Introduction to Machine Learning Evaluation: Measures for Binary - PowerPoint PPT Presentation

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Introduction to Machine Learning Evaluation: Measures for Binary Classification: ROC Measures compstat-lmu.github.io/lecture_i2ml IMBALANCED BINARY LABELS Classify all as no disease (green) high accuracy. Accuracy Paradox c

Introduction to Machine Learning Evaluation: Measures for Binary Classification: ROC Measures compstat-lmu.github.io/lecture_i2ml
IMBALANCED BINARY LABELS Classify all as “no disease” (green) → high accuracy. Accuracy Paradox � c Introduction to Machine Learning – 1 / 9
IMBALANCED COSTS Classify incorrectly as “no disease” → very high cost � c Introduction to Machine Learning – 2 / 9
CONFUSION MATRIX True Class y + − + Pred. TP FP ˆ y FN TN − + : “positive” class − : “negative” class n + : number of observations in + n − : number of observations in − � c Introduction to Machine Learning – 3 / 9
LABELS: ROC METRICS From the confusion matrix (binary case), we can calculate "ROC" metrics. True Class y + − TP + Pred. TP FP PPV = TP + FP TN ˆ y FN TN NPV = − FN + TN TP TN Accuracy = TP + TN TPR = TNR = TP + FN FP + TN TOTAL True Positive Rate: How many of the true 1s did we predict as 1? True Negative Rate: How many of the true 0s did we predict as 0? Positive Predictive Value: If we predict 1 how likely is it a true 1? Negative Predictive Value: If we predict 0 how likely is it a true 0? � c Introduction to Machine Learning – 4 / 9
HISTORY ROC ROC = receiver operating characteristics Initially developed by electrical engineers and radar engineers during World War II for detecting enemy objects in battlefields. http://media.iwm.org.uk/iwm/mediaLib//39/media-39665/large.jpg Still has the funny name. � c Introduction to Machine Learning – 5 / 9
LABELS: ROC Example � c Introduction to Machine Learning – 6 / 9
MORE METRICS AND ALTERNATIVE TERMINOLOGY Unfortunately, for many concepts in ROC, 2-3 different terms exist. Clickable version/picture source Interactive diagram � c Introduction to Machine Learning – 7 / 9
LABELS: F 1 -MEASURE A measure that balances two conflicting goals Maximising Positive Predictive Value 1 Maximising True Positive Rate 2 is the harmonic mean of PPV and TPR: PPV · TPR F 1 = 2 PPV + TPR Note: still doesn’t account for the number of true negatives. � c Introduction to Machine Learning – 8 / 9
LABELS: F 1 -MEASURE Tabulated F 1 -Score for different TPR (rows) and PPV (cols) combinations. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0 0.00 0.00 0.00 0.00 0.00 0.2 0 0.20 0.27 0.30 0.32 0.33 0.4 0 0.27 0.40 0.48 0.53 0.57 0.6 0 0.30 0.48 0.60 0.69 0.75 0.8 0 0.32 0.53 0.69 0.80 0.89 1.0 0 0.33 0.57 0.75 0.89 1.00 → Tends more towards the lower of the 2 combined values. TPR = 0 or PPV = 0 ⇒ F 1 of 0 Predicting always "neg": F 1 = 0 Predicting always "pos": F 1 = 2 PPV / ( PPV + 1 ) = 2 n + / ( n + + n ) , which will be rather small, if the size of the positive class n + is small. � c Introduction to Machine Learning – 9 / 9

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