Chapter 18 From Data to Knowledge Decision Trees Chapter 18 From Data to Knowledge

Types of learning Classification: Regression Unsupervised Learning From examples labelled with the “class” create a decision procedure that will predict the class. Regression From examples labelled with a real valued, create a decision procedure that will predict the value. Unsupervised Learning From examples generate groups that are interesting to the user.

Concerns Representational Bias Generalization Accuracy Is the learned concept correct? Gold Standard Comprehensibility Medical diagnosis Efficiency of Learning Efficiency of Learned Procedure

Classification Examples Medical records on patients with diseases. Bank loan records on individuals. DNA sequences corresponding to “motif”. Digit images of digits. See UCI Machine Learning Data Base

Regression Stock histories -> stock future price Patient data -> internal heart pressure House data -> house value Representation is key.

Unsupervised Learning Astronomical maps -> groups of stars that astronomers found useful. Patient Data -> new diseases Treatments depend on correct disease class Gene data -> corregulated genes and transcription factors Often exploratory

Weather Data: Four Features: windy, play, outlook: nominal Temperature: numeric outlook = sunny | humidity <= 75: yes (2.0) | humidity > 75: no (3.0) outlook = overcast: yes (4.0) outlook = rainy | windy = TRUE: no (2.0) | windy = FALSE: yes (3.0)

Dumb DT Algorithm Build tree: ( discrete features only) If all entries below node are homogenous, stop Else pick a feature at random, create a node for feature and form subtrees for each of the values of the feature. Recurse on each subtree. Will this work?

Properties of Dumb Algorithm Complexity Homogeneity cost is O(DataSize) Splitting is O(DataSize) Times number of node in tree = bd on work Accuracy on training set perfect Accuracy on test set Not so perfect: almost random

Recall: Iris petalwidth <= 0.6: Iris-setosa (50.0) : | | petallength <= 4.9: Iris-versicolor (48.0/1.0) | | petallength > 4.9 | | | petalwidth <= 1.5: Iris-virginica (3.0) | | | petalwidth > 1.5: Iris-versicolor (3.0/1.0) | petalwidth > 1.7: Iris-virginica (46.0/1.0)

Heuristic DT algorithm Entropy Set with mixed classes c1, c2,..ck Entropy(S) = - sum lg(pi)*pi where pi is probability of class ci. (estimated) Sum weighted entropies of each subtrees, where weight is proportion of examples in the subtree. This defines a quality measure on features.

Shannon Entropy Entropy is the only function that: Is 0 when only 1 class present Is k if 2^k classes, equally present Is “additive” ie. E(X,Y) = E(X)+E(Y) if X and Y are independent. Entropy sometimes called uncertainty and sometimes information. Uncertainty defined on RV where “draws” are from the set of classes.

Shannon Entropy Properties Probability of guessing the state/class is 2^{-Entropy(S)} Entropy(S) = average number of yes/no questions needed to reveal the state/class.

Majority Function Suppose 2n boolean features. Class defined by n or more features are on. How big is the tree? At least 2n choose n leaves. Prototype Function: At least k of n are true is a common medical concept. Concepts that are prototypical do not match the representational bias of DTS.

Dts with real valued attributes Idea: convert to solved problem For each real valued attribute f with values v1, v2,… vn (sorted) and binary features: f1< (v1+v2)/2 f2 < (v2+v3/2) etc Other approaches possible. E.g. fi<any vj so no sorting needed

DTs ->Rules (j48.part) For each leaf, we make a rule by collecting the tests to the leaf. Number of rules = number of leaves Simplification: test each condition on a rule and see if dropping it harms accuracy. Can we go from Rules to DTs Not easily. Hint: no root.

Summary Comprehensible if tree is not large. Effective if small number of features sufficient. Bias. Does multi-class problems naturally. Can be extended for regression. Easy to implement and low complexity