def dda_expected_entropy(qs):
"""return d/da[E[H|a*qs]], a function of alpha"""
# Agrees with test_diff!
sum_qs = float(sum(qs))
h_inf = h(normalize(qs), units='nats')
h_0 = 0 #expected_entropy_from_alphas([0 for q in qs])
Z = h_inf #*log(2) # in nats
return lambda alpha: ((sum_qs * polygamma(1, alpha * sum_qs + 1) - sum(
qj**2 / sum_qs * polygamma(1, alpha * qj + 1) for qj in qs)) / (Z))
def dda_expected_entropy(qs):
"""return d/da[E[H|a*qs]], a function of alpha"""
# Agrees with test_diff!
sum_qs = float(sum(qs))
h_inf = h(normalize(qs),units='nats')
h_0 = 0 #expected_entropy_from_alphas([0 for q in qs])
Z = h_inf#*log(2) # in nats
return lambda alpha: ((sum_qs*polygamma(1,alpha*sum_qs+1) -
sum(qj**2/sum_qs*polygamma(1,alpha*qj+1) for qj in qs))/
(Z))
def h_mle(xs,units='bits'):
"""Compute MLE estimator of entropy"""
p_hats = frequencies(xs)
return h(p_hats,units=units)