Week 41 Neural networks and constructing a neural network code
Contents
Plan for week 41
Lecture Thursday October 12
Introduction to Neural networks
Artificial neurons
Neural network types
Feed-forward neural networks
Convolutional Neural Network
Recurrent neural networks
Other types of networks
Multilayer perceptrons
Why multilayer perceptrons?
Illustration of a single perceptron model and a multi-perceptron model
Examples of XOR, OR and AND gates
Does Logistic Regression do a better Job?
Adding Neural Networks
Mathematical model
Mathematical model
Mathematical model
Mathematical model
Mathematical model
Matrix-vector notation
Matrix-vector notation and activation
Activation functions
Activation functions, Logistic and Hyperbolic ones
Relevance
The multilayer perceptron (MLP)
From one to many layers, the universal approximation theorem
Deriving the back propagation code for a multilayer perceptron model
Definitions
Derivatives and the chain rule
Derivative of the cost function
Bringing it together, first back propagation equation
Derivatives in terms of \( z_j^L \)
Bringing it together
Final back propagating equation
Setting up the Back propagation algorithm
Setting up the Back propagation algorithm
Setting up the Back propagation algorithm
Setting up a Multi-layer perceptron model for classification
Defining the cost function
Example: binary classification problem
The Softmax function
Developing a code for doing neural networks with back propagation
Collect and pre-process data
Train and test datasets
Define model and architecture
Layers
Weights and biases
Feed-forward pass
Matrix multiplications
Choose cost function and optimizer
Optimizing the cost function
Regularization
Matrix multiplication
Improving performance
Full object-oriented implementation
Evaluate model performance on test data
Adjust hyperparameters
Visualization
scikit-learn implementation
Visualization
Testing our code for the XOR, OR and AND gates
The AND and XOR Gates
Representing the Data Sets
Setting up the Neural Network
The Code using Scikit-Learn
Lecture Thursday October 12
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