Machine learning

History

Dominant approach:

Feeding vast amounts of data to algorithms

Dominant approach:

Example in image recognition:

Rather than coding explicitly all the possible ways—pixel by pixel—that a picture can represent an object, image/label pairs are fed to a neural network

Parameters get adjusted in an iterative and automated manner

Neurons

Biological

Artificial

Neurons

Biological

Artificial

Biological neuron: an electrically excitable cell receives information through the dendrites & transmits a compiled output through the axons

Neurons

Biological

Artificial

Artificial neuron: the weighted sum of a set of numeric inputs is passed through an activation function before yielding a numeric output

Activation

Threshold potential

Activation functions

Activation

Threshold potential

Activation functions

Biological neuron: all-or-nothing action potential; greater stimuli don’t produce stronger signals but increase firing frequency

Activation

Threshold potential

Activation functions

Artificial neuron: many activation functions have been tried; choices based on problem & available computing budget

Softmax activation function

$$\sigma (\mathbf{z}{)}_i=\frac{e^{z_i}}{\sum _{j=1}^K{e}^{z_j}}$$ $$\text{ for }i=1,\dots ,K\text{ and }\mathbf{z}=(z_1,\dots ,z_K)\in {\mathbb{R}}^K$$

Vector of real numbers  →  vector of numbers between 0 and 1 which add to 1

Relu: rectifier activation function

$$f(x)=max(0,x)$$

Neural networks

Biological

Artificial

Neural networks

Biological

Artificial

Biological network: tremendously complex organization

Neural networks

Biological

Artificial

Natural network: organized in layers

Neural networks

Single layer of artificial neurons   →   Unable to learn even some of the simple mathematical functions (Marvin Minsky & Seymour Papert)

How do neural networks learn?

Building a model

First, we need an architecture: size, depth, types of layers, etc.
This is set before training and does not change.

Building a model

Then we need parameters.
Those are set to some initial values, but will change during training.

Training a model

To train the model, we need labelled examples (input/output pairs).

Training a model

The inputs are features: characteristics describing our data.
The outputs are labels: the variable we are predicting, also called targets.

Training a model

We split the labelled data into a training set (often c. 80%) & a testing set (the rest).

Training a model

Training inputs and parameters are fed to the architecture.

Training a model

We get predictions as outputs.

Training a model

A metric (e.g. error rate) compares predictions & training labels: this is a measure of model performance.

Training a model

Because it is not always sensitive enough to changes in parameter values,
we compute a loss function …

Training a model

… which allows to adjust the parameters slightly through backpropagation.
This cycle gets repeated at each step.

Training a model

At the end of the training process, what matters is the combination of architecture and trained parameters.

A model

That’s what constitute a model.

A model

A model can be considered as a regular program.

Testing a model

We test the model on labelled data it has never seen: the testing data.
No training data is used here!

Testing a model

The testing loss informs us on how well our model performs with data it was not trained on.

Using a model

Finally, the model can be used to obtain outputs we really care about from unlabelled inputs. We are now using it just like a regular program.

Questions?