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logsumexptrick.py
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logsumexptrick.py
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# How to add a list of probabilities together that are
# represented as "log probabilities", to avoid underflow.
from sys import float_info
from math import log, exp
# This effectively acts as probability 0 in the form of log probability.
min_log_prob = -float_info.max
# Adding a list of probabilities represented as log probabilities.
def logsumexp(vals):
if len(vals) == 0:
return min_log_prob
m = max(vals)
if m == min_log_prob:
return min_log_prob
else:
return m + log(sum([exp(val - m) for val in vals]))
# Example of use.
if __name__ == '__main__':
# Two probabilities.
prob1 = 0.0001
prob2 = 0.000001
# Now represented as log probabilities.
logprob1 = log(prob1)
logprob2 = log(prob2)
# The log of the sum of the two probabilities.
logsummed = logsumexp([logprob1, logprob2])
# Converting log probability back to probability by exponentiation.
summed = exp(logsummed)
print("prob1 + prob2 =", summed)
# Multiplication of probabilities is simply by adding
# log probabilities together.
logmultiplied = logprob1 + logprob2
multiplied = exp(logmultiplied)
print("prob1 * prob2 =", multiplied)