Ranking Metrics

rank_metrics.py

"""Information Retrieval metrics

Useful Resources:
http://www.cs.utexas.edu/~mooney/ir-course/slides/Evaluation.ppt
http://www.nii.ac.jp/TechReports/05-014E.pdf
http://www.stanford.edu/class/cs276/handouts/EvaluationNew-handout-6-per.pdf
http://hal.archives-ouvertes.fr/docs/00/72/67/60/PDF/07-busa-fekete.pdf
Learning to Rank for Information Retrieval (Tie-Yan Liu)
"""
import numpy as np


def mean_reciprocal_rank(rs):
    """Score is reciprocal of the rank of the first relevant item

    First element is 'rank 1'.  Relevance is binary (nonzero is relevant).

    Example from http://en.wikipedia.org/wiki/Mean_reciprocal_rank
    >>> rs = [[0, 0, 1], [0, 1, 0], [1, 0, 0]]
    >>> mean_reciprocal_rank(rs)
    0.61111111111111105
    >>> rs = np.array([[0, 0, 0], [0, 1, 0], [1, 0, 0]])
    >>> mean_reciprocal_rank(rs)
    0.5
    >>> rs = [[0, 0, 0, 1], [1, 0, 0], [1, 0, 0]]
    >>> mean_reciprocal_rank(rs)
    0.75

    Args:
        rs: Iterator of relevance scores (list or numpy) in rank order
            (first element is the first item)

    Returns:
        Mean reciprocal rank
    """
    rs = (np.asarray(r).nonzero()[0] for r in rs)
    return np.mean([1. / (r[0] + 1) if r.size else 0. for r in rs])


def r_precision(r):
    """Score is precision after all relevant documents have been retrieved

    Relevance is binary (nonzero is relevant).

    >>> r = [0, 0, 1]
    >>> r_precision(r)
    0.33333333333333331
    >>> r = [0, 1, 0]
    >>> r_precision(r)
    0.5
    >>> r = [1, 0, 0]
    >>> r_precision(r)
    1.0

    Args:
        r: Relevance scores (list or numpy) in rank order
            (first element is the first item)

    Returns:
        R Precision
    """
    r = np.asarray(r) != 0
    z = r.nonzero()[0]
    if not z.size:
        return 0.
    return np.mean(r[:z[-1] + 1])


def precision_at_k(r, k):
    """Score is precision @ k

    Relevance is binary (nonzero is relevant).

    >>> r = [0, 0, 1]
    >>> precision_at_k(r, 1)
    0.0
    >>> precision_at_k(r, 2)
    0.0
    >>> precision_at_k(r, 3)
    0.33333333333333331
    >>> precision_at_k(r, 4)
    Traceback (most recent call last):
        File "<stdin>", line 1, in ?
    ValueError: Relevance score length < k


    Args:
        r: Relevance scores (list or numpy) in rank order
            (first element is the first item)

    Returns:
        Precision @ k

    Raises:
        ValueError: len(r) must be >= k
    """
    assert k >= 1
    r = np.asarray(r)[:k] != 0
    if r.size != k:
        raise ValueError('Relevance score length < k')
    return np.mean(r)


def average_precision(r):
    """Score is average precision (area under PR curve)

    Relevance is binary (nonzero is relevant).

    >>> r = [1, 1, 0, 1, 0, 1, 0, 0, 0, 1]
    >>> delta_r = 1. / sum(r)
    >>> sum([sum(r[:x + 1]) / (x + 1.) * delta_r for x, y in enumerate(r) if y])
    0.7833333333333333
    >>> average_precision(r)
    0.78333333333333333

    Args:
        r: Relevance scores (list or numpy) in rank order
            (first element is the first item)

    Returns:
        Average precision
    """
    r = np.asarray(r) != 0
    out = [precision_at_k(r, k + 1) for k in range(r.size) if r[k]]
    if not out:
        return 0.
    return np.mean(out)


def mean_average_precision(rs):
    """Score is mean average precision

    Relevance is binary (nonzero is relevant).

    >>> rs = [[1, 1, 0, 1, 0, 1, 0, 0, 0, 1]]
    >>> mean_average_precision(rs)
    0.78333333333333333
    >>> rs = [[1, 1, 0, 1, 0, 1, 0, 0, 0, 1], [0]]
    >>> mean_average_precision(rs)
    0.39166666666666666

    Args:
        rs: Iterator of relevance scores (list or numpy) in rank order
            (first element is the first item)

    Returns:
        Mean average precision
    """
    return np.mean([average_precision(r) for r in rs])


def dcg_at_k(r, k, method=0):
    """Score is discounted cumulative gain (dcg)

    Relevance is positive real values.  Can use binary
    as the previous methods.

    There is a typographical error on the formula referenced in the original definition of this function:
    http://www.stanford.edu/class/cs276/handouts/EvaluationNew-handout-6-per.pdf
    log2(i) should be log2(i+1)
    
    The formulas here are derived from
    https://en.wikipedia.org/wiki/Discounted_cumulative_gain#Discounted_Cumulative_Gain
    
    The formulas return the same results when r contains only binary values
    
    >>> r = [3, 2, 3, 0, 1, 2]
    >>> dcg_at_k(r, 1)
    3.0
    >>> dcg_at_k(r, 1, method=1)
    7.0
    >>> dcg_at_k(r, 2)
    4.2618595071429155
    >>> dcg_at_k(r, 2, method=1)
    8.8927892607143733
    >>> dcg_at_k(r, 6)
    6.8611266885935018
    >>> dcg_at_k(r, 6, method=1)
    13.848263629272981

    Args:
        r: Relevance scores (list or numpy array) in rank order
            (first element is the most relevant item)
        k: Number of results to consider
        method: If 0 then sum rel_i / log2(i + 1) [not log2(i)]
                If 1 then sum (2^rel_i - 1) / log2(i + 1)
                
    Returns:
        Discounted cumulative gain
    """
    r = np.asfarray(r)[:k]
    if r.size:
        if method == 0:
            return np.sum(r / np.log2(np.arange(2, r.size + 2)))
        elif method == 1:
            return np.sum(np.subtract(np.power(2, r), 1) / np.log2(np.arange(2, r.size + 2)))
        else:
            raise ValueError('method must be 0 or 1.')
    return 0.


def ndcg_at_k(r, k, method=0):
    """Score is normalized discounted cumulative gain (ndcg)

    Relevance is positive real values.  Can use binary
    as the previous methods.

    >>> r = [3, 2, 3, 0, 1, 2]
    >>> ndcg_at_k(r, 1)
    1.0
    >>> ndcg_at_k(r, 1, method=1)
    1.0
    >>> ndcg_at_k(r, 2)
    0.87104906425515294
    >>> ndcg_at_k(r, 2, method=1)
    0.77894125300883343
    >>> ndcg_at_k(r, 6)
    0.96080819433606168
    >>> ndcg_at_k(r, 6, method=1)
    0.94881074856789849

    Args:
        r: Relevance scores (list or numpy array) in rank order
            (first element is the most relevant item)
        k: Number of results to consider
        method: If 0 then sum rel_i / log2(i + 1) [not log2(i)]
                If 1 then sum (2^rel_i - 1) / log2(i + 1)
                
    Returns:
        Normalized discounted cumulative gain
    """
    dcg_max = dcg_at_k(sorted(r, reverse=True), k, method)
    if not dcg_max:
        return 0.
    return dcg_at_k(r, k, method) / dcg_max


if __name__ == "__main__":
    import doctest
    doctest.testmod()

@gumption
Good finding :D
Thank you!