====== 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.