Python numpy performing very slow

Question

I'm trying to implement hidden markov model training in python and the resultant numpy code seems very slow. It takes 30 minutes to train a model. Below is my code and I do agree that it is terribly inefficient. I tried learning about numpy vectorization and advanced indexing methods, but couldn't figure it as how to use them in my code. I could determine that much of the execution is concentrated and more then 99% of the execution time is taken by the reestimate() function, especially the part where it prints CHK5 and CHK6.

    def reestimate(self):
        newTransition = numpy.zeros(shape=(int(self.num_states),int(self.num_states)))
        newOutput = numpy.zeros(shape=(int(self.num_states),int(self.num_symbols)))
        numerator = numpy.zeros(shape=(int(self.num_obSeq),))
        denominator = numpy.zeros(shape=(int(self.num_obSeq),))
        sumP = 0
        i = 0
        print "CHK1"
        while i < self.num_states:
            j=0
            while j < self.num_states:
                if j < i or j > i + self.delta:
                    newTransition[i][j] = 0
                else:
                    k=0
                    print "CHK2"
                    while k < self.num_obSeq:
                        numerator[k] = denominator[k] = 0
                        self.setObSeq(self.obSeq[k])

                        sumP += self.computeAlpha()
                        self.computeBeta()
                        t=0
                        while t < self.len_obSeq - 1:
                            numerator[k] += self.alpha[t][i] * self.transition[i][j] * self.output[j][self.currentSeq[t + 1]] * self.beta[t + 1][j]
                            denominator[k] += self.alpha[t][i] * self.beta[t][i]
                            t += 1
                        k += 1
                    denom=0
                    k=0
                    print "CHK3"
                    while k < self.num_obSeq:
                        newTransition[i,j] += (1 / sumP) * numerator[k]
                        denom += (1 / sumP) * denominator[k]
                        k += 1
                    newTransition[i,j] /= denom
                    newTransition[i,j] += self.MIN_PROBABILITY
                j += 1
            i += 1
        sumP = 0
        i = 0
        print "CHK4"
        while i < self.num_states:
            j=0
            while j < self.num_symbols:
                k=0
                while k < self.num_obSeq:
                    numerator[k] = denominator[k] = 0
                    self.setObSeq(self.obSeq[k])
                    # print self.obSeq[k]
                    sumP += self.computeAlpha()
                    self.computeBeta()
                    t=0
                    print "CHK5"
                    while t < self.len_obSeq - 1:
                        if self.currentSeq[t] == j:
                            numerator[k] += self.alpha[t,i] * self.beta[t,i]
                        denominator[k] += self.alpha[t,i] * self.beta[t,i]
                        t += 1
                    k += 1
                denom=0
                k=0
                print "CHK6"
                while k < self.num_obSeq:
                    newOutput[i,j] += (1 / sumP) * numerator[k]
                    denom += (1 / sumP) * denominator[k]
                    k += 1
                newOutput[i,j] /= denom
                newOutput[i,j] += self.MIN_PROBABILITY,
                j += 1
            i += 1
        self.transition = newTransition
        self.output = newOutput

    def train(self):
        i = 0
        while i < 20:
            self.reestimate()
            print "reestimating....." ,i
            i += 1

Answer 1

It is straightforward to vectorize your inner loops. Here is an example for the second part of your code (untested of course):

print "CHK4"
for i in xrange(self.num_states):
    for j in xrange(self.num_symbols):
        for k in xrange(self.num_obSeq):
            self.setObSeq(self.obSeq[k])
            # print self.obSeq[k]
            sumP += self.computeAlpha()
            self.computeBeta()
            alpha_times_beta = self.alpha[:,i] * self.beta[:,i]
            numerator[k] = numpy.sum(alpha_times_beta[self.currentSeq == j])
            denominator[k] = numpy.sum(alpha_times_beta)
        denom = numpy.sum(denominator)
        newOutput[i,j] = numpy.sum(numerator) / (sumP * denom) + self.MIN_PROBABILITY
self.transition = newTransition
self.output = newOutput

It might be possible to also vectorize the outer loops, but by far the biggest gain is usually obtained by focusing on the inner loops only. Some comments:

• It seems that most of your while loops can be turned into for loops. Even though this does not make a lot of difference for speed, it is the preferred way if you know the number of iterations before the loop.

• The convention is to use import numpy as np, and use np.function in the rest of the code

• Simple loops that just compute a sum (accum = 0; for item in vector: accum += item) should be vectorized like accum = np.sum(vector).

• Conditional summing in a loop can be converted to a vectorized sum with boolean indexing, so accum = 0; for i in range(n): if cond[i]: accum += vector[i] can be replaced with accum = np.sum(vector[cond])

I am interested to know how much faster your code becomes after these modifications, I guess you can easily gain more than a factor 10.