Add average precision

[ablaom]

Replaces #70. From that PR:

Docstring

AveragePrecision()

Return a callable measure for computing the average precision. Aliases: average_precision.

AveragePrecision()(ŷ, y)

Evaluate AveragePrecision() on predictions ŷ, given ground truth observations y. It is expected that ŷ be a vector of distributions over the binary set of unique elements of y; specifically, ŷ should have eltype <:UnivariateFinite from the CategoricalDistributions.jl package.

Average precision is the area under the empirical precision-recall curve, understood as a step function. This is to be contrasted with measures going under the name "area under the precision-recall curve", in which the step function is usually replaced by a piece-wise linear approximation. Generally, differences between the two are only obvious when the number of observations is small, but it is faster to compute average precision.

Reference: Wikipedia entry, Average precision

Definition

Adopting each distinct predicted probability $p_1, p_2, \ldots, p_k$ for the positive class as a soft probability threshold for predicting an actual class, and assuming these thresholds are arranged in decreasing order, we obtain corresponding recalls $R_1, R_2, \ldots, R_k$ (monotonically increasing) and precisions $P_1, P_2, \ldots, P_k$. Adding an extra recall, $R_{k+1} = 1$, the average precision implemented here is defined as

$\sum_{j=1}^k P_j (R_{j+1} - R_j)$

In some other implementations, such as scikit-learn, $P_j$ is replaced by $P_{j+1}$. However, this requires the definition of a precision for unit recall, in the case the predicted positive class probabilities exclude 1.0, and this is avoided here.

Core implementation: Functions.average_precision.

Generally, an observation obs in MLUtils.eachobs(y) is expected to satisfy ScientificTypes.scitype(obs)<:``ScientificTypesBase.OrderedFactor{2}.

See also precision_recall_curve.

For a complete dictionary of available measures, keyed on constructor, run measures().

Traits

consumes_multiple_observations = true
can_report_unaggregated = false
kind_of_proxy = LearnAPI.Distribution()
observation_scitype = ScientificTypesBase.OrderedFactor{2}
can_consume_tables = false
supports_weights = false
supports_class_weights = false
orientation = StatisticalMeasuresBase.Score()
external_aggregation_mode = StatisticalMeasuresBase.Mean()
human_name = average precision

[ablaom]

@OkonSamuel Thanks for your review. All suggestions have been adopted.