Beginning Anomaly Detection Using

v) for every 

possible 

v given V, the set of all possible training inputs. We take that, and we want to 

maximize that product with respect to the weights 

W, so we want the weights to be 

increasing the joint probability (that product of all possible 

v layers).

We can also rewrite this in terms of maximizing the expected value of the log 

probability as shown in Figure 

5-17

.

Figure 5-17.  We take the log of p(v) for some v that’s a part of the whole training set 

V. Then we sum those terms up (think back to the log rules) and find the average of 

them all. That is what we want to maximize with respect to the weights 

W

The notation E [ ] stands for the 

expected value. In probability, E(X) is the expected 

value of some random variable X and can be thought of as the 

mean. In our case, we are 

trying to maximize the mean value of the log probability. Once again, 

V is the set of all 

training inputs.

So to explain what the formula means, we use log rules to rewrite the joint 

probability as a summation instead, and then we seek to maximize the average of that 

sum with respect to 

W, the weights. We want to adjust the weights so that we continue to 

maximize this expected value for every input in the entire training set.

The formulas pertaining to the RBM can get more complicated and detailed, but the 

ones listed so far should hopefully be enough to help you gain a good understanding 

of what an RBM is and how it works. At its core, the RBM is a probabilistic model that 

operates in accordance with a set of formulas. Additionally, the goal of the formulas is to 

help the RBM learn a probability distribution to represent V, explaining why the RBM is 

an