Table of Contents

Lecture 1

Lecture 1

1.1 - Why do we need machine learning ?

Because we don't know how to write the corresponding program!
Good at:
- Recognizing patterns
- Recognizing anomalies
- Doing prediction
Here we use the MNIST database of hand-written digits.

1.2 - What are neural networks ?

Each neuron has:
- An axon
- A Dentritic tree
Synapses can adapt. They are very slow, and very low power

1.3 - Some simple models of neurons

For a linear neuron, the output is : \(y = b + \sum\limits_i x_i w_i\)
where “b” is a bias term, xi, the activity on input term i, and wi the weight of input term i.

Binary threshold neurons

we have a threshold used to decide if we output 0 or 1: two formulations:
- \(z = \sum\limits_i x_i w_i\) then y=1 if z > \(\theta\) or y=0 otherwise.
- \(z = b + \sum\limits_i x_i w_i\) then y=1 if z > 0 or y=0 otherwise.

Rectified linear neurons

\(z = b + \sum\limits_i x_i w_i\) then y=z if z > 0 or y=0 otherwise.

Sigmoid neurons

\(z = b + \sum\limits_i x_i w_i\) then \(y = \frac{1}{1+e^{-z}}\)

Stochastic binary neurons

\(z = b + \sum\limits_i x_i w_i\) then \(p(y=1) = \frac{1}{1+e^{-z}}\)

1.4 - A simple example of learning

Simple neural net with on input layer and one output layer.
To train the network, we increment the weights from active pixels to the correct class.
We also decrement the weights to all the classes the network guesses.

1.5 - Three types of learning

Supervised learning
- Regression
- Classification
Reinforcement learning
Unsupervised learning

Supervised learning

We start by choosing a model-class : \(y=f(x; W)\)
Learning means adjusting the parameters to reduce the discrepancy between real output t and the model output y.
For regression the measure the error we usually use a term such as \(\frac 12 (t-y)^2\)
For classification we have other error measure functions.

Reinforcement learning

About rewards in the future. Difficult to handle.

Unsupervised learning

Usefull to get “an understanding” (eg. an internal representation) of the input without labeling it.
Providing compact low-dimensional representation of input. (there is also PCA, but this one is linear)
Provides economical high dimensional representation
Finds sensible clusters in the input.