Machine Learning: Decision Trees Homework 4 assigned courtesy: Geoffrey Hinton, Yann LeCun, Tan, Steinbach, Kumar

What is machine learning? It is very hard to write programs that solve problems like recognizing a face. We don’t know what program to write because we don’t know how its done. Even if we had a good idea about how to do it, the program might be horrendously complicated. Instead of writing a program by hand, we collect lots of examples that specify the correct output for a given input. A machine learning algorithm then takes these examples and produces a program that does the job. The program produced by the learning algorithm may look very different from a typical hand-written program. It may contain millions of numbers. If we do it right, the program works for new cases as well as the ones we trained it on.

Handwriting/face recognition/detection

Visual object/action recognition Aeroplanes Bicycles Birds Boats Buses Cars Cats Trains Cows Chairs Dogs Horses

Different types of learning Supervised Learning: given training examples of inputs and corresponding outputs, produce the “correct” outputs for new inputs. Example: character recognition. Unsupervised Learning: given only inputs as training, find structure in the world: discover clusters, manifolds, characterize the areas of the space to which the observed inputs belong Reinforcement Learning: an agent takes inputs from the environment, and takes actions that affect the environment. Occasionally, the agent gets a scalar reward or punishment. The goal is to learn to produce action sequences that maximize the expected reward.

Applications handwriting recognition, OCR: reading checks and zip codes, handwriting recognition for tablet PCs. speech recognition, speaker recognition/verification security: face detection and recognition, event detection in videos. text classification: indexing, web search. computer vision: object detection and recognition. diagnosis: medical diagnosis (e.g. pap smears processing) adaptive control: locomotion control for legged robots, navigation for mobile robots, minimizing pollutant emissions for chemical plants, predicting consumption for utilities... fraud detection: e.g. detection of “unusual” usage patterns for credit cards or calling cards. database marketing: predicting who is more likely to respond to an ad campaign. (...and the antidote) spam filtering. games (e.g. backgammon). Financial prediction (many people on Wall Street use machine learning).

Learning ≠ memorization rote learning is easy: just memorize all the training examples and their corresponding outputs. when a new input comes in, compare it to all the memorized samples, and produce the output associated with the matching sample. PROBLEM: in general, new inputs are different from training samples. The ability to produce correct outputs or behavior on previously unseen inputs is called GENERALIZATION. rote learning is memorization without generalization. The big question of Learning Theory (and practice): how to get good generalization with a limited number of examples.

Look ahead Supervised learning Decision trees Linear models Neural networks Unsupervised learning K-means clustering http://www-stat.stanford.edu/~tibs/ElemStatLearn/ Full text in PDF

Learning from examples

Examples of Classification Task Handwriting recognition Face detection Speech recognition Object recognition

Learning from examples

Uses different biases in predicting Russel’s waiting habbits Decision Trees --Examples are used to --Learn topology --Order of questions K-nearest neighbors If patrons=full and day=Friday then wait (0.3/0.7) If wait>60 and Reservation=no then wait (0.4/0.9) Association rules --Examples are used to --Learn support and confidence of association rules SVMs Neural Nets --Examples are used to --Learn topology --Learn edge weights Naïve bayes (bayesnet learning) --Examples are used to --Learn topology --Learn CPTs

Decision Tree Classification Task

Apply Model to Test Data Start from the root of tree. Refund MarSt TaxInc YES NO Yes No Married Single, Divorced < 80K > 80K

Apply Model to Test Data Refund MarSt TaxInc YES NO Yes No Married Single, Divorced < 80K > 80K

Apply Model to Test Data Refund Yes No NO MarSt Single, Divorced Married TaxInc NO < 80K > 80K NO YES

Apply Model to Test Data Refund Yes No NO MarSt Single, Divorced Married TaxInc NO < 80K > 80K NO YES

Apply Model to Test Data Refund Yes No NO MarSt Single, Divorced Married TaxInc NO < 80K > 80K NO YES

Apply Model to Test Data Refund Yes No NO MarSt Married Assign Cheat to “No” Single, Divorced TaxInc NO < 80K > 80K NO YES

Decision Tree Classification Task

Decision Tree Induction Many Algorithms: Hunt’s Algorithm (one of the earliest) CART ID3, C4.5 http://www2.cs.uregina.ca/~dbd/cs831/notes/ ml/dtrees/c4.5/tutorial.html SLIQ,SPRINT http://www.cs.waikato.ac.nz/ml/weka/

Tree Induction Greedy strategy. Split the records based on an attribute test that optimizes certain criterion. Issues Determine how to split the records How to specify the attribute test condition? How to determine the best split? Determine when to stop splitting

Tree Induction Greedy strategy. Split the records based on an attribute test that optimizes certain criterion. Issues Determine how to split the records How to specify the attribute test condition? How to determine the best split? Determine when to stop splitting

How to Specify Test Condition? Depends on attribute types Nominal Ordinal Continuous Depends on number of ways to split 2-way split Multi-way split

Splitting Based on Nominal Attributes Multi-way split: Use as many partitions as distinct values. Binary split: Divides values into two subsets. Need to find optimal partitioning. CarType Family Sports Luxury CarType {Sports, Luxury} {Family} CarType {Family, Luxury} {Sports} OR

Splitting Based on Continuous Attributes Different ways of handling Discretization to form an ordinal categorical attribute Static – discretize once at the beginning Dynamic – ranges can be found by equal interval bucketing, equal frequency bucketing (percentiles), or clustering. Binary Decision: (A < v) or (A  v) consider all possible splits and finds the best cut can be more compute intensive

Tree Induction Greedy strategy. Split the records based on an attribute test that optimizes certain criterion. Issues Determine how to split the records How to specify the attribute test condition? How to determine the best split? Determine when to stop splitting

How to determine the Best Split Greedy approach: Nodes with homogeneous class distribution are preferred Need a measure of node impurity: Non-homogeneous, High degree of impurity Homogeneous, Low degree of impurity

Entropy The entropy of a random variable V with values vk, each with probability P(vk) is: 𝐻 𝑉 =− 𝑘 𝑃( 𝑣 𝑘 ) 𝑙𝑜𝑔 2 𝑃 (𝑣 𝑘 )

Splitting Criteria based on INFO Entropy at a given node t: (NOTE: p( j | t) is the relative frequency of class j at node t). Measures homogeneity of a node. Maximum (log nc) when records are equally distributed among all classes implying least information Minimum (0.0) when all records belong to one class, implying most information

How to Find the Best Split Before Splitting: M0 A? B? Yes No Yes No Node N1 Node N2 Node N3 Node N4 M1 M2 M3 M4 M12 M34 Gain = M0 – M12 vs M0 – M34

Examples for computing Entropy P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Entropy = – 0 log 0 – 1 log 1 = – 0 – 0 = 0 P(C1) = 1/6 P(C2) = 5/6 Entropy = – (1/6) log2 (1/6) – (5/6) log2 (1/6) = 0.65 P(C1) = 2/6 P(C2) = 4/6 Entropy = – (2/6) log2 (2/6) – (4/6) log2 (4/6) = 0.92

Splitting Based on INFO... Information Gain: Parent Node, p is split into k partitions; ni is number of records in partition i Measures Reduction in Entropy achieved because of the split. Choose the split that achieves most reduction (maximizes GAIN) Used in ID3 and C4.5

S The Information Gain Computation P+ : N+ /(N++N-) P- : N- /(N++N-) I(P+ ,, P-) = -P+ log(P+) - P- log(P- ) N+ N- N1+ N1- N2+ N2- Nk+ Nk- Splitting on feature f The difference is the information gain So, pick the feature with the largest Info Gain I.e. smallest residual info I(P1+ ,, P1-) I(P2+ ,, P2-) I(Pk+ ,, Pk-) S [Ni+ + Ni- ]/[N+ + N-] I(Pi+ ,, Pi-) i=1 k Given k mutually exclusive and exhaustive events E1….Ek whose probabilities are p1….pk The “information” content (entropy) is defined as S i -pi log2 pi A split is good if it reduces the entropy..

V(M) = 2/4 * I(1/2,1/2) + 2/4 * I(1/2,1/2) A simple example I(1/2,1/2) = -1/2 *log 1/2 -1/2 *log 1/2 = 1/2 + 1/2 =1 I(1,0) = 1*log 1 + 0 * log 0 = 0 V(M) = 2/4 * I(1/2,1/2) + 2/4 * I(1/2,1/2) = 1 V(A) = 2/4 * I(1,0) + 2/4 * I(0,1) = 0 V(N) = 2/4 * I(1/2,1/2) + 2/4 * I(1/2,1/2) So Anxious is the best attribute to split on Once you split on Anxious, the problem is solved

Decision Tree Based Classification Advantages: Inexpensive to construct Extremely fast at classifying unknown records Easy to interpret for small-sized trees Accuracy is comparable to other classification techniques for many simple data sets

Tree Induction Greedy strategy. Split the records based on an attribute test that optimizes certain criterion. Issues Determine how to split the records How to specify the attribute test condition? How to determine the best split? Determine when to stop splitting

Underfitting and Overfitting Underfitting: when model is too simple, both training and test errors are large

Overfitting due to Noise Decision boundary is distorted by noise point

Notes on Overfitting Overfitting results in decision trees that are more complex than necessary Training error no longer provides a good estimate of how well the tree will perform on previously unseen records Need new ways for estimating errors

How to Address Overfitting Pre-Pruning (Early Stopping Rule) Stop the algorithm before it becomes a fully-grown tree Typical stopping conditions for a node: Stop if all instances belong to the same class Stop if all the attribute values are the same More restrictive conditions: Stop if number of instances is less than some user-specified threshold Stop if class distribution of instances are independent of the available features (e.g., using  2 test) Stop if expanding the current node does not improve impurity measures (e.g., Gini or information gain).

How to Address Overfitting… Post-pruning Grow decision tree to its entirety Trim the nodes of the decision tree in a bottom-up fashion If generalization error improves after trimming, replace sub-tree by a leaf node. Class label of leaf node is determined from majority class of instances in the sub-tree

Decision Boundary Border line between two neighboring regions of different classes is known as decision boundary Decision boundary is parallel to axes because test condition involves a single attribute at-a-time

Oblique Decision Trees x + y < 1 Class = + Class = Test condition may involve multiple attributes More expressive representation Finding optimal test condition is computationally expensive