Venn predictors using lazy learners

Abstract

Probabilistic classification requires well-calibrated probability estimates, i.e., the predicted class probabilities must correspond to the true probabilities. Venn predictors, which can be used on top of any classifier, are automatically valid multiprobability predictors, making them extremely suitable for probabilistic classification. A Venn predictor outputs multiple probabilities for each label, so the predicted label is associated with a probability interval. While all Venn predictors are valid, their accuracy and the size of the probability interval are dependent on both the underlying model and some interior design choices. Specifically, all Venn predictors use so called Venn taxonomies for dividing the instances into a number of categories, each such taxonomy defining a different Venn predictor. A frequently used, but very basic taxonomy, is to categorize the instances based on their predicted label. In this paper, we investigate some more finegrained taxonomies, that use not only the predicted label but also some measures related to the confidence in individual predictions. The empirical investigation, using 22 publicly available data sets and lazy learners (kNN) as the underlying models, showed that the probability estimates from the Venn predictors, as expected, were extremely well-calibrated. Most importantly, using the basic (i.e., label-based) taxonomy produced significantly more accurate and informative Venn predictors compared to the more complex alternatives. In addition, the results also showed that when using lazy learners as underlying models, a transductive approach significantly outperformed an inductive, with regard to accuracy and informativeness. This result is in contrast to previous studies, where other underlying models were used