alias_multinomial.py

import torch
import numpy as np

class AliasMethod(object):
    '''
        From: https://hips.seas.harvard.edu/blog/2013/03/03/the-alias-method-efficient-sampling-with-many-discrete-outcomes/
    '''
    def __init__(self, probs):

        K = len(probs)
        self.prob = torch.zeros(K)
        self.alias = torch.LongTensor([0]*K)

        # Sort the data into the outcomes with probabilities
        # that are larger and smaller than 1/K.
        smaller = []
        larger = []
        for kk, prob in enumerate(probs):
            self.prob[kk] = K*prob
            if self.prob[kk] < 1.0:
                smaller.append(kk)
            else:
                larger.append(kk)

        # Loop though and create little binary mixtures that
        # appropriately allocate the larger outcomes over the
        # overall uniform mixture.
        while len(smaller) > 0 and len(larger) > 0:
            small = smaller.pop()
            large = larger.pop()

            self.alias[small] = large
            self.prob[large] = (self.prob[large] - 1.0) + self.prob[small]

            if self.prob[large] < 1.0:
                smaller.append(large)
            else:
                larger.append(large)

        for last_one in smaller+larger:
            self.prob[last_one] = 1

    def draw(self, *size):
        '''
            Draw N samples from multinomial
        '''
        K = self.alias.size(0)

        kk = torch.LongTensor(np.random.randint(0,K, size=size)).view(-1)
        prob = self.prob[kk]
        alias = self.alias[kk]
        # b is whether a random number is greater than q
        b = torch.bernoulli(prob)
        oq = kk.mul(b.long())
        oj = alias.mul((1-b).long())

        return (oq + oj).view(size)