Contrastive Divergence Step

Problem

One Gibbs step of contrastive divergence for a restricted Boltzmann machine. Compute hidden probabilities sigmoid(W v + b_h), sample binary hidden units after random.seed(seed) using one random.random() per unit, then return the visible reconstruction probabilities sigmoid(W^T h + b_v).

The signature is contrastive_divergence_step(visible, weights, bias_v, bias_h, seed). W has shape (num_hidden, num_visible).

Hint

CD approximates the model distribution gradient with one round trip through the hidden layer.

Test cases

case 1

in: [[1,0],[[1,0],[0,1]],[0,0],[0,0],0]

expected: [0.5,0.5]

case 2

in: [[1,1],[[1,1]],[0,0],[0],5]

expected: [0.7310585786,0.7310585786]

case 3

in: [[0,0],[[1,0],[0,1]],[0,0],[0,0],1]

expected: [0.7310585786,0.5]

case 4

in: [[2,-1],[[1,0],[0,1]],[0.1,-0.1],[0.2,0.2],42]

expected: [0.7502601056,0.7109495026]

Starter codePython

import math
import random
def contrastive_divergence_step(visible, weights, bias_v, bias_h, seed):
    # Your code here
    pass

4 test cases · run your code against them in the editor