Perceptron and linear models

Let's consider the example of a regression problem where we have two input variables and one output or dependent variable and illustrate the use of ANN for creating a model that can predict the value of the output variable for a set of input variables:

Figure 4.2 Sample training data

In this example, we have x1 and x2 as input variables and y as the output variable. The training data consists of five data points and the corresponding values of the dependent variable, y. The goal is to predict the value of y when x1 = 6 and x2 = 10. Any given continuous function can be implemented exactly by a three-layer neural network with n neurons in the input layer, 2n + 1 neurons in the hidden layer and m neurons in the hidden layer. Let's represent this with a simple neural network:

Figure 4.3 ANN notations

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