Learning without thought is labor lost; thought without learning is perilous.

– Confucius [500 BCE]

It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.

– Albert Einstein [1934]

In Chapters 7 and 8, learning was divorced from reasoning. An alternative is to explicitly use probabilistic reasoning, as in Chapter 9, with data providing evidence that can be conditioned on. This provides a theoretical basis for much of machine learning, including regularization and measures of simplicity. This chapter uses probability for supervised and unsupervised learning, as well as learning of belief networks.