SIMS 290-2: Applied Natural Language Processing

1
SIMS 290-2 Applied Natural Language Processing
Barbara Rosario October 4, 2004    
2
Today

• Algorithms for Classification
• Binary classification
• Perceptron
• Winnow
• Support Vector Machines (SVM)
• Kernel Methods
• Multi-Class classification
• Decision Trees
• Naïve Bayes
• K nearest neighbor

3
Binary Classification examples

• Spam filtering (spam, not spam)
• Customer service message classification (urgent
  vs. not urgent)
• Information retrieval (relevant, not relevant)
• Sentiment classification (positive, negative)
• Sometime it can be convenient to treat a
  multi-way problem like a binary one one class
  versus all the others, for all classes

4
Binary Classification

• Given some data items that belong to a positive
  (1 ) or a negative (-1 ) class
• Task Train the classifier and predict the class
  for a new data item
• Geometrically find a separator

5
Linear versus Non Linear algorithms

• Linearly separable data if all the data points
  can be correctly classified by a linear
  (hyperplanar) decision boundary

6
Linearly separable data
7
Non linearly separable data
8
Non linearly separable data
Non Linear Classifier
9
Linear versus Non Linear algorithms

• Linear or Non linear separable data?
• We can find out only empirically
• Linear algorithms (algorithms that find a linear
  decision boundary)
• When we think the data is linearly separable
• Advantages
• Simpler, less parameters
• Disadvantages
• High dimensional data (like for NLT) is usually
  not linearly separable
• Examples Perceptron, Winnow, SVM
• Note we can use linear algorithms also for non
  linear problems (see Kernel methods)

10
Linear versus Non Linear algorithms

• Non Linear
• When the data is non linearly separable
• Advantages
• More accurate
• Disadvantages
• More complicated, more parameters
• Example Kernel methods
• Note the distinction between linear and non
  linear applies also for multi-class
  classification (well see this later)

11
Simple linear algorithms

• Perceptron and Winnow algorithm
• Linear
• Binary classification
• Online (process data sequentially, one data point
  at the time)
• Mistake driven
• Simple single layer Neural Networks

12
Linear binary classification

• Data (xi,yi)i1...n
• x in Rd (x is a vector in d-dimensional
  space)
• ? feature vector
• y in -1,1
• ? label (class, category)
• Question
• Design a linear decision boundary wx b
  (equation of hyperplane) such that the
  classification rule associated with it has
  minimal probability of error
• classification rule
• y sign(w x b) which means
• if wx b gt 0 then y 1
• if wx b lt 0 then y -1

13
Linear binary classification

• Find a good hyperplane
• (w,b) in Rd1
• that correctly classifies data points as much
  as possible
• In online fashion one data point at the time,
  update weights as necessary

wx b 0
Classification Rule y sign(wx b)
14
Perceptron algorithm

• Initialize w1 0
• Updating rule For each data point x
• If class(x) ! decision(x,w)
• then
• wk1 ? wk yixi
• k ? k 1
• else
• wk1 ? wk
• Function decision(x, w)
• If wx b gt 0 return 1
• Else return -1

wk
1
0
-1
wk x b 0
15
Perceptron algorithm

• Online can adjust to changing target, over time
• Advantages
• Simple and computationally efficient
• Guaranteed to learn a linearly separable problem
  (convergence, global optimum)
• Limitations
• Only linear separations
• Only converges for linearly separable data
• Not really efficient with many features

16
Winnow algorithm

• Another online algorithm for learning perceptron
  weights
• f(x) sign(wx b)
• Linear, binary classification
• Update-rule again error-driven, but
  multiplicative (instead of additive)

17
Winnow algorithm

• Initialize w1 0
• Updating rule For each data point x
• If class(x) ! decision(x,w)
• then
• wk1 ? wk yixi ? Perceptron
• wk1 ? wk exp(yixi) ? Winnow
• k ? k 1
• else
• wk1 ? wk
• Function decision(x, w)
• If wx b gt 0 return 1
• Else return -1

wk
1
0
-1
wk x b 0
18
Perceptron vs. Winnow

• Assume
• N available features
• only K relevant items, with KltltN
• Perceptron number of mistakes O( K N)
• Winnow number of mistakes O(K log N)
• Winnow is more robust to high-dimensional feature
  spaces

19
Perceptron vs. Winnow

• Perceptron
• Online can adjust to changing target, over time
• Advantages
• Simple and computationally efficient
• Guaranteed to learn a linearly separable problem
• Limitations
• only linear separations
• only converges for linearly separable data
• not really efficient with many features

• Winnow
• Online can adjust to changing target, over time
• Advantages
• Simple and computationally efficient
• Guaranteed to learn a linearly separable problem
• Suitable for problems with many irrelevant
  attributes
• Limitations
• only linear separations
• only converges for linearly separable data
• not really efficient with many features
• Used in NLP

20
Weka

• Winnow in Weka

21
Large margin classifier

• Another family of linear algorithms
• Intuition (Vapnik, 1965)
• If the classes are linearly separable
• Separate the data
• Place hyper-plane far from the data large
  margin
• Statistical results guarantee good generalization

BAD
22
Large margin classifier

• Intuition (Vapnik, 1965) if linearly separable
• Separate the data
• Place hyperplane far from the data large
  margin
• Statistical results guarantee good generalization

GOOD
? Maximal Margin Classifier
23
Large margin classifier

• If not linearly separable
• Allow some errors
• Still, try to place hyperplane far from each
  class

24
Large Margin Classifiers

• Advantages
• Theoretically better (better error bounds)
• Limitations
• Computationally more expensive, large quadratic
  programming

25
Support Vector Machine (SVM)

• Large Margin Classifier
• Linearly separable case
• Goal find the hyperplane that maximizes the
  margin

26
Support Vector Machine (SVM)

• Text classification
• Hand-writing recognition
• Computational biology (e.g., micro-array data)
• Face detection
• Face expression recognition
• Time series prediction

27
Non Linear problem
28
Non Linear problem
29
Non Linear problem

• Kernel methods
• A family of non-linear algorithms
• Transform the non linear problem in a linear one
  (in a different feature space)
• Use linear algorithms to solve the linear problem
  in the new space

30
Main intuition of Kernel methods

• (Copy here from black board)

31
Basic principle kernel methods

• ? Rd ? RD (D gtgt d)

Xx z
32
Basic principle kernel methods

• Linear separability more likely in high
  dimensions
• Mapping ? maps input into high-dimensional
  feature space
• Classifier construct linear classifier in
  high-dimensional feature space
• Motivation appropriate choice of ? leads to
  linear separability
• We can do this efficiently!

33
Basic principle kernel methods

• We can use the linear algorithms seen before
  (Perceptron, SVM) for classification in the
  higher dimensional space

34
Multi-class classification

• Given some data items that belong to one of M
  possible classes
• Task Train the classifier and predict the class
  for a new data item
• Geometrically harder problem, no more simple
  geometry

35
Multi-class classification
36
Multi-class classification Examples

• Author identification
• Language identification
• Text categorization (topics)

37
(Some) Algorithms for Multi-class classification

• Linear
• Parallel class separators Decision Trees
• Non parallel class separators Naïve Bayes
• Non Linear
• K-nearest neighbors

38
Linear, parallel class separators (ex Decision
Trees)
39
Linear, NON parallel class separators (ex Naïve
Bayes)
40
Non Linear (ex k Nearest Neighbor)
41
Decision Trees

• Decision tree is a classifier in the form of a
  tree structure, where each node is either
• Leaf node - indicates the value of the target
  attribute (class) of examples, or
• Decision node - specifies some test to be carried
  out on a single attribute-value, with one branch
  and sub-tree for each possible outcome of the
  test.
• A decision tree can be used to classify an
  example by starting at the root of the tree and
  moving through it until a leaf node, which
  provides the classification of the instance.

42
Training Examples
Goal learn when we can play Tennis and when we
cannot
43
Decision Tree for PlayTennis
Outlook
Sunny
Overcast
Rain
Humidity
Wind
Yes
High
Normal
Strong
Weak
No
Yes
Yes
No
44
Decision Tree for PlayTennis
Outlook
Sunny
Overcast
Rain
Humidity
High
Normal
No
Yes
45
Decision Tree for PlayTennis
Outlook Temperature Humidity Wind PlayTennis
Sunny Hot High
Weak ?
46
Decision Tree for Reuter classification
47
Decision Tree for Reuter classification
48
Building Decision Trees

• Given training data, how do we construct them?
• The central focus of the decision tree growing
  algorithm is selecting which attribute to test at
  each node in the tree. The goal is to select the
  attribute that is most useful for classifying
  examples.
• Top-down, greedy search through the space of
  possible decision trees.
• That is, it picks the best attribute and never
  looks back to reconsider earlier choices.

49
Building Decision Trees

• Splitting criterion
• Finding the features and the values to split on
• for example, why test first cts and not vs?
• Why test on cts lt 2 and not cts lt 5 ?
• Split that gives us the maximum information gain
  (or the maximum reduction of uncertainty)
• Stopping criterion
• When all the elements at one node have the same
  class, no need to split further
• In practice, one first builds a large tree and
  then one prunes it back (to avoid overfitting)
• See Foundations of Statistical Natural Language
  Processing, Manning and Schuetze for a good
  introduction

50
Decision Trees Strengths

• Decision trees are able to generate
  understandable rules.
• Decision trees perform classification without
  requiring much computation.
• Decision trees are able to handle both continuous
  and categorical variables.
• Decision trees provide a clear indication of
  which features are most important for prediction
  or classification.

51
Decision Trees weaknesses

• Decision trees are prone to errors in
  classification problems with many classes and
  relatively small number of training examples.
• Decision tree can be computationally expensive to
  train.
• Need to compare all possible splits
• Pruning is also expensive
• Most decision-tree algorithms only examine a
  single field at a time. This leads to rectangular
  classification boxes that may not correspond well
  with the actual distribution of records in the
  decision space.

52
Decision Trees

• Decision Trees in Weka

53
Naïve Bayes
More powerful that Decision Trees
54
Naïve Bayes Models

• Graphical Models graph theory plus probability
  theory
• Nodes are variables
• Edges are conditional probabilities

A
P(A) P(BA) P(CA)
55
Naïve Bayes Models

• Graphical Models graph theory plus probability
  theory
• Nodes are variables
• Edges are conditional probabilities
• Absence of an edge between nodes implies
  independence between the variables of the nodes

A
P(A) P(BA) P(CA)
56
Naïve Bayes for text classification
57
Naïve Bayes for text classification
earn
Shr
per
58
Naïve Bayes for text classification
Topic
w1
w3
wn-1

• The words depend on the topic P(wi Topic)
• P(ctsearn) gt P(tennis earn)
• Naïve Bayes assumption all words are independent
  given the topic
• From training set we learn the probabilities
  P(wi Topic) for each word and for each topic in
  the training set

59
Naïve Bayes for text classification
Topic
w1
w3
wn-1

• To Classify new example
• Calculate P(Topic w1, w2, wn) for each topic
• Bayes decision rule
• Choose the topic T for which
• P(T w1, w2, wn) gt P(T w1, w2, wn) for
  each T? T

60
Naïve Bayes Math

• Naïve Bayes define a joint probability
  distribution
• P(Topic , w1, w2, wn) P(Topic)? P(wi Topic)
• We learn P(Topic) and P(wi Topic) in training
• Test we need P(Topic w1, w2, wn)
• P(Topic w1, w2, wn) P(Topic , w1, w2,
  wn) / P(w1, w2, wn)

61
Naïve Bayes Strengths

• Very simple model
• Easy to understand
• Very easy to implement
• Very efficient, fast training and classification
• Modest space storage
• Widely used because it works really well for text
  categorization
• Linear, but non parallel decision boundaries

62
Naïve Bayes weaknesses

• Naïve Bayes independence assumption has two
  consequences
• The linear ordering of words is ignored (bag of
  words model)
• The words are independent of each other given the
  class False
• President is more likely to occur in a context
  that contains election than in a context that
  contains poet
• Naïve Bayes assumption is inappropriate if there
  are strong conditional dependencies between the
  variables
• (But even if the model is not right, Naïve
  Bayes models do well in a surprisingly large
  number of cases because often we are interested
  in classification accuracy and not in accurate
  probability estimations)

63
Naïve Bayes

• Naïve Bayes in Weka

64
k Nearest Neighbor Classification

• Nearest Neighbor classification rule to classify
  a new object, find the object in the training set
  that is most similar. Then assign the category of
  this nearest neighbor
• K Nearest Neighbor (KNN) consult k nearest
  neighbors. Decision based on the majority
  category of these neighbors. More robust than k
  1
• Example of similarity measure often used in NLP
  is cosine similarity

65
1-Nearest Neighbor
66
1-Nearest Neighbor
67
3-Nearest Neighbor
68
3-Nearest Neighbor
Assign the category of the majority of the
neighbors
69
k Nearest Neighbor Classification

• Strengths
• Robust
• Conceptually simple
• Often works well
• Powerful (arbitrary decision boundaries)
• Weaknesses
• Performance is very dependent on the similarity
  measure used (and to a lesser extent on the
  number of neighbors k used)
• Finding a good similarity measure can be
  difficult
• Computationally expensive

70
Summary

• Algorithms for Classification
• Linear versus non linear classification
• Binary classification
• Perceptron
• Winnow
• Support Vector Machines (SVM)
• Kernel Methods
• Multi-Class classification
• Decision Trees
• Naïve Bayes
• K nearest neighbor
• On Wednesday Weka