An introduction to Machine Learning

An introduction to
Machine Learning
Pierre Geurts
p.geurts@ulg.ac.be

Department of EE and CS &
GIGA-R, Bioinformatics and modelling
University of Liège

Outline
● Introduction
● Supervised Learning
● Other learning protocols/frameworks

2

Machine Learning: definition
 Machine Learning is concerned with the development,
the analysis, and the application of algorithms that
allow computers to learn
 Learning:
 A computer learns if it improves its performance at
some task with experience (i.e. by collecting data)
 Extracting a model of a system from the sole
observation (or the simulation) of this system in some
situations.
 A model = some relationships between the variables
used to describe the system.
 Two main goals: make prediction and better
understand the system
3

Machine learning: when ?
 Learning is useful when:
 Human expertise does not exist (navigating on Mars),
 Humans are unable to explain their expertise (speech
recognition)
 Solution changes in time (routing on a computer
network)
 Solution needs to be adapted to particular cases (user
biometrics)
 Example: It is easier to write a program that learns to
play checkers or backgammon well by self-play rather
than converting the expertise of a master player to a
program.
4

Applications: autonomous driving
 DARPA Grand challenge 2005: build a robot capable
of navigating 175 miles through desert terrain in less
than 10 hours, with no human intervention
 The actual wining time of Stanley [Thrun et al., 05]
was 6 hours 54 minutes.

http://www.darpa.mil/grandchallenge/ 5

Applications: recommendation system
 Netflix prize: predict how much someone is going to love a
movie based on their movies preferences
 Data: over 100 million ratings that over 480,000 users
gave to nearly 18,000 movies
 Reward: $1,000,000 dollars if 10% improvement with
respect to Netflix's current system

http://www.netflixprize.com 6

Applications: credit risk analysis
 Data:

 Logical rules automatically learned from data:

7

Applications
 Machine learning has a wide spectrum of applications
including:
 Retail: Market basket analysis, Customer relationship
management (CRM)
 Finance: Credit scoring, fraud detection
 Manufacturing: Optimization, troubleshooting
 Medicine: Medical diagnosis
 Telecommunications: Quality of service optimization,
routing
 Bioinformatics: Motifs, alignment
 Web mining: Search engines
 ...
8

Related ﬁelds

 Artiﬁcial Intelligence: smart algorithms
 Statistics: inference from a sample
 Computer Science: efficient algorithms and complex
models
 Systems and control: analysis, modeling, and control
of dynamical systems
 Data Mining: searching through large volumes of data

9

Problem definition
One part of the data
Data generation mining process

Raw data
 Each step generates many questions:
 Data generation: data types, sample
Preprocessing size, online/offline...
 Preprocessing: normalization,
missing values, feature
Preprocessed data
selection/extraction...
 Machine learning: hypothesis,
Machine choice of learning
learning paradigm/algorithm...
 Hypothesis validation: cross-
Hypothesis validation, model deployment...

Validation

Knowledge/Predictive model
10

Glossary
 Data=a table (dataset, database, sample)
Variables (attributes, features) =
measurements made on objects

VAR 1 VAR 2 VAR 3 VAR 4 VAR 5 VAR 6 VAR 7 VAR 8 VAR 9 VAR 10 VAR 11 ...
Object 1 0 1 2 0 1 1 2 1 0 2 0 ...
Object 2 2 1 2 0 1 1 0 2 1 0 2 ...
Object 3 0 0 1 0 1 1 2 0 2 1 2 ...
Object 4 1 1 2 2 0 0 0 1 2 1 1 ...
Object 5 0 1 0 2 1 0 2 1 1 0 1 ...
Object 6 0 1 2 1 1 1 1 1 1 1 1 ...
Object 7 2 1 0 1 1 2 2 2 1 1 1 ...
Object 8 2 2 1 0 0 0 1 1 1 1 2 ...
Object 9 1 1 0 1 0 0 0 0 1 2 1 ...
Object 10 1 2 2 0 1 0 1 2 1 0 1 ...
... ... ... ... ... ... ... ... ... ... ... ... ...

Objects (samples, observations,
individuals, examples, patterns) Dimension=number of variables
Size=number of objects

 Objects: samples, patients, documents, images...
 Variables: genes, proteins, words, pixels...

11

Outline
● Introduction
 Introduction
 Model selection, cross-validation, overfitting
 Some supervised learning algorithms
 Beyond classification and regression

12

Supervised learning

Inputs Output

A1 A2 A3 A4 Y Supervised
-0.69 -0.72 Y 0.47 Healthy learning
-2.3 -1.2 N 0.15 Disease
0.32
0.37
-0.9
-1
N
Y
-0.76
-0.59
Healthy
Disease Ŷ = h(A1,A2,A3,A4)
-0.67 -0.53 N 0.33 Healthy
0.51 -0.09 Y -0.05 Disease
model,
Learning sample hypothesis

 Goal: from the database (learning sample), find a
function h of the inputs that approximates at best the
output
 Symbolic output ⇒ classification problem,
 Numerical output ⇒ regression problem 13

Two main goals
 Predictive:
Make predictions for a new sample described by its
attributes
A1 A2 A3 A4 Y
0.83 -0.54 T 0.68 Healthy
-2.3 -1.2 F -0.83 Disease
0.08 0.63 F 0.76 Healthy
0.06 -0.29 T -0.57 Disease
-0.98 -0.18 F -0.38 Healthy
-0.68 0.82 T -0.95 Disease
0.92 -0.33 F -0.48 ?

 Informative:
Help to understand the relationship between the inputs
and the output
Y=disease if A3=F and A2<0.3

Find the most relevant inputs

14

Example of applications
 Biomedical domain: medical diagnosis, differentiation
of diseases, prediction of the response to a
treatment...

Gene expression, Metabolite concentrations...

A1 A2 ... A4 Y
-0.61 0.23 ... 0.49 Healthy
-2.3 -1.2 ... -0.11 Disease
Patients -0.82 -0.41 ... 0.24 Healthy
-0.74 -0.1 ... -0.15 Disease
-0.14 0.98 ... -0.13 Healthy
-0.37 0.27 ... -0.67 Disease

15

 Perceptual tasks: handwritten character recognition,
speech recognition...
Inputs:
● a grey intensity [0,255] for

each pixel
● each image is

represented by a vector of
pixel intensities
● eg.: 32x32=1024

dimensions

Output:
● 9 discrete values

● Y={0,1,2,...,9}

16

 Time series prediction: predicting electricity load,
network usage, stock market prices...

17

Outline
● Introduction
 Introduction

18

Illustrative problem

 Medical diagnosis from two measurements (eg., weights
and temperature)

1
M1 M2 Y
0.52 0.18 Healthy
0.44 0.29 Disease
0.89 0.88 Healthy

M2
0.99 0.37 Disease
... ... ...
0.95 0.47 Disease
0.29 0.09 Healthy
0
0 1
M1

 Goal: find a model that classifies at best new cases for
which M1 and M2 are known

19

Learning algorithm
 A learning algorithm is defined by:
 a family of candidate models (=hypothesis space H)
 a quality measure for a model
 an optimization strategy
 It takes as input a learning sample and outputs a
function h in H of maximum quality
1
a model
obtained by
supervised
G2

learning

0
0 1
G1
20

Linear model
Disease if w0+w1*M1+w2*M2>0
h(M1,M2)=
Normal otherwise

1

M2
0
0 1
M1

 Learning phase: from the learning sample, find the
best values for w0, w1 and w2
 Many alternatives even for this simple model (LDA,
Perceptron, SVM...)
21

Quadratic model

Disease if w0+w1*M1+w2*M2+w3*M12+w4*M22>0
h(M1,M2)=
Normal otherwise

1

M2
0
0 1
M1

best values for w0, w1,w2, w3 and w4
 Many alternatives even for this simple model (LDA,
Perceptron, SVM...) 22

Artificial neural network

Disease if some very complex function of M1,M2>0
h(M1,M2)=
Normal otherwise

1

M2
0
0 1
M1

numerous parameters of the very complex function

23

Which model is the best?
linear quadratic neural net
1 1 1

0 0 0
0 1 0 1 0 1

 Why not choose the model that minimises the error
rate on the learning sample? (also called re-
substitution error)
 How well are you going to predict future data drawn
from the same distribution? (generalisation error)

24

The test set method

1.Randomly choose 30% of the data
1
to be in a test sample
2.The remainder is a learning
sample
3.Learn the model from the learning
0
0 1
sample
4.Estimate its future performance on
the test sample

25

Which model is the best?
linear quadratic neural net
1 1 1

0 0 0
0 1 0 1 0 1
LS error= 3.4% LS error= 1.0% LS error= 0%
TS error= 3.5% TS error= 1.5% TS error= 3.5%

 We say that the neural network overfits the data
 Overfitting occurs when the learning algorithm starts
fitting noise.
 (by opposition, the linear model underfits the data)

26

The test set method

 Upside:
 very simple
 Computationally efficient

 Downside:
 Wastes data: we get an estimate of the best method to
apply to 30% less data
 Very unstable when the database is small (the test
sample choice might just be lucky or unlucky)

27

Leave-one-out Cross Validation

For k=1 to N
 remove the kth object from the
1
learning sample
 learn the model on the remaining
objects
 apply the model to get a prediction
0
0 1
for the kth object
report the proportion of
missclassified objects

28

Leave-one-out Cross Validation

 Upside:
 Does not waste the data (you get an estimate of the
best method to apply to N-1 data)
 Downside:
 Expensive (need to train N models)
 High variance

29

k-fold Cross Validation
 Randomly partition the dataset into k subsets (for example
10)

TS

 For each subset:
 learn the model on the objects that are not in the subset
 compute the error rate on the points in the subset
 Report the mean error rate over the k subsets
 When k=the number of objects ⇒ leave-one-out cross
validation
30

Which kind of Cross Validation?
 Test set:
 Cheap but waste data and unreliable when few data
 Leave-one-out:
 Doesn't waste data but expensive
 k-fold cross validation:
 compromise between the two
 Rule of thumb:
 a lot of data (>1000): test set validation
 small data (100-1000): 10-fold CV
 very small data(<100): leave-one-out CV

31

CV-based complexity control
Error

Under-fitting Over-fitting

CV error

LS error

Optimal complexity Complexity
32

Complexity

 Controlling complexity is called regularization or
smooting
 Complexity can be controlled in several ways
 The size of the hypothesis space: number of candidate
models, range of the parameters...
 The performance criterion: learning set performance
versus parameter range, eg. minimizes
Err(LS)+λ C(model)
 The optimization algorithms: number of iterations,
nature of the optimization problem (one global optimum
versus several local optima)...
33

CV-based algorithm choice
 Step 1: compute 10-fold (or test set or LOO) CV error
for different algorithms

Algo 4
Algo 2
CV Algo 1 Algo 3
error

 Step 2: whichever algorithm gave best CV score: learn
a new model with all data, and that's the predictive
model
 What is the expected error rate of this model?

34

Warning: Intensive use of CV can overfit
 If you compare many (complex) models, the
probability that you will find a good one by chance on
your data increases
 Solution:
 Hold out an additional test set before starting the
analysis (or, better, generate this data afterwards)
 Use it to estimate the performance of your final
model
(For small datasets: use two stages of 10-fold CV)

35

A note on performance measures

True class Model 1 Model 2
1
2
Negative
Negative
Positive
Negative
Negative
Negative
 Which of these two models
3 Negative Positive Positive is the best?
4 Negative Positive Negative
5
6
Negative
Negative
Negative
Negative
Negative
Negative
 The choice of an error or
7
8
Negative
Negative
Negative
Negative
Positive
Negative
quality measure is highly
9 Negative Negative Negative application dependent.
10 Positive Positive Positive
11 Positive Positive Negative
14 Positive Negative Negative
15 Positive Positive Negative

36

A note on performance measures
 The error rate is not the only way to assess a predictive
model
 In binary classification, results can be summarized in a
contingency table (aka confusion matrix)
Predicted class
Actual class p n Total
p True Positive False Negative P
n False Positive True Negative N

 Various criterion
Error rate = (FP+FN)/(N+P) Sensitivity = TP/P (aka recall)

Accuracy = (TP+TN)/(N+P) Specificity = TN/(TN+FP)
= 1-Error rate
Precision = TP/(TP+FP) (aka PPV)
37

ROC and Precision/recall curves
 Each point corresponds to a particular choice of the
decision threshold
True Positive Rate
(Sensitivity)

Precision
False Positive Rate Recall
(1-Specificity) (Sensitivity)

38

Outline
 Introduction
 Model selection, cross-validation, overfitting
 Some supervised learning algorithms
 k-NN
 Linear methods
 Artificial neural networks
 Support vector machines
 Decision trees
 Ensemble methods
 Beyond classification and regression

39

Comparison of learning algorithms
 Three main criteria:
 Accuracy:
 Measured by the generalization error (estimated by CV)
 Efficiency:
 Computing times and scalability for learning and testing
 Interpretability:
 Comprehension brought by the model about the input-
output relationship
 Unfortunately, there is usually a tradeoff between
these criteria

40

1-Nearest Neighbor (1-NN)
(prototype based method, instance based learning, non-parametric
method)

 One of the simplest learning algorithm:
 outputs as a prediction the output associated to the
sample which is the closest to the test object
M1 M2 Y
1 0.32 0.81 Healthy
2 0.15 0.38 Disease
3 0.39 0.34 Healthy
4 0.62 0.11 Disease
5 0.92 0.43 ?
?
 2 2
d  5,1 =  0. 32−0 . 92   0 . 81−0 . 43  =0 . 71
d  5,2 =  0. 15− 0 .92   0 . 38−0 . 43  =0 . 77
2 2

d  5,3 =  0. 39−0 . 92   0 . 34− 0. 43  =0 . 71
2 2

d  5,4 =  0 .62−0 . 92   0 . 43−0 . 43  = 0 . 44
2 2

 closest=usually of minimal Euclidian distance
41

Obvious extension: k-NN

?

 Find the k nearest neighbors (instead of only the first
one) with respect to Euclidian distance
 Output the most frequent class (classification) or the
average outputs (regression) among the k neighbors.

42

Effect of k on the error
Error


CV error

LS error

Optimal k k
43

Small exercise

 In this classification problem
with two inputs:
 What it the resubstitution
error (LS error) of 1-NN?
 What is the LOO error of 1-
NN?
 What is the LOO error of 3-
NN?
 What is the LOO error of
22-NN?

Andrew Moore
44

k-NN
 Advantages:
 very simple
 can be adapted to any data type by changing the
distance measure
 Drawbacks:
 choosing a good distance measure is a hard problem
 very sensitive to the presence of noisy variables
 slow for testing

45

Linear methods
 Find a model which is a linear combinations of the inputs
 Regression: y=w 0 w 1 x 1 w 2 x 2 ...w n w n
 Classification: y=c 1 if w 0 w1 x1 ...w n x n 0 , c 2 otherwise

 Several methods exist to find coefficients w0,w1... corresponding
to different objective functions, optimization algorithms, eg.:
 Regression: least-square regression, ridge regression, partial
least square, support vector regression, LASSO...
 Classification: linear discriminant analysis, PLS-discriminant 46
analysis, support vector machines...

Example: ridge regression
 Find w that minimizes (λ>0):

∑i  y i −w x i  ∥w∥
2 2

 From simple algebra, the solution is given by:
r T −1 T
w = X X  I  X y

where X is the input matrix and y is the output vector
 λ regulates complexity (and avoids problems related to
the singularity of XTX)

47

Example: perceptron
 Find w that minimizes:
∑i  y i −w x i 2
using gradient descent: given a training example  x , y 
  y−wT x
∀ j w j w j  x j

 Online algorithm, ie. that treats every example in turn
(vs Batch algorithm that treats all examples at once)
 Complexity is regulated by the learning rate η and the
number of iterations
 Can be adapted to classification
48

Linear methods

 Advantages:
 simple
 there exist fast and scalable variants
 provide interpretable models through variable weights
(magnitude and sign)
 Drawbacks:
 often not as accurate as other (non-linear) methods

49

Non-linear extensions
 Generalization of linear methods:
 y=w 0 w1 1  xw 2 2  x 2 ...w n n  x
 Any linear methods can be applied (but regularization
becomes more important)
 Artificial neural networks (with a single hidden layer):
 y= g ∑ W j g ∑ w i , j x i 
j i
where g is a non linear function (eg. sigmoid)
 (a non linear function of a linear combination of non
linear functions of linear combinations of inputs)
 Kernel methods:
 y=∑ w i i  x  ⇔ y=∑  j k  x j , x 
i j
where k  x , x ' =〈 x ,  x ' 〉 is the dot-product in the
feature space and j indexes training examples 50

Artificial neural networks

 Supervised learning method initially inspired by the
behaviour of the human brain
 Consists of the inter-connection of several small units
 Essentially numerical but can handle classification and
discrete inputs with appropriate coding
 Introduced in the late 50s, very popular in the 90s

51

Hypothesis space: a single neuron

1 A2

A1 x w0
x w1 +

A2 x w2
+ tanh Y _
… A1

AN x wN
tanh
Y=tanh(w1*A1+w2*A2+…+wN*AN+w0) +1

-1

52

Hypothesis space:
Multi-layers Perceptron
 Inter-connection of several neurons (just like in the human
brain)
Hidden layer
Input layer
Output layer

 With a sufficient number of neurons and a sufficient
number of layers, a neural network can model any function
of the inputs. 53

Learning
 Choose a structure
 Tune the value of the parameters (connections
between neurons) so as to minimize the learning
sample error.
 Non-linear optimization by the back-propagation
algorithm. In practice, quite slow.
 Repeat for different structures
 Select the structure that minimizes CV error

54

Illustrative example
1

1 neuron

G2
0
0 1
G1
1
2 +2 neurons

G2
0
0 1
10 +10 neurons G1
1

... ...

G2

0 55
0 1
G1

Artificial neural networks

 Advantages:
 Universal approximators
 May be very accurate (if the method is well used)
 Drawbacks:
 The learning phase may be very slow
 Black-box models, very difficult to interprete
 Scalability

56

Support vector machines

 Recent (mid-90's) and very successful method
 Based on two smart ideas:
 large margin classifier
 kernelized input space

57

Linear classifier

 Where would you place a linear classifier?

58

Margin of a linear classifier

 The margin = the
width that the
boundary could be
increased by before
hitting a datapoint.

59

Maximum-margin linear classifier
 The linear classifier
with the maximum
margin (= Linear
SVM)
 Intuitively, this feels
safest
 Works very well in
practice

Support vectors: the
samples the closest to the
hyperplane 60

Mathematically
 Linearly separable case: amount at solving the
following quadratic programming optimization problem:
1 2
minimizes ∥w∥
2
T
subject to y i w x i −b1, ∀ i=1,... , N

 Decision function:
T
 y=1 if w x−b0, y =−1 otherwise
 Non linearly separable case:
1
∥w∥ C ∑  i
2
minimizes
2 i
T
subject to y i w x i −b1−i , ∀ i=1,... , N
61

Non-linear boundary
– What about this problem?
x1 x12

φ

x2 x22
 Solution:
 map the data into a new feature space where the
boundary is linear
 Find the maximum margin model in this new space

62

The kernel trick
 Intuitively:
 You don't need to compute explicitly the mapping φ
 All you need is a (special) similarity measure between
objects (like for the kNN)
 This similarity measure is called a kernel
 Mathematically:
 The maximum-margin classifier in some feature space
can be written only in terms of dot-products in that
feature space:
k(x,x')=<φ(x),φ(x')>

63

Mathematically
 Primal form of the optimization problem:
1 2
minimizes ∥w∥
2
subject to y i 〈 w ,  xi 〉−b1, ∀ i=1,... , N
 Dual form:
1
minimizes ∑ i − ∑ i  j yi y j 〈 xi  ,  x j 〉
i 2 i, j
subject to i 0 and ∑ i y i =0
i

w=∑ i y i  x i 
i

 Decision function:
 y=1 if 〈 w , x 〉=∑ i y i 〈 x i  ,  x〉=∑ i y i k  x i , x0
i i
 y=−1 otherwise 64

G1 G2 Y
1 0.21 0.64 C1
2 0.57 0.26 C2
3 0.21 0.68 C2
4 0.69 0.52 C1
5 0.83 0.96 C1
6 0.48 -0.52 C2

kernel matrix
1 2 3 4 5 6
1 1 0.14 0.96 0.17 0.01 0.24
2 0.14 1 0.02 0.17 0.22 0.67 SVM
3 0.96 0.02 1 0.15 0.27 0.07
4 0.17 0.7 0.15 1 0.37 0.55 algorithm
5 0.01 0.22 0.27 0.37 1 -0.25
6 0.24 0.67 0.07 0.55 -0.25 1

Y
Class labels 1 C1
2 C2
3 C2 Classification
G1 Y
1 ACGCTCTATAG C1
4 C1 model
5 C1
2 ACTCGCTTAGA C2 6 C2
3 GTCTCTGAGAG C2
4 CGCTAGCGTCG C1
5 CGATCAGCAGC C1
6 GCTCGCGCTCG C2

65

Examples of kernels
 Linear kernel:
k(x,x')= <x,x'>
 Polynomial kernel
k(x,x')=(<x,x'>+1)d
(main parameter: d, the maximum degree)
 Radial basis function kernel:
k(x,x')=exp(-||x-x'||2/(22))
(main parameter: , the spread of the distribution)
● + many kernels that have been defined for structured
data types (eg. texts, graphs, trees, images)
66

Feature ranking with linear kernel

 With a linear kernel, the model looks like:
C1 if w0+w1*x1+w2*x2+...+wK*xK>0
h(x1,x2,...,xK)=
C2 otherwise

 Most important variables are those corresponding to
large |wi|

100
|w|
75

50

25

0

variables
67

SVM parameters

 Mainly two sets of parameters in SVM:
 Optimization algorithm's parameters:
 Control the number of training errors versus the margin
(when the learning sample is not linearly separable)
 Kernel's parameters:
 choice of particular kernel
 given this choice, usually one complexity parameter
 eg, the degree of the polynomial kernel
 Again, these parameters can be determined by cross-
validation

68


 Advantages:
 State-of-the-art accuracy on many problems
 Can handle any data types by changing the kernel
(many applications on sequences, texts, graphs...)
 Drawbacks:
 Tuning the parameter is very crucial to get good results
and somewhat tricky
 Black-box models, not easy to interprete

69

A note on kernel methods
 The kernel trick can be applied to any (learning)
algorithm whose solution can be expressed in terms of
dot-products in the original input space
 It makes a non-linear algorithm from a linear one
 Can work in a very highly dimensional space (even
infinite) without requiring to explicitly compute the
features
 Decouple the representation stage from the learning
stage. The same learning machine can be applied to a
large range of problems
 Examples: ridge regression, perceptron, PCA, k-
means...
70

Decision (classification) trees

 A learning algorithm that can handle:
 Classification problems (binary or multi-valued)
 Attributes may be discrete (binary or multi-valued) or
continuous.
 Classification trees were invented at least twice:
 By statisticians: CART (Breiman et al.)
 By the AI community: ID3, C4.5 (Quinlan et al.)

71

Decision trees

 A decision tree is a tree where:
 Each interior node tests an attribute
 Each branch corresponds to an attribute value
 Each leaf node is labeled with a class

A1
a13
a11
a12
A2 A3
c1
a21 a22 a31 a32

c1 c2 c2 c1

72

A simple database: playtennis

Day Outlook Temperature Humidity Wind Play Tennis
D1 Sunny Hot High Weak No
D2 Sunny Hot High Strong No
D3 Overcast Hot High Weak Yes
D4 Rain Mild Normal Weak Yes
D5 Rain Cool Normal Weak Yes
D6 Rain Cool Normal Strong No
D7 Overcast Cool High Strong Yes
D8 Sunny Mild Normal Weak No
D9 Sunny Hot Normal Weak Yes
D10 Rain Mild Normal Strong Yes
D11 Sunny Cool Normal Strong Yes
D12 Overcast Mild High Strong Yes
D13 Overcast Hot Normal Weak Yes
D14 Rain Mild High Strong No

73

A decision tree for playtennis

Outlook
Sunny Rain
Overcast
Humidity Wind
yes
High Normal Strong Weak

no yes no yes

Should we play tennis on D15?
Day Outlook Temperature Humidity Wind Play Tennis
D15 Sunny Hot High Weak ?

74

Top-down induction of DTs
 Choose « best » attribute
 Split the learning sample
 Proceed recursively until each object is correctly classified

Outlook
Rain
Sunny
Overcast
Day Outlook Temp. Humidity Wind Play Day Outlook Temp. Humidity Wind Play

D1 Sunny Hot High Weak No D4 Rain Mild Normal Weak Yes

D2 Sunny Hot High Strong No D5 Rain Cool Normal Weak Yes

D8 Sunny Mild High Weak No D6 Rain Cool Normal Strong No

D9 Sunny Hot Normal Weak Day Yes Outlook Temp. Humidity Wind Play
D10 Rain Mild Normal Strong Yes

D11 Sunny Cool Normal Strong D3 Yes Overcast Hot High Weak Yes
D14 Rain Mild High Strong No

D7 Overcast Cool High Strong Yes

D12 Overcast Mild High Strong Yes

D13 Overcast Hot Normal Weak Yes

75

Top-down induction of DTs

Procedure learn_dt(learning sample, LS)
 If all objects from LS have the same class

 Create a leaf with that class
 Else
 Find the « best » splitting attribute A
 Create a test node for this attribute
 For each value a of A
 Build LSa= {o  LS | A(o) is a}
 Use Learn_dt(LSa) to grow a subtree from LSa.

76

Which attribute is best ?

A1=? [29+,35-] A2=? [29+,35-]
T F T F

[21+,5-] [8+,30-] [18+,33-] [11+,2-]

 A “score” measure is defined to evaluate splits
 This score should favor class separation at each step (to
shorten the tree depth)
 Common score measures are based on information theory

I (LS, A) H( LS)  | LS left | H(LS left )  | LSright | H(LS right)
| LS | | LS |
77

Effect of number of nodes on error
Error


CV error

LS error

Optimal complexity Nb nodes
78

How can we avoid overfitting?

 Pre-pruning: stop growing the tree earlier, before it
reaches the point where it perfectly classifies the
learning sample

 Post-pruning: allow the tree to overfit and then post-
prune the tree

 Ensemble methods (later)

79

Post-pruning
Error


CV error

2. Tree pruning

1. Tree growing LS error

Optimal complexity Nb nodes
80

Numerical variables

 Example: temperature as a number instead of a
discrete value
 Two solutions:
 Pre-discretize: Cold if Temperature<70, Mild between 70 and
75, Hot if Temperature>75
 Discretize during tree growing:

Temperature
65.4 >65.4

no yes

optimization of the threshold to maximize the score

81

Illustrative example
1
M2<0.33?

yes no

M2
Healthy M1<0.91?
0
0 1
M1<0.23? M2<0.91? M1

Healthy Sick
M2<0.75?
M2<0.49?
Healthy Sick
M2<0.65? Sick

Sick Healthy

82

Regression trees
Trees for regression problems: exactly the same model but
with a number in each leaf instead of a class

Outlook
Rain
Sunny
Overcast
Humidity Wind
45.6
High Normal Strong Weak

22.3 Temperature 64.4 7.4
<71 >71

1.2 3.4

83

Interpretability and attribute selection
 Interpretability
 Intrinsically, a decision tree is highly interpretable
 A tree may be converted into a set of “if…then”
rules.
 Attribute selection
 If some attributes are not useful for classification,
they will not be selected in the (pruned) tree
 Of practical importance, if measuring the value of a
variable is costly (e.g. medical diagnosis)
 Decision trees are often used as a pre-processing for
other learning algorithms that suffer more when
there are irrelevant variables

84

Attribute importance

 In many applications, all variables do not contribute
equally in predicting the output.
 We can evaluate variable importances with trees

Outlook

Humidity
Wind
Temperature

85

Decision and regression trees

 Advantages:
 very fast and scalable method (able to handle a very
large number of inputs and objects)
 provide directly interpretable models and give an idea of
the relevance of attributes
 Drawbacks:
 high variance (more on this later)
 often not as accurate as other methods

86

Ensemble methods

...

Sick Healthy
... Sick

Sick

 Combine the predictions of several models built with a learning
algorithm. Often improve very much accuracy.
 Often used in combination with decision trees for efficiency
reasons
 Examples of algorithms: Bagging, Random Forests, Boosting...

87

Bagging: motivation
 Different learning samples yield different models,
especially when the learning algorithm overfits the data
1 1

0 0
0 1 0 1

As there is only one optimal model, this variance is source
of error
 Solution: aggregate several models to obtain a more
stable one
1

88
0
0 1

Bagging: bootstrap aggregating
Boostrap sampling
(sampling with replacement) 0

...
0 0 10

...

Sick Healthy
... Sick

Sick

Note: the more models, the better. 89

Bootstrap sampling

 Sampling with replacement

G1 G2 Y G1 G2 Y
1 0.74 0.68 Healthy 3 0.86 0.09 Healthy
2 0.78 0.45 Disease 7 -0.34 -0.45 Healthy
3 0.86 0.09 Healthy 2 0.78 0.45 Disease
4 0.2 0.61 Disease 9 0.1 0.3 Healthy
5 0.2 -5.6 Healthy 3 0.86 0.09 Healthy
6 0.32 0.6 Disease 10 -0.34 -0.65 Healthy
7 -0.34 -0.45 Healthy 1 0.74 0.68 Healthy
8 0.89 -0.34 Disease 8 0.89 -0.34 Disease
9 0.1 0.3 Healthy 6 0.32 0.6 Disease
10 -0.34 -0.65 Healthy 10 -0.34 -0.65 Healthy

 Some objects do not appear, some objects appear
several times

90

Boosting
 Idea of boosting: combine many « weak » models to
produce a more powerful one.
 Weak model = a model that underfits the data (strictly,
in classification, a model slightly better than random
guessing)

 Adaboost:
 At each step, adaboost forces the learning algorithm to focus
on the cases from the learning sample misclassified by the
last model
 The predictions of the models are combined through a
weighted vote. More accurate models have more weights in
the vote.
Eg., by duplicating
the missclassified
examples in the
learning sample 91

Boosting
LS

LS1 LS2 …
LST

...
…

Healthy Sick Healthy
w1 w2 wT

Healthy

92

Interpretability and efficiency
 When combined with decision trees, ensemble methods loose
interpretability and efficiency
 However,
 We still can use the ensemble to compute the importance of
variables (by averaging it over all trees)
100

75

50

25

0

 Ensemble methods can be parallelized and boosting type
algorithm uses smaller trees. So, the increase of computing
times is not so detrimental. 93

Example on microarray data
 72 patients, 7129 gene expressions, 2 classes of Leukemia
(ALL and AML) (Golub et al., Science, 1999)
 Leave-one-out error with several variants

Method Error
1 decision tree 22.2% (16/72)
Random forests (k=85,T=500) 9.7% (7/72)
Extra-trees (sth=0.5, T=500) 5.5% (4/72)
Adaboost (1 test node, T=500) 1.4% (1/72)

 Variable importance with boosting
100
Importance

75

50

25

0
94
variables

Method comparison
Method Accuracy Efficiency Interpretability Ease of use
kNN ++ + + ++
DT + +++ +++ +++
Linear ++ +++ ++ +++
Ensemble +++ +++ ++ +++
ANN +++ + + ++
SVM ++++ + + +

 Note:
 The relative importance of the criteria depends on
the specific application
 These are only general trends. Eg., in terms of
accuracy, no algorithm is always better than all 95
others.

Outline
● Introduction
 Introduction

96

Beyond classification and regression
 All supervised learning problems can not be turned
into standard classification or regression problems
 Examples:
 Graph predictions
 Sequence labeling
 image segmentation

97

Structured output approaches
 Decomposition:
 Reduce the problem to several simpler classification or
regression problems by decomposing the output
 Not always possible and does not take into account
interactions between suboutputs
 Kernel output methods
 Extend regression methods to handle an output space
endowed with a kernel
 This can be done with regression trees or ridge regression
for example
 Large margin methods
 Use SVM-based approaches to learn a model that scores
directly input-output pairs:
y=arg max y ' ∑ w i  i  x , y '  98
i

Outline
 Introduction
 Supervised learning
 Other learning protocols/frameworks
● Semi-supervised learning
● Transductive learning
● Active learning
● Reinforcement learning
● Unsupervised learning

99

Labeled versus unlabeled data
 Unlabeled data=input-output pairs without output value
 In many settings, unlabeled data is cheap but labeled
data can be hard to get
 labels may require human experts
 human annotation is expensive, slow, unreliable
 labels may require special devices
 Examples:
 Biomedical domain
 Speech analysis
 Natural language parsing
 Image categorization/segmentation
 Network measurement 100

Semi-supervised learning
 Goal: exploit both labeled and unlabeled data to build
better models than using each one alone
A1 A2 A3 A4 Y
0.01 0.37 T 0.54 Healthy
labeled data -2.3 -1.2 F 0.37 Disease
0.69 -0.78 F 0.63 Healthy
-0.56 -0.89 T -0.42
unlabeled data -0.85 0.62 F -0.05
-0.17 0.09 T 0.29
test data -0.09 0.3 F 0.17 ?

 Why would it improve?

101

Some approaches
 Self-training
 Iteratively label some unlabeled examples with a model
learned from the previously labeled examples
 Semi-supervised SVM (S3VM)
 Enumerate all possible labeling of the unlabeled
examples
 Learn an SVM for each labeling
 Pick the one with the largest margin

102

Some approaches
 Graph-based algorithms
 Build a graph over the (labeled and unlabeled)
examples (from the inputs)
 Learn a model that predicts well labeled examples and
is smooth over the graph

103

Transductive learning
 Like supervised learning but we have access to the
test data from the beginning and we want to exploit it
 We don't want a model, only compute predictions for
the unlabeled data
 Simple solution:
 Apply semi-supervised learning techniques using the
test data as unlabeled data to get a model
 Use the resulting model to make predictions on the test
data
 There exist also specific algorithms that avoid building
a model

104

Active learning
 Goal:
 given unlabeled data, find (adaptively) the examples to
label in order to learn an accurate model
 The hope is to reduce the number of labeled instances
with respect to the standard batch SL
 Usually, in an online setting:
 choose the k “best” unlabeled examples
 determine their labels
 update the model and iterate
 Algorithms differ in the way the unlabeled examples
are selected
 Example: choose the k examples for which the model
predictions are the most uncertain
105

Reinforcement learning
Learning form interactions

a0 a1 a2
s0 s1 s2 ...
r0 r1 r2

Goal: learn to choose sequence of actions (= policy) that
maximizes 2
r 0 r 1 r 2 ... , where 01 106

RL approaches
 System is usually modeled by
 state transition probabilities P  st 1∣s t , at 
 reward probabilities P r t1∣st , at 
(= Markov Decision Process)
 Model of the dynamics and reward is known try to
compute optimal policy by dynamic programming
 Model is unknown
 Model-based approaches first learn a model of the
dynamics and then derive an optimal policy from it (DP)
 Model-free approaches learn directly a policy from
the observed system trajectories
107

Reinforcement versus supervised learning
 Batch-mode SL: learn a mapping from input to output from
observed input-output pairs
 Batch-mode RL: learn a mapping from state to action from
observed (state,action,reward) triplets
 Online active learning: combine SL and (online) selection
of instances to label
 Online RL: combine policy learning with control of the
system and generation of the training trajectories
 Note:
 RL would reduce to SL if the optimal action was known
in each state
 SL is used inside RL to model system dynamics and/or
value functions 108

Examples of applications
 Robocup Soccer Teams (Stone & Veloso, Riedmiller et al.)
 Inventory Management (Van Roy, Bertsekas, Lee
&Tsitsiklis)
 Dynamic Channel Assignment, Routing (Singh &
Bertsekas, Nie & Haykin, Boyan & Littman)
 Elevator Control (Crites & Barto)
 Many Robots: navigation, bi-pedal walking, grasping,
switching between skills...
 Games: TD-Gammon and Jellyfish (Tesauro, Dahl)

109

Unsupervised learning
 Unsupervised learning tries to find any regularities in
the data without guidance about inputs and outputs

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19
-0.27 -0.15 -0.14 0.91 -0.17 0.26 -0.48 -0.1 -0.53 -0.65 0.23 0.22 0.98 0.57 0.02 -0.55 -0.32 0.28 -0.33
-2.3 -1.2 -4.5 -0.01 -0.83 0.66 0.55 0.27 -0.65 0.39 -1.3 -0.2 -3.5 0.4 0.21 -0.87 0.64 0.6 -0.29
0.41 0.77 -0.44 0 0.03 -0.82 0.17 0.54 -0.04 0.6 0.41 0.66 -0.27 -0.86 -0.92 0 0.48 0.74 0.49
0.28 -0.71 -0.82 0.27 -0.21 -0.9 0.61 -0.57 0.44 0.21 0.97 -0.27 0.74 0.2 -0.16 0.7 0.79 0.59 -0.33
-0.28 0.48 0.79 -0.14 0.8 0.28 0.75 0.26 0.3 -0.78 -0.72 0.94 -0.78 0.48 0.26 0.83 -0.88 -0.59 0.71
0.01 0.36 0.03 0.03 0.59 -0.5 0.4 -0.88 -0.53 0.95 0.15 0.31 0.06 0.37 0.66 -0.34 0.79 -0.12 0.49
-0.53 -0.8 -0.64 -0.93 -0.51 0.28 0.25 0.01 -0.94 0.96 0.25 -0.12 0.27 -0.72 -0.77 -0.31 0.44 0.58 -0.86
0.04 0.94 -0.92 -0.38 -0.07 0.98 0.1 0.19 -0.57 -0.69 -0.23 0.05 0.13 -0.28 0.98 -0.08 -0.3 -0.84 0.47
-0.88 -0.73 -0.4 0.58 0.24 0.08 -0.2 0.42 -0.61 -0.13 -0.47 -0.36 -0.37 0.95 -0.31 0.25 0.55 0.52 -0.66
-0.56 0.97 -0.93 0.91 0.36 -0.14 -0.9 0.65 0.41 -0.12 0.35 0.21 0.22 0.73 0.68 -0.65 -0.4 0.91 -0.64

 Are there interesting groups of variables or samples?
outliers? What are the dependencies between
variables?

110

Unsupervised learning methods

 Many families of problems exist, among which:
 Clustering: try to find natural groups of
samples/variables
 eg: k-means, hierarchical clustering
 Dimensionality reduction: project the data from a high-
dimensional space down to a small number of
dimensions
 eg: principal/independent component analysis, MDS
 Density estimation: determine the distribution of data
within the input space
 eg: bayesian networks, mixture models.
111

Clustering

 Goal: grouping a collection of objects into subsets or
“clusters”, such that those within each cluster are more
closely related to one another than objects assigned to
different clusters

112

Clustering

variables
 Clustering rows
grouping similar objects
 Clustering columns
grouping similar variables
objects

across samples
 Bi-Clustering/Two-way
clustering
grouping objects that are
Bi-cluster
Cluster of
objects
similar across a subset of
Cluster of variables
variables

113

Clustering

 Two essential components of cluster analysis:
 Distance measure: A notion of distance or similarity of
two objects: When are two objects close to each other?
 Cluster algorithm: A procedure to minimize distances
of objects within groups and/or maximize distances
between groups

114

Examples of distance measures
 Euclidean distance measures
average difference across coordinates
 Manhattan distance measures
average difference across
coordinates, in a robust way
 Correlation distance measures
difference with respect to trends

115

Clustering algorithms
 Popular algorithms for clustering
 hierarchical clustering
 K-means
 SOMs (Self-Organizing Maps)
 autoclass, mixture models...
 Hierarchical clustering allows the choice of the
dissimilarity matrix.
 k-Means and SOMs take original data directly as input.
Attributes are assumed to live in Euclidean space.

116

Hierarchical clustering
Agglomerative clustering:
1. Each object is assigned to its own cluster
2. Iteratively:
 the two most similar clusters are joined and
replaced by a new one
 the distance matrix is updated with this new cluster
replacing the two joined clusters

(divisive clustering would start from a big cluster)

117

Distance between two clusters
 Single linkage uses the smallest distance

 Complete linkage uses the largest distance

 Average linkage uses the average distance

118


(wikipedia)

119

Dendrogram
 Hierarchical clustering are visualized through dendrograms
 Clusters that are joined are combined by a line
 Height of line is distance between clusters
 Can be used to determine visually the number of
clusters

120

 Strengths
 No need to assume any particular number of clusters
 Can use any distance matrix
 Find sometimes a meaningful taxonomy
 Limitations
 Find a taxonomy even if it does not exist
 Once a decision is made to combine two clusters it
cannot be undone
 Not well theoretically motivated

121

k-Means clustering

 Partitioning algorithm with a prefixed number k of
clusters
 Use Euclidean distance between objects
 Try to minimize the sum of intra-cluster variances
k
∑ ∑ d 2  o,c j 
j= 1 o∈Cluster j
where cj is the center of cluster j and d2 is the Euclidean
distance

122

k-Means clustering

123

k-Means clustering

124

k-Means clustering

125

k-Means clustering
 Strengths
 Simple, understandable
 Can cluster any new point (unlike hierarchical
clustering)
 Well motivated theoretically
 Limitations
 Must fix the number of clusters beforehand
 Sensitive to the initial choice of cluster centers
 Sensitive to outliers

126

Suboptimal clustering
 You could obtain any of these from a random start of
k-means

 Solution: restart the algorithm several times

127

Principal Component Analysis

 An exploratory technique used to reduce the
dimensionality of the data set to a smaller space (2D,
3D)

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
PC1 PC2
0.25 0.93 0.04 -0.78 -0.53 0.57 0.19 0.29 0.37 -0.22 0.36 0.1
-2.3 -1.2 -4.5 -0.51 -0.76 0.07 0.81 0.95 0.99 0.26 -2.3 -1.2
-0.29 -1 0.73 -0.33 0.52 0.13 0.13 0.53 -0.5 -0.48 0.27 -0.89
-0.16 -0.17 -0.26 0.32 -0.08 -0.38 -0.48 0.99 -0.95 0.34 -0.19 0.7
0.07 -0.87 0.39 0.5 -0.63 -0.53 0.79 0.88 0.74 -0.14 -0.77 -0.7
0.61 0.15 0.68 -0.94 0.5 0.06 -0.56 0.49 0 -0.77 -0.65 -0.99

 Transform some large number of variables into a
smaller number of uncorrelated variables called
principal components (PCs)

128

Objectives of PCA

 Reduce dimensionality (pre-processing for other
methods)
 Choose the most useful (informative) variables
 Compress the data
 Visualize multidimensional data
 to identify groups of objects
 to identify outliers

129

Basic idea
 Goal: map data points into a few dimensions while
trying to preserve the variance of the data as much as
possible

First
component

Second
component

130

Each component is a linear combination of
the original variables
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 PC1 PC2
-0.39 -0.38 0.29 0.65 0.15 0.73 -0.57 0.91 -0.89 -0.17 0.62 -0.33
-2.3 -1.2 -4.5 -0.15 0.86 -0.85 0.43 -0.19 -0.83 -0.4 -2.3 -1.2
0.9 0.4 -0.11 0.62 0.94 0.97 0.1 -0.41 0.01 0.1 0.88 0.31
-0.82 -0.31 0.14 0.22 -0.49 -0.76 0.27 0 -0.43 -0.81 -0.18 -0.05
0.71 0.39 -0.09 0.26 -0.46 -0.05 0.46 0.39 -0.01 0.64 -0.39 -0.01
-0.25 0.27 -0.81 -0.42 0.62 0.54 -0.67 -0.15 -0.46 0.69 -0.61 0.53
Scores for
each sample
and PC
PC1=0.2*A1+3.4*A2-4.5*A3 VAR(PC1)=4.5  45%
PC2=0.4*A4+5.6*A5+2.3*A7 VAR(PC2)=3.3  33%
... ...
Loading of a variable For each component, we
 Gives an idea of its importance in
have a measure of the
the component percentage of the variance
 Can be use for selecting
of the initial data that it
biomarkers contains
131

Books
 Reference textbooks for the course
 The elements of statistical learning: data mining, inference, and
prediction. T. Hastie et al, Springer, 2001
 Pattern Recognition and Machine Learning (Information Science and
Statistics). C.M.Bishop, Springer, 2004
 Other textbooks
 Pattern classification (2nd edition). R.Duda, P.Hart, D.Stork, Wiley
Interscience, 2000
 Introduction to Machine Learning. Ethan Alpaydin, MIT Press, 2004.
 Machine Learning. Tom Mitchell, McGraw Hill, 1997.

132

Books
 More advanced topics
 kernel methods for pattern analysis. J. Shawe-Taylor and N. Cristianini.
Cambridge University Press, 2004
 Reinforcement Learning: An Introduction. R.S. Sutton and A.G. Barto.
MIT Press, 1998
 Neuro-Dynamic Programming. D.P Bertsekas and J.N. Tsitsiklis. Athena
Scientific, 1996
 Semi-supervised learning. Chapelle et al., MIT Press, 2006
 Predicting structured data. G. Bakir et al., MIT Press, 2007

133

Softwares

 Pepito
 www.pepite.be
 Free for academic research and education
 WEKA
 http://www.cs.waikato.ac.nz/ml/weka/
 Many R and Matlab packages
 http://www.kyb.mpg.de/bs/people/spider/
 http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html


134

Journals

 Journal of Machine Learning Research
 Machine Learning
 IEEE Transactions on Pattern Analysis and Machine
Intelligence
 Journal of Artificial Intelligence Research
 Neural computation
 Annals of Statistics
 IEEE Transactions on Neural Networks
 Data Mining and Knowledge Discovery
 ...
135

Conferences
 International Conference on Machine Learning (ICML)
 European Conference on Machine Learning (ECML)
 Neural Information Processing Systems (NIPS)
 Uncertainty in Artificial Intelligence (UAI)
 International Joint Conference on Artiﬁcial Intelligence
(IJCAI)
 International Conference on Artiﬁcial Neural Networks
(ICANN)
 Computational Learning Theory (COLT)
 Knowledge Discovery and Data mining (KDD)
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An introduction to Machine Learning

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An introduction to Machine Learning