Platt sigmoid estimation with scipy.optimize.fmin_bfgs

from math import log
import numpy as np
from scipy.optimize import fmin_bfgs

def bfgs_sigmoid_train(F, Y, use_grad=True):
    # Reference: Platt, "Probabilistic Outputs for Support Vector Machines"

    # Bayesian priors (see Platt end of section 2.2)
    prior0 = sum(1.0 for y in Y if y <=0)
    prior1 = Y.shape[0] - prior0
    T = np.zeros(Y.shape)
    T[Y > 0] = (prior1 + 1) / (prior1 + 2)
    T[Y <= 0] = 1 / (prior0 + 2)
    T1 = 1.0 - T

    AB0 = np.array([0.0, log((prior0 + 1.0) / (prior1 + 1.0))])

    def objective(AB):
        # From Platt (beginning of Section 2.2)
        E = np.exp(AB[0] * F + AB[1])
        P = 1.0 / (1.0 + E)
        return -(np.dot(T, np.log(P)) + np.dot(T1, np.log(1.0 - P)))

    def grad(AB):
        # gradient of the objective function
        E = np.exp(AB[0] * F + AB[1])
        P = 1.0 / (1.0 + E)
        TEP_minus_T1P = P * (T * E - T1)
        dA = np.dot(TEP_minus_T1P, F)
        dB = np.sum(TEP_minus_T1P)
        return np.array([dA, dB])

    if use_grad:
        return fmin_bfgs(objective, AB0, fprime=grad)
    else:
        return fmin_bfgs(objective, AB0)



if __name__ == '__main__':
    exF = np.array([5, -4, 1.0])
    exY = np.array([1, -1, -1])
    # computed from my python port of the C++ code in LibSVM
    lin_libsvm_solution = np.array([-0.20261354391187855, 0.65236314980010512])
    assert np.linalg.norm(lin_libsvm_solution - bfgs_sigmoid_train(exF, exY, use_grad=True)) < 0.001
    assert np.linalg.norm(lin_libsvm_solution - bfgs_sigmoid_train(exF, exY, use_grad=False)) < 0.001