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Restricted Boltzmann Machine

  • Last Updated : 23 Nov, 2020

What are Boltzmann Machines?

It is a network of neurons in which all the neurons are connected to each other. In this machine, there are two layers named visible layer or input layer and hidden layer. The visible layer is denoted as v and the hidden layer is denoted as the h. In Boltzmann machine, there is no output layer. Boltzmann machines are random and generative neural networks capable of learning internal representations and are able to represent and (given enough time) solve tough combinatoric problems.

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The Boltzmann distribution (also known as Gibbs Distribution) which is an integral part of Statistical Mechanics and also explain the impact of parameters like Entropy and Temperature on the Quantum States in Thermodynamics. Due to this, it is also known as Energy-Based Models (EBM). It was invented in 1985 by Geoffrey Hinton, then a Professor at Carnegie Mellon University, and Terry Sejnowski, then a Professor at Johns Hopkins University

What are Restricted Boltzmann Machines (RBM)?

A restricted term refers to that we are not allowed to connect the same type layer to each other. In other words, the two neurons of the input layer or hidden layer can’t connect to each other. Although the hidden layer and visible layer can be connected to each other.

As in this machine, there is no output layer so the question arises how we are going to identify, adjust the weights and how to measure the that our prediction is accurate or not. All the question has 1 answer is Restricted Boltzmann Machine.

The RBM algorithm was proposed by Geoffrey Hinton (2007), which learns probability distribution over its sample training data inputs. It has seen wide applications in different areas of supervised/unsupervised machine learning such as feature learning, dimensionality reduction, classification, collaborative filtering, and topic modeling.

Consider the example movie rating discussed in the recommender system section.

Movies like Avengers, Avatar, and Interstellar have strong associations with the latest fantasy and science fiction factor. Based on the user rating RBM will discover latent factors that can explain the activation of movie choices. In short, RBM describes variability among correlated variables of input dataset in terms of a potentially lower number of unobserved variables.

The energy function is given by  

\mathrm{E}(\mathrm{v}, \mathrm{h})=-\mathrm{a}^{\mathrm{T}} \mathrm{v}-\mathrm{b}^{\mathrm{T}} \mathrm{h}-\mathrm{v}^{\mathrm{T}} \mathrm{Wh}

How do Restricted Boltzmann Machines work?

In RBM there are two phases through which the entire RBM works:

1st Phase: In this phase, we take the input layer and using the concept of weights and biased we are going to activate the hidden layer. This process is said to be Feed Forward Pass. In Feed Forward Pass we are identifying the positive association and negative association.  

Feed Forward Equation:

  • Positive Association — When the association between the visible unit and the hidden unit is positive. 
  • Negative Association — When the association between the visible unit and the hidden unit is negative.

2nd Phase: As we don’t have any output layer. Instead of calculating the output layer, we are reconstructing the input layer through the activated hidden state. This process is said to be Feed Backward Pass. We are just backtracking the input layer through the activated hidden neurons. After performing this we have reconstructed Input through the activated hidden state. So, we can calculate the error and adjust weight in this way:  

Feed Backward Equation:

  • Error = Reconstructed Input Layer-Actual Input layer
  • Adjust Weight = Input*error*learning rate (0.1)  

After doing all the steps we get the pattern that is responsible to activate the hidden neurons. To understand how it works.

Let us consider an example in which we have some assumption that V1 visible unit activates the h1 and h2 hidden unit and V2 visible unit activates the h2 and h3 hidden. Now when any new visible unit let V5 has come into the machine and it also activates the h1 and h2 unit. So, we can back trace then hidden unit easily and also identify that the characterizes of the new V5 neuron is matching with the V1. This is because the V1 also activate the same hidden unit earlier.  

Restricted Boltzmann Machines

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