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  3. Quantitative Risk Management in Python

Exercise

Single layer neural networks

To become comfortable using neural networks it will be helpful to start with a simple approximation of a function.

You'll train a neural network to approximate a mapping between an input, x, and an output, y. They are related by the square root function, i.e. \(y = \sqrt{x}\).

The input vector x is given to you. You'll first compute the square root of x using Numpy's sqrt() function, generating the output series y. Then you'll create a simple neural network and train the network on the x series.

After training, you'll then plot both the y series and the output of the neural network, to see how closely the network approximates the square root function.

The Sequential and Dense objects from the Keras library are also available in your workspace.

Instructions

100 XP
  • Create the output training values using Numpy's sqrt() function.
  • Create the neural network with one hidden layer of 16 neurons, one input value, and one output value.
  • Compile and fit the neural network on the training values, for 100 epochs
  • Plot the training values (in blue) against the neural network's predicted values.