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The concept of updating (or conditioning or revising) a probabilitydistribution is fundamental in (machine) learning and in predictive codingtheory. The two main approaches for doing so are called Pearl's rule andJeffrey's rule. Here we make, for the first time, mathematically precise whatdistinguishes them: Pearl's rule increases validity (expected value) andJeffrey's rule decreases (Kullback-Leibler) divergence. This forms an instanceof a more general distinction between learning from what's right and learningfrom what's wrong. The difference between these two approaches is illustratedin a mock cognitive scenario.

Learning from What's Right and Learning from What's Wrong