaluate recommendations with rank-biased precision [MZ08].
RecipRank	Compute the reciprocal rank [KV97] of the first relevant
GeometricRankWeight	Geometric cascade weighting for result ranks.
LogRankWeight	Logarithmic weighting for result ranks, as used in NDCG.
RankWeight	Base class for rank weighting models.

Functions

log_rank_biased_precision(good, log_weights, ...)	Compute the natural logarithm of rank-biased precision from log-space weights.
rank_biased_precision(good, weights[, normalization])	Compute rank-biased precision given explicit weights.

Package Contents

lenskit.metrics.ranking.log_rank_biased_precision(good, log_weights, log_normalization)

Compute the natural logarithm of rank-biased precision from log-space weights.

This is the log-space analogue of rank_biased_precision():

\[\ln \operatorname{RBP} = \operatorname{logsumexp}_{i \in \text{good}} \ln w_i - \ln Z\]

Working in log space means the rank discounts are never exponentiated and then summed, so scores far below the float64 subnormal floor remain representable instead of collapsing to zero. A list that retrieves none of its test items has \(\operatorname{RBP} = 0\), and therefore returns \(-\infty\) — a valid measurement, not a missing one.

Parameters:

• good (numpy.ndarray) – Boolean array indicating relevant items at each position.

• log_weights (numpy.ndarray) – Natural log of the weight for each item position (same length as good).

• log_normalization (float) – Natural log of the normalization factor.

Returns:

The natural log of the RBP score, or -inf when no position is relevant.

Stability:

Experimental

Return type:

float

lenskit.metrics.ranking.rank_biased_precision(good, weights, normalization=1.0)

Compute rank-biased precision given explicit weights.

Parameters:

• good (numpy.ndarray) – Boolean array indicating relevant items at each position.

• weights (numpy.ndarray) – Weight for each item position (same length as good).

• normalization (float) – Optional normalization factor, defaults to 1.0.

Returns:

RBP score

Return type:

float