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A restricted Boltzmann machine (RBM) is a generative stochastic artificial neural network which learns a probability distribution over its set of inputs. Please see Figure 1.6.

Bernoulli’s RBM has binary type of hidden and visible units hi and vi, respectively, and a matrix of weights w. It also has bias weights ai and bi for visible and hidden units, respectively. With these, the energy equation can be written as follows:

(1.1)

The probability distribution over the hidden and visible layers in terms of energy is as follows:

(1.2)

Z is a normalizing constant just to make the sum of all probabilities equal to 1.

The conditional probability of h given v is as follows:

(1.3)

The conditional probability of v given h is as follows:

(1.4)

The individual activation probabilities are as follows:

(1.5)

(1.6)