Fig. 2.

Illustration of different inter-relationships of prediction tasks. a The two classification tasks of separating colors (blue vs orange) and shapes (crosses vs circles) are unrelated, both on the feature- and the output-level. The color classification can be performed by only considering feature x₁ while shape information is irrelevant. Similarly, shapes can be classified using feature x₂ with color being irrelevant. b The two tasks are related on a feature-level but not on their outputs. In both tasks, the features x₁ and x₂ need to be considered for classifying colors and shapes, however, shape information remains irrelevant for separating colors, and vice versa. While in both tasks the exact same features are being used, they are combined in different ways. c The two tasks are related both on a feature- and an output-level. Solving one of the tasks also solves the other. Shape and color information is highly correlated. The dashed green and gray lines indicate the optimal decision boundaries for color and shape classification, respectively.