# The appeal for probabilistic models

Probabilitsic models of cognition is a truly great idea. It is the kind we need in AI in order to make tangible progress. Side note: because the content is not easily accessible, few people can appreciate how great the content is, and this is a bit sad.

Anyhow, these ideas are really great (If you haven’t read it: trust me. If you don’t want to, read it and convince yourselves). And I want to consider the question: how did we get down this path to begin with, and why is it a good path to go down to ?

In Theory-based Bayesian models of inductive learning and reasoning, Joshua B. Tenenbaum, Thomas L. Griffiths, and Charles Kemp explain:

Human cognition rests on a unique talent for extracting generalizable knowledge from a few specific examples. Consider how a child might first grasp the meaning of a common word, such as ‘horse’

They consider the general problem that Tenenbaum often refers to as
`How does the mind get so much from so little`

. A special case would be “one-shot learning” that they
mention, but the problem goes beyond just that: we want to explain not just the one-shot learning cases,
but all the machinery that makes it possible. How do you even get in a state where one-shot learning is
possible ?

Most previous accounts of inductive generalization represent one of two approaches. The first focuses on relatively domain-general, knowledge-independent statistical mechanisms of inference, based on similarity, association, correlation or other statistical metrics [1,4– 13]. This approach has led to successful mathematical models of human generalization in laboratory tasks, but fails to account for many important phenomena of learning and reasoning in complex, real-world domains, such as intuitive biology, intuitive physics or intuitive psychology. The second approach aims to capture more of the richness of human inference, by appealing to sophisticated domain-specific knowledge representations, or intuitive theories [14–20]. An intuitive theory may be thought of as a system of related concepts, together with a set of causal laws, structural constraints, or other explanatory principles, that guide inductive inference in a particular domain. However, theory-based approaches to induction have been notoriously difficult to formalize, particularly in terms that make quantitative predictions about behavior or can be understood in terms of rational statistical inference.

So we have two approaches, both traditionally viewed as opposites:

- statistical: knowledge-independent, based on similarity, association, correlation.
- intuitive theories: a system of related concepts, together with a set of causal laws.

They propose a kind of merger:

We will argue for an alternative approach, where structured knowledge and statistical inference cooperate rather than compete, allowing us to build on the insights of both traditions. We cast induction as a form of Bayesian statistical inference over structured probabilistic models of the world.

And this is great. Learning becomes some kind of probabilistic program induction, and inference a search in program input (and/or execution) space.

These models can be seen as probabilistic versions of intuitive theories [14,18,20] or schemas [21,22], capturing the knowledge about a domain that enables inductive generalization from sparse data

And this is why you should read Probabilitsic models of cognition is a truly great idea. In it, Noah D. Goodman and Joshua B. Tenenbaum go into very concrete details (execute-directly-into-your-browser concrete) about how those probabilistic models work.