Data Mining (and machine learning) ROC curves Rule Induction CW3

Two classes is a common and special case

Two classes is a common and special case Medical applications: cancer, or not? Computer Vision applications: landmine, or not? Security applications: terrorist, or not? Biotech applications: gene, or not? … …

Two classes is a common and special case Medical applications: cancer, or not? Computer Vision applications: landmine, or not? Security applications: terrorist, or not? Biotech applications: gene, or not? … … Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

Two classes is a common and special case True Positive: these are ideal. E.g. we correctly detect cancer Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

Two classes is a common and special case True Positive: these are ideal. E.g. we correctly detect cancer False Positive: to be minimised – cause false alarm – can be better to be safe than sorry, but can be very costly. Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

Two classes is a common and special case True Positive: these are ideal. E.g. we correctly detect cancer False Positive: to be minimised – cause false alarm – can be better to be safe than sorry, but can be very costly. False Negative: also to be minimised – miss a landmine / cancer very bad in many applications Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

Two classes is a common and special case True Positive: these are ideal. E.g. we correctly detect cancer False Positive: to be minimised – cause false alarm – can be better to be safe than sorry, but can be very costly. False Negative: also to be minimised – miss a landmine / cancer very bad in many applications True Negative?: Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

Sensitivity and Specificity: common measures of accuracy in this kind of 2-class tasks Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

Sensitivity and Specificity: common measures of accuracy in this kind of 2-class task Sensitivity = TP/(TP+FN) - how much of the real ‘Yes’ cases are detected? How well can it detect the condition? Specificity = TN/(FP+TN) - how much of the real ‘No’ cases are correctly classified? How well can it rule out the condition? Predicted Y Predicted N Actually Y True Positive False Negative Actually N False Positive True Negative

YES NO

YES NO

Sensitivity: 100% Specificity: 25% YES NO YES NO

Sensitivity: 93.8% Specificity: 50% YES NO

Sensitivity: 81.3% Specificity: 83.3% YES NO YES NO

Sensitivity: 56.3% Specificity: 100% YES NO YES NO

detects all cancer cases (or whatever) Sensitivity: 100% Specificity: 25% YES NO YES NO 100% Sensitivity means: detects all cancer cases (or whatever) but possibly with many false positives

misses some cancer cases (or whatever) but no false positives Sensitivity: 56.3% Specificity: 100% YES NO YES NO 100% Specificity means: misses some cancer cases (or whatever) but no false positives

Sensitivity and Specificity: common measures of accuracy in this kind of 2-class tasks Sensitivity = TP/(TP+FN) - how much of the real TRUE cases are detected? How sensitive is the classifier to TRUE cases? A highly sensitive test for cancer: if “NO” then you be sure it’s “NO” Specificity = TN/(TN+FP) - how sensitive is the classifier to the negative cases? A highly specific test for cancer: if “Y” then you be sure it’s “Y”. With many trained classifiers, you can ‘move the line’ in this way. E.g. with NB, we could use a threshold indicating how much higher the log likelihood for Y should be than for N

ROC curves David Corne, and Nick Taylor, Heriot-Watt University - dwcorne@gmail.com These slides and related resources: http://www.macs.hw.ac.uk/~dwcorne/Teaching/dmml.html

Rule Induction Rules are useful when you want to learn a clear / interpretable classifier, and are less worried about squeezing out as much accuracy as possible There are a number of different ways to ‘learn’ rules or rulesets. Before we go there, what is a rule / ruleset?

Rules IF Condition … Then Class Value is …

YES NO Rules are Rectangular IF (X>0)&(X<5)&(Y>0.5)&(Y<5) THEN YES 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

YES NO Rules are Rectangular IF (X>5)&(X<11)&(Y>4.5)&(Y<5.1) THEN NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

A Ruleset IF Condition1 … Then Class = A IF Condition2 … Then Class = A IF Condition3 … Then Class = B IF Condition4 … Then Class = C …

What’s wrong with this ruleset? (two things) YES NO What’s wrong with this ruleset? (two things) 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

What about this ruleset? YES NO What about this ruleset? 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Two ways to interpret a ruleset:

Two ways to interpret a ruleset: As a Decision List IF Condition1 … Then Class = A ELSE IF Condition2 … Then Class = A ELSE IF Condition3 … Then Class = B ELSE IF Condition4 … Then Class = C … ELSE … predict Background Majority Class

Two ways to interpret a ruleset: As an unordered set IF Condition1 … Then Class = A IF Condition2 … Then Class = A IF Condition3 … Then Class = B IF Condition4 … Then Class = C Check each rule and gather votes for each class If no winner, predict background majority class

Three broad ways to learn rulesets

Three broad ways to learn rulesets 1. Just build a decision tree with ID3 (or something else) and you can translate the tree into rules!

Three broad ways to learn rulesets 2. Use any good search/optimisation algorithm. Evolutionary (genetic) algorithms are the most common. You will do this coursework 3. This means simply guessing a ruleset at random, and then trying mutations and variants, gradually improving them over time.

Three broad ways to learn rulesets 3. A number of ‘old’ AI algorithms exist that still work well, and/or can be engineered to work with an evolutionary algorithm. The basic idea is: iterated coverage

Take each class in turn .. YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Pick a random member of that class in the training set YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Extend it as much as possible without including another class YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Extend it as much as possible without including another class YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Extend it as much as possible without including another class YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Extend it as much as possible without including another class YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Next class YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

Next class YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

And so on… YES NO 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12

CW3 Run expts program that evolves a ruleset Try different sizes of training and test set Observe ‘overfitting’ and report