Jialiang Bao, Joseph Boyd, James Forkey, Shengwen Han, Trevor Hodde, Yumou Wang 10/01/2013
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1 Simple Classifiers Jialiang Bao, Joseph Boyd, James Forkey, Shengwen Han, Trevor Hodde, Yumou Wang 1
2 Overview Pruning 2
3 Section 3.1: Simplicity First Pruning Always start simple! Accuracy can be misleading. 3
4 Section 3.1: Simplicity First Imagine two datasets: Pruning 4
5 Section 3.1: Simplicity First Now apply your favorite classifier: Pruning 60% 80 % Which is better? 5
6 Section 3.1: Simplicity First Compare to simple classifier (ZeroR or OneR): Pruning 60% 10% 80 % 90 % It depends on the dataset 6
7 Section 3.1: Simplicity First Pruning 60% 10% 60% accuracy is a big improvement over the simple classifier s accuracy of 10% 7
8 Section 3.1: Simplicity First Pruning 80 % 90 % 80% accuracy for the complex classifier seems good, but its worse than the simple classifier. 8
9 Section 3.1: Simplicity First Pruning Two simple classifiers: ZeroR Always choose most common value of target class OneR One attribute does all the work 9
10 Section 3.2: Pruning is a general problem Any ML method may overfit the training data Work well on independent test data? 10
11 Section 3.2: Example1:Weather.numeric OneR Pruning Making a rule on Temp is quite complex. OneR has a parameter to limit the complexity. 11
12 Section 3.2: Remove outlook Pruning 12
13 Section 3.2: Pruning 13
14 Section 3.2: Pruning 14
15 Section 3.2: Example2:Diabetes ZeroR 65% Pruning 15
16 Section 3.2: minbucketsize=1 Pruning pedi 16
17 Section 3.2: Pruning 17
18 Section 3.2: Pruning Evaluating on training set is misleading How to choose the best ML method using training, test, validation sets all together 18
19 Section 3.3: (OneR: One attribute does all the work) Opposite strategy: use all the attributes Naïve Bayes method Two assumptions: Attributes are equally important a priori statistically independent Pruning knowing the value of one attribute says nothing about the value of the other Independence assumption is never correct But often works well in practice 19
20 Section 3.3: Pruning Bayes method By Thomas Bayes, British mathematician, Probability of event H given evidence E Pr[ H ] is a priori probability of H Probability of event before evidence is seen Pr[ H E ] is a posteriori probability of H Probability of event after evidence is seen 20
21 Section 3.3: Naïve assumption: Evidence splits into parts that are independent Pruning 21
22 Section 3.3: Pruning 22
23 Section 3.3: Pruning 23
24 Section 3.3: Pruning 24
25 Section 3.3: Avoid zero frequencies: start all counts at 1 Pruning 25
26 Section 3.3: Naïve Bayes : all attributes contribute equally and independently Works surprisingly well Why? classification doesn t need accurate probability estimates so long as the greatest probability is assigned to the correct class Adding redundant attributes causes problems (e.g. identical attributes) -> attribute selection Pruning 26
27 J48 Top-down recursive divide and conquer Select attribute for root node Split instances into subsets Repeat recursively for each branch The Problem? Find the best attribute to split at each stage 27
28 How to select the best attribute The quest for purity Find the attribute with the least fluctuation That is, the node we gain the most information from Information theory: measure information gain in bits entropy(p 1,p 2, p n ) = - p 1 logp 1 - p 2 logp 2. p n logp n Information gain Amount of information gained by knowing the value of the attribute (entropy of distribution before the split ) (entropy of distribution after it) 28
29 Example We want: entropy(play) entropy(play outlook) P(play = yes) = 9/14 P(play = no) =5/14 Entropy(play) = 9/14log 2 (9/14) 5/14 log 2 (5/14) =.940 Find entropy for outlook = sunny, overcast, and rainy Entropy(outlook = sunny) 2/5log 2 (2/5) 3/5log 2 (3/5) =.971 Entropy(outlook = overcast) 4/4log 2 (4/4) 0 log 2 0 = 0 Entropy(outlook = rain) 3/5log 2 (3/5) 2/5log 2 (2/5) =
30 Example (cont d) We want: entropy(play) entropy(play outlook) Entropy(play) =.940 Entropy(outlook = sunny) =.971 Entropy(outlook = overcast) = 0 Entropy(outlook = rain).971 Find entropy(play outlook) P(rain) = 5/14 P(overcast = 4/14 P(sunny) = 5/14 Entropy(play outlook) 5/14(.971) (4/14) 5/14(.971) =.694 Entropy(play) entropy(play outlook) =
31 Reality Cool. How about a real world decision tree? They re actually pretty intuitive for humans We don t have to worry about choosing attributes J48 does it for us! J48 does it for us! 31
32 Reality Cool. How about a real world decision tree? They re actually pretty intuitive for humans We don t have to worry about choosing attributes J48 does it for us! Vulnerable to overfitting 32
33 Section 3.5: Pruning Pruning Decision Tree Pruning is a technique used in machine learning that reduces the size of a decision tree by removing sections that provide little classification power The goal is to reduce complexity of the classifer and improve accuracy through the reduction of overfitting. 33 Section 3.5: Pruning
34 Section 3.5: Pruning Pruning happens automatically by most classifiers after the tree is constructed Example: Breast Cancer data set with J48 Classifier Pruning Click on the highlighted box to see a list of options to run the classifier with 34 Section 3.5: Pruning
35 Section 3.5: Pruning Pruning Select an option for unpruned 35 Section 3.5: Pruning
36 Section 3.5: Pruning Pruning Default, pruned J48 classifier is about 75% accurate 36 Section 3.5: Pruning
37 Section 3.5: Pruning Pruning Accuracy drops to about 69% when unpruned! 37 Section 3.5: Pruning
38 Section 3.5: Pruning Pruning Typically, a classifier will stop splitting nodes once they get very small Classifiers will build the full tree and then start working in from the leaves. A statistical test is used to determine which leaves will be pruned Interior nodes can also be pruned to move lower levels of the tree upward (this is the default behavior) How do classifiers do their pruning? Section 3.5: Pruning 38
39 Section 3.5: Pruning Pruning Over-fitting! Classifier works well on training data, but the independent test data is too complex Sometimes a decision tree is too complex Simplifying the tree could improve accuracy as well as performance Pruning is not restricted to trees! Can be used on other data structures to improve performance Why Pruning? Section 3.5: Pruning 39
40 Section 3.6: Pruning Rote learning: simplest form of learning To classify a new instance, search training set for one that is most like it The instances themselves are the knowledge lazy learning: do nothing till you make predictions No decision tree 40
41 Section 3.6: Same class Pruning 41
42 Section 3.6: Search training set for one that is most like it Pruning Thus, we need a similarity function Training data young: 20, 22, 28, 30 middle-age: 36, 38, 65, 56 elderly: 75, 78, 95, 100 Average Test data
43 Section 3.6: What is noisy instances? Pruning They are incorrect instances in the training set 43
44 Section 3.6: Pruning 44
45 Section 3.6: Pruning Advantages: Accurate because it will make predictions based on current data Disadvantages: Speed slow because it will recalculate each time 45
46 Thank you! Any Questions? 46
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Séance «IDT» de l'ue «apprentissage automatique» Bruno Bouzy bruno.bouzy@parisdescartes.fr www.mi.parisdescartes.fr/~bouzy Outline Induction task ID3 Entropy (disorder) minimization Noise Unknown attribute
Decision Trees. None Some Full > No Yes. No Yes. No Yes. No Yes. No Yes. No Yes. No Yes. Patrons? WaitEstimate? Hungry? Alternate?
Decision rees Decision trees is one of the simplest methods for supervised learning. It can be applied to both regression & classification. Example: A decision tree for deciding whether to wait for a place
ML techniques. symbolic techniques different types of representation value attribute representation representation of the first order
MACHINE LEARNING Definition 1: Learning is constructing or modifying representations of what is being experienced [Michalski 1986], p. 10 Definition 2: Learning denotes changes in the system That are adaptive
Generative v. Discriminative classifiers Intuition
Logistic Regression (Continued) Generative v. Discriminative Decision rees Machine Learning 10701/15781 Carlos Guestrin Carnegie Mellon University January 31 st, 2007 2005-2007 Carlos Guestrin 1 Generative