introduction
TRANSCRIPT
What is Machine Learning?
Learning
algorithm
TRAININGDATA Answer
Trained
machine
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
Machine Vision
Syst
em d
iagn
osis
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
Mad
elon
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
40
DEXTER
0 5 10 15 20 25 30 35 40 45 500
20
40
DOROTHEA
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
0
0.2
0.40.6
0.8
1
1.21.4
1.6
1.8
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
mxi
y ={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
0.5-0.5
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 y
xj 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
For a given threshold on f(x), you get a point on the ROC curve.
Positive class success rate
(hit rate, sensitivity)
1 - negative class success rate (false alarm rate, 1-specificity)
Lift Curve
OMGini =
O M
Fraction of customers selected
Hit rate =
Frac.
good custom
ers select.
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/selFalse alarm rate = type I errate = 1-specificity
Hit rate = 1-type II errate = sensitivity = recall = test power
Performance Assessment
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: 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. Matlab code. 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 for classification, 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