Statistics and learning An introduction to Machine Learning

Emmanuel Rachelson and Matthieu Vignes ISAE SupAero

Friday 22nd November 2013

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Machine Learning

Let’s talk about Machine Learning! Keywords?

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A few examples I

Given 20 years of clinical data, will this patient have a second heart attack in the next 5 years?

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A few examples I

Given 20 years of clinical data, will this patient have a second heart attack in the next 5 years?

I

What price for this stock, 6 months from now?

E. Rachelson & M. Vignes (ISAE)

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A few examples I

Given 20 years of clinical data, will this patient have a second heart attack in the next 5 years?

I

What price for this stock, 6 months from now?

I

Is this handwritten number a 7?

E. Rachelson & M. Vignes (ISAE)

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A few examples I

Given 20 years of clinical data, will this patient have a second heart attack in the next 5 years?

I

What price for this stock, 6 months from now?

I

Is this handwritten number a 7?

I

Is this e-mail a spam?

Enlarge your thesis!

E. Rachelson & M. Vignes (ISAE)

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A few examples I

Given 20 years of clinical data, will this patient have a second heart attack in the next 5 years?

I

What price for this stock, 6 months from now?

I

Is this handwritten number a 7?

I

Is this e-mail a spam?

I

Can I cluster together different customers? words? genes?

E. Rachelson & M. Vignes (ISAE)

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2013

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A few examples I

Given 20 years of clinical data, will this patient have a second heart attack in the next 5 years?

I

What price for this stock, 6 months from now?

I

Is this handwritten number a 7?

I

Is this e-mail a spam?

I

Can I cluster together different customers? words? genes?

I

What is the best strategy when playing Counter Strike? or “coinche”?

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A (tentative) taxonomy Different kinds of learning tasks: Task Data: based on. . . I Supervized T = {(xi , yi )}i=1..n I Unsupervized T = {xi }i=1..n I Reinforcement T = {(xi , ui , ri , x0i )}i=1..n

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Target: learn. . . f (x) = y x ∈ Xk P π(x) = u / max rt

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A (tentative) taxonomy Different kinds of learning tasks: Task Data: based on. . . I Supervized T = {(xi , yi )}i=1..n I Unsupervized T = {xi }i=1..n I Reinforcement T = {(xi , ui , ri , x0i )}i=1..n

Target: learn. . . f (x) = y x ∈ Xk P π(x) = u / max rt

Different kinds of learning contexts: I

Offline, batch, non-interactive: all samples are given at once.

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Online, incremental: samples arrive one after the other.

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Active: the algorithm asks for the next sample.

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Reference textbook

The Elements of Statistical Learning, second edition. Trevor Hastie, Robert Tibshirani, Jerome Friedman. Springer series in Statistics, 2009. E. Rachelson & M. Vignes (ISAE)

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Supervized Learning – vocabulary

inputs independent variables predictors features X (random variables) xi (observation of X)

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outputs dependent variables responses targets Y (random variables) yi (observation of X)

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Outputs Nature of outputs: I

Quantitative or ordered: yi ∈ R → Regression task.

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Qualitative or unordered: yi ∈ {0; 1} → Classification task.

In both cases: fitting a function f (x) = y to the data. Questions: I

yi ∈ N? yi ∈ {red, blue, green, yellow}? yi ∈ RN ?

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What about noise; still fitting f (x) = y?

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What about generalization? Overfitting? Overspecialization?

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Supervized learning problem

Given the value of X, make a good prediction Yˆ of the dependent variable Y , given a training set of samples T = {(xi , yi )}i=1..n .

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The process of Supervized Learning

From Supervized Machine Learning: A Review of Classification Techniques, S. B. Kotsiantis, Informatica, 31:249–268, 2007. E. Rachelson & M. Vignes (ISAE)

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Focus of the next classes

An introduction to: I

Naive Bayes classification

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Support vector machines and kernel methods,

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Neural networks,

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Decision trees and Boosting,

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Markov Chain Monte Carlo (MCMC) model selection.

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Examples of other, uncovered topics in supervised learning and keywords: I

Wavelets,

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Bias-variance tradeoff,

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Cross-validation,

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L1 regularization and the LASSO,

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Vapnik-Chernovenkis dimension,

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Bagging,

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Nearest-neighbour methods,

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Random forests,

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and much more! Welcome to the wonderful world of Machine Learning!

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