SoftRank: from scores to rank distributions

softrank_distribution

"""
Demo script to compute rank distributions given pairwise preference probabilities.

Data:
- pairwise preference probabilities (not including self)

Output:
- distribution over ranks

Michael Taylor, John Guiver, Stephen Robertson and Tom Minka, "SoftRank: Optimising Non-Smooth Rank Metrics", WSDM 2008.
"""

pi_j = list()


def main():
    global pi_j

    P = [
        [0.01, 0.4],     # pi_1j
        [0.1, 0.6],     # pi_2j
        [0.9, 0.99],     # pi_3j
    ]

    num_documents = len(P)
    num_ranks = num_documents

    for j in range(num_documents):
        pi_j = P[j]
        pdist = [0] * num_ranks
        for r in range(num_ranks):
            pdist[r] = p_func(r, num_documents-2)
            pdist.reverse()                         # why???
        print(pdist)


def p_func(r, i):
    if r < 0:
        return 0.0
    if i == -1:
        if r == 0:
            return 1.0
        else:
            return 0.0
    else:
        return p_func(r - 1, i - 1) * pi_j[i] + p_func(r, i - 1) * (1.0 - pi_j[i])


if __name__ == '__main__':
    main()