Choose list variable given probability of each variable

问题

I've been trying to code a program that uses the softmax activation function in the middle.

Right now, I have a list of probabilities like this:

P[0.10,0.25,0.60,0.05]

The sum of all the variables in P is always 1.

I wanted a way to pick the index of the list given the probability attached to it. Or, in other words, a function that returned

0 - 10% of the time
1 - 25% of the time
2 - 60% of the time
3 - 5% of the time

I've absolutely no idea where to start on this. Any help would be appreciated. :)

回答1:

You can easily achieve this with numpy. It has a choice function which accepts the parameter of probabilities.

np.random.choice(
  ['pooh', 'rabbit', 'piglet', 'Christopher'], 
  5,
  p=[0.5, 0.1, 0.1, 0.3]
)

回答2:

Basically, make a cumulative probability distribution (CDF) array. Basically, the value of the CDF for a given index is equal to the sum of all values in P equal to or less than that index. Then you generate a random number between 0 and 1 and do a binary search (or linear search if you want). Here's some simple code for it.

from bisect import bisect
from random import random

P = [0.10,0.25,0.60,0.05]

cdf = [P[0]]
for i in xrange(1, len(P)):
    cdf.append(cdf[-1] + P[i])

random_ind = bisect(cdf,random())

of course you can generate a bunch of random indices with something like

rs = [bisect(cdf, random()) for i in xrange(20)]

yielding

[2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2]

(results will, and should vary). Of course, binary search is rather unnecessary for so few of possible indices, but definitely recommended for distributions with more possible indices.

回答3:

Hmm interesting, how about...

Generate a number between 0 and 1.
Walk the list substracting the probability of each item from your number.
Pick the item that, after substraction, took your number down to 0 or below.

That's simple, O(n) and should work :)

回答4:

This problem is equivalent to sampling from a categorical distribution. This distribution is commonly conflated with the multinomial distribution which models the result of multiple samples from a categorical distribution.

In numpy, it is easy to sample from the multinomial distribution using numpy.random.multinomial, but a specific categorical version of this does not exist. However, it can be accomplished by sampling from the multinomial distribution with a single trial and then returning the non-zero element in the output.

import numpy as np
pvals = [0.10,0.25,0.60,0.05]
ind = np.where(np.random.multinomial(1,pvals))[0][0]

回答5:

import random

probs = [0.1, 0.25, 0.6, 0.05]
r = random.random()
index = 0
while(r >= 0 and index < len(probs)):
  r -= probs[index]
  index += 1
print index - 1

来源：https://stackoverflow.com/questions/4437250/choose-list-variable-given-probability-of-each-variable

标签

python

probability