Introduction Machine Learning

Introduction to

Machine Learning

Isabelle [email protected]

What is Machine Learning?

Learningalgorithm

TRAININGDATA Answer

Trainedmachine

Query

What for?

• Classification• Time series prediction• Regression• Clustering

Some Learning Machines

• Linear models • Kernel methods• Neural networks• Decision trees

Applications

inputs

training examples

10

102

103

104

105

Bioinformatics

Ecology

OCRHWR

MarketAnalysis

TextCategorization

MachineVision

Syst

em d

iagno

sis

10 102 103 104 105

Banking / Telecom / Retail

• Identify:– Prospective customers– Dissatisfied customers– Good customers– Bad payers

• Obtain:– More effective advertising– Less credit risk– Fewer fraud– Decreased churn rate

Biomedical / Biometrics

• Medicine:– Screening– Diagnosis and prognosis– Drug discovery

• Security:– Face recognition– Signature / fingerprint / iris

verification– DNA fingerprinting 6

Computer / Internet

• Computer interfaces:– Troubleshooting wizards – Handwriting and speech– Brain waves

• Internet– Hit ranking– Spam filtering– Text categorization– Text translation– Recommendation 7

Challenges

inputs

training examples

10

102

103

104

105

Arcene, Dorothea, Hiva

Sylva

GisetteGina

Ada

Dexter, Nova

Made

lon

10 102 103 104 105

NIPS 2003 & WCCI 2006

Ten Classification Tasks

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50100150

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50100150

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50100150

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50100150

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

50100150

ADA

GINA

HIVA

NOVA

SYLVA

0 5 10 15 20 25 30 35 40 45 500

20

40ARCENE

0 5 10 15 20 25 30 35 40 45 500

20

40DEXTER

0 5 10 15 20 25 30 35 40 45 500

20

40DOROTHEA

0 5 10 15 20 25 30 35 40 45 500

20

40GISETTE

0 5 10 15 20 25 30 35 40 45 500

20

40MADELON

Test BER (%)

Challenge Winning Methods

00.20.40.60.8

11.21.41.61.8

Linear/Kernel

NeuralNets

Trees/RF

NaïveBayes

Gisette (HWR)Gina (HWR)Dexter (Text)Nova (Text)Madelon (Artificial)Arcene (Spectral)Dorothea (Pharma)Hiva (Pharma)Ada (Marketing)Sylva (Ecology)

BE

R/<

BE

R>

Conventions

X={xij}

n

mxiy ={yj}

α

w

Learning problem

Colon cancer, Alon et al 1999

Unsupervised learningIs there structure in data?

Supervised learningPredict an outcome y.

Data matrix: X

m lines = patterns (data points, examples): samples, patients, documents, images, …

n columns = features: (attributes, input variables): genes, proteins, words, pixels, …

Linear Models

• f(x) = w • x +b = Σj=1:n wj xj +b Linearity in the parameters, NOT in the input components.

• f(x) = w • Φ(x) +b = Σj wj φj(x) +b (Perceptron)

• f(x) = Σi=1:m αi k(xi,x) +b (Kernel method)

Artificial Neurons

x1

x2

xn

1

Σ f(x)

w1

w2

wn

b

f(x) = w • x + b

Axon

Synapses

Activation of other neurons Dendrites

Cell potential

Activation function

McCulloch and Pitts, 1943

Linear Decision Boundary

-0.50

0.5-0.

00.5

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

X1X2

X3

x1x2

x3

hyperplane

x1

x2

Perceptron

Rosenblatt, 1957

f(x)

f(x) = w • Φ(x) + b

φ1(x)

1

x1

x2

xn

φ2(x)

φN(x)

Σw1

w2

wN

b

NL Decision Boundary

x1

x2

-0.5

0

0.5

-0.5

0

0.5-0.5

0

0.5

Hs.128749Hs.234680

Hs.

7780

x1

x2

x3

Kernel Method

Potential functions, Aizerman et al 1964

f(x) = Σi αi k(xi,x) + b

k(x1,x)

1

x1

x2

xn

Σα1

α2

αm

b

k(x2,x)

k(xm,x)

k(. ,. ) is a similarity measure or “kernel”.

Hebb’s Rule

wj ← wj + yi xij

AxonΣ

yxj wj

Synapse

Activation of another neuron

Dendrite

Link to “Naïve Bayes”

Kernel “Trick” (for Hebb’s rule)

• Hebb’s rule for the Perceptron:

w = Σi yi Φ(xi)

f(x) = w • Φ(x) = Σi yi Φ(xi) • Φ(x)

• Define a dot product: k(xi,x) = Φ(xi) • Φ(x)

f(x) = Σi yi k(xi,x)

Kernel “Trick” (general)

• f(x) = Σi αi k(xi, x)

• k(xi, x) = Φ(xi) • Φ(x)

• f(x) = w • Φ(x)

• w = Σi αi Φ(xi)

Dual forms

A kernel is:• a similarity measure• a dot product in some feature space: k(s, t) = Φ(s) • Φ(t)

But we do not need to know the Φ representation.

Examples:

• k(s, t) = exp(-||s-t||2/σ2) Gaussian kernel

• k(s, t) = (s • t)q Polynomial kernel

What is a Kernel?

Multi-Layer Perceptron

Back-propagation, Rumelhart et al, 1986

Σxj

Σ

Σ

“hidden units”

internal “latent” variables

Chessboard Problem

Tree Classifiers

CART (Breiman, 1984) or C4.5 (Quinlan, 1993)

At each step, choose the feature that

“reduces entropy” most. Work towards “node purity”.

All the data

f1

f2

Choose f2

Choose f1

Iris Data (Fisher, 1936)

Linear discriminant Tree classifier

Gaussian mixture Kernel method (SVM)

setosavirginica

versicolor

Figure from Norbert Jankowski and Krzysztof Grabczewski

x1

x2

Fit / Robustness Tradeoff

x1

x2

15

x1

x2

Performance evaluation

x1

x2

f(x) = 0

f(x) > 0

f(x) < 0

f(x) = 0

f(x) > 0

f(x) < 0

x1

x2

x1

x2

f(x) = -1

f(x) > -1

f(x) < -1f(x) = -1

f(x) > -1

f(x) < -1

Performance evaluation

x1

x2

x1

x2

f(x) = 1

f(x) > 1

f(x) < 1

f(x) = 1

f(x) > 1

f(x) < 1

Performance evaluation

ROC Curve

100%

100%

For a given threshold on f(x), you get a point on the ROC curve. Actu

al ROC

0

Positive class success rate

(hit rate, sensitivity)

1 - negative class success rate (false alarm rate, 1-specificity)

Random ROC

Ideal ROC curve

ROC Curve

Ideal ROC curve (AUC=1)

100%

100%

0 ≤ AUC ≤ 1

Actual R

OC

Random ROC (AUC=0.5)

0

Positive class success rate

(hit rate, sensitivity)

1 - negative class success rate (false alarm rate, 1-specificity)

For a given threshold on f(x), you get a point on the ROC curve.

Lift Curve

OMGini =

O M

Fraction of customers selected

Hit

rate

= F

rac.

goo

dcu

stom

ers s

elec

t.

Random lift

Ideal Lift

100%

100%Customers ranked according to f(x); selection of the top ranking customers.

Gini=2 AUC-1

0 ≤ Gini ≤ 1

Actual L

ift

0

Predictions: F(x)

Class -1 Class +1

Truth:y

Class -1 tn fp

Class +1 fn tp

Cost matrixPredictions: F(x)

Class -1 Class +1

Truth:y

Class -1 tn fp

Class +1 fn tp

neg=tn+fp

Total

pos=fn+tp

sel=fp+tprej=tn+fnTotal m=tn+fp+fn+tp

False alarm = fp/neg

Class +1 / Total

Hit rate = tp/pos

Frac. selected = sel/m

Cost matrix

Class+1/Total

Precision= tp/sel

False alarm rate = type I errate = 1-specificityHit rate = 1-type II errate = sensitivity = recall = test power

Compare F(x) = sign(f(x)) to the target y, and report:• Error rate = (fn + fp)/m• {Hit rate , False alarm rate} or {Hit rate , Precision} or {Hit rate , Frac.selected} • Balanced error rate (BER) = (fn/pos + fp/neg)/2 = 1 – (sensitivity+specificity)/2• F measure = 2 precision.recall/(precision+recall)

Vary the decision threshold θ in F(x) = sign(f(x)+θ), and plot: • ROC curve

Performance Assessment

: Hit rate vs. False alarm rate• Lift curve: Hit rate vs. Fraction selected• Precision/recall curve: Hit rate vs. Precision

Predictions: F(x)

Class -1 Class +1

Truth:y

Class -1 tn fp

Class +1 fn tp

neg=tn+fp

Total

pos=fn+tp

sel=fp+tprej=tn+fnTotal m=tn+fp+fn+tp

False alarm = fp/neg

Class +1 / Total

Hit rate = tp/pos

Frac. selected = sel/m

Cost matrixPredictions: F(x)

Class -1 Class +1

Truth:y

Class -1 tn fp

Class +1 fn tp

neg=tn+fp

Total

pos=fn+tp

sel=fp+tprej=tn+fnTotal m=tn+fp+fn+tp

Cost matrix

What is a Risk Functional?

A function of the parameters of the learning machine, assessing how much it is expected to fail on a given task.

Examples:• Classification:

– Error rate: (1/m) Σi=1:m 1(F(xi)≠yi)– 1- AUC (Gini Index = 2 AUC-1)

• Regression: – Mean square error: (1/m) Σi=1:m(f(xi)-yi)2

How to train?

• Define a risk functional R[f(x,w)]• Optimize it w.r.t. w (gradient descent,

mathematical programming, simulated annealing, genetic algorithms, etc.)

Parameter space (w)

R[f(x,w)]

w*(… to be continued in the next lecture)

How to Train?

• Define a risk functional R[f(x,w)]• Find a method to optimize it, typically

“gradient descent”wj ← wj - η ∂R/∂wj

or any optimization method (mathematical programming, simulated annealing, genetic algorithms, etc.)

(… to be continued in the next lecture)

Summary

• With linear threshold units (“neurons”) we can build:– Linear discriminant (including Naïve Bayes)– Kernel methods– Neural networks– Decision trees

• The architectural hyper-parameters may include:– The choice of basis functions φ (features)– The kernel – The number of units

• Learning means fitting:– Parameters (weights)– Hyper-parameters– Be aware of the fit vs. robustness tradeoff

Want to Learn More?

• Pattern Classification, R. Duda, P. Hart, and D. Stork. Standard pattern recognition textbook. Limited to classification problems. Matlabcode. http://rii.ricoh.com/~stork/DHS.html

• The Elements of statistical Learning: Data Mining, Inference, and Prediction. T. Hastie, R. Tibshirani, J. Friedman, Standard statistics textbook. Includes all the standard machine learning methods forclassification, regression, clustering. R code. http://www-stat-class.stanford.edu/~tibs/ElemStatLearn/

• Linear Discriminants and Support Vector Machines, I. Guyon and D. Stork, In Smola et al Eds. Advances in Large Margin Classiers. Pages 147--169, MIT Press, 2000.http://clopinet.com/isabelle/Papers/guyon_stork_nips98.ps.gz

• Feature Extraction: Foundations and Applications. I. Guyon et al, Eds. Book for practitioners with datasets of NIPS 2003 challenge, tutorials, best performing methods, Matlab code, teaching material.http://clopinet.com/fextract-book