Contents
How are neural networks used in multivariate regression?
The input to a neuron in any non-input layer is taken to be a linearly weighted function of the outputs (i.e. activations) of the neurons in the previous layer. We use identity as the activation function here, so the output of a neuron is the same as the input it gets.
When does a neural net converge to a unique model?
Further, when we do not employ hidden layers there will be a unique model that the neural net will converge to, no matter the initial guess.
How are neural networks used in a computational framework?
One could consider using this neural network model as a replacement for that function in a computational framework. The function represented by the neural network model could be as simple as rotating the input vector, or perform a prescribed nonlinear transformation of the same for example.
How to generate training data with neural nets?
Here is a sample python code snippet to generate the training data. The neural net employs identity is the activation function and the cost function is the sum of squared errors at the output layer.
This is exactly the same cost function that a least squares approach to the problem minimizes in order to estimate the best fitting . While the neural network does this in an iterative fashion with SGD, the least squares approach has a closed-form solution and gets it all in one shot as:
Can a neural network be used for learning?
The point is that even though the neural nets we use here are rather simple we will come face to face with choosing a learning rate that works.
Which is the activation function of a neural net?
The neural net employs identity is the activation function and the cost function is the sum of squared errors at the output layer. The implementation of the feed forward, backward propagation, and the stochastic gradient descent technique are as described in Michael Nielsen’s web book Neural Networks and Deep Learning.