Characterizing Uncertainty in Decision Trees through Imprecise - PowerPoint PPT Presentation

Characterizing Uncertainty in Decision Trees through Imprecise Splitting Rules ISIPTA 2019 Malte Nalenz & Thomas Augustin July 6, 2019 Malte Nalenz & Thomas Augustin Characterizing Uncertainty in Decision Trees through Imprecise Splitting Rules July 6, 2019 1 / 5

2 1 0 x2 −1 −2 −3 −2 −1 0 1 2 x1 Malte Nalenz & Thomas Augustin Characterizing Uncertainty in Decision Trees through Imprecise Splitting Rules July 6, 2019 2 / 5

2 1 0 x2 −1 −2 −3 −2 −1 0 1 2 x1 Oberservations close to the decision boundarie(s) more uncertain, as small perturbations lead to different prediction Malte Nalenz & Thomas Augustin Characterizing Uncertainty in Decision Trees through Imprecise Splitting Rules July 6, 2019 2 / 5

Instead of using a single splitpoint x ≤ t 0 we propose to consider a neighbourhood: T = { t − k = x − k , · · · , t 0 , · · · , t k = x k } , where t 0 is the candidate split and t k and t − k the k’th datapoints with higher and lower ordered covariate values as reasonable alternative splitting values. Malte Nalenz & Thomas Augustin Characterizing Uncertainty in Decision Trees through Imprecise Splitting Rules July 6, 2019 3 / 5

3 2 1 x2 0 -1 -2 -2 -1 0 1 2 3 x1 Malte Nalenz & Thomas Augustin Characterizing Uncertainty in Decision Trees through Imprecise Splitting Rules July 6, 2019 4 / 5