Probability, programs, and the mind: Building structured Bayesian models of cognition

Probability, programs, and the mind: Building structured Bayesian models of cognition Noah D. Goodman (ngoodman@stanford.edu) Department of Psychology, Stanford University, Stanford CA 94305 USA Joshua B. Tenenbaum (jbt@mit.edu) Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge MA 02139 USA Objectives and scope The tutorial will include several in-depth case studies where the probabilistic programming viewpoint is particu- larly useful. After introducing the basic phenomena of prob- abilistic reasoning—explaining away, screening off, etc—we will turn to the representation of intuitive theories and the connection between probabilistic programs, intuitive theo- ries, and mental simulation. We will focus in particular on folk physics and folk psychology, showing that they can be captured as probabilistic programs, that this explains data from human experiments, and that they can be productively integrated together. Human thought is remarkably flexible: we can think about infinitely many different situations despite uncertainty and novelty. Probabilistic models of cognition (Chater, Tenen- baum, & Yuille, 2006) have been successful at explaining a wide variety of learning and reasoning under uncertainty. They have borrowed tools from statistics and machine learn- ing to explain phenomena from perception (Yuille & Kersten, 2006) to language (Chater & Manning, 2006). Traditional symbolic models (e.g. Newell, Shaw, & Simon, 1958; An- derson & Lebiere, 1998), by contrast, excel at explaining the productivity of thought, which follows from compositional- ity of symbolic representations. Indeed, there has been a gradual move toward more structured probabilistic models (Tenenbaum, Kemp, Griffiths, & Goodman, 2011) that incor- porate aspects of symbolic methods into probabilistic model- ing. Unfortunately this movement has resulted in a complex “zoo” of Bayesian models. We have recently introduced the idea that using programs, and particularly probabilistic pro- grams, as the representational substrate for probabilistic mod- eling tames this unruly zoo, fully unifies probabilistic with symbolic approaches, and opens new possibilities in cogni- tive modeling. The goal of this tutorial is to introduce prob- abilistic models of cognition from the point of view of prob- abilistic programming, both as a unifying idea for cognitive modeling and as a practical tool. The probabilistic programming language Church (Goodman, Mansinghka, Roy, Bonawitz, & Tenenbaum, 2008), mathematically grounded on the stochastic λ-calculus, provides a universal language for representing probabilistic models. We will use Church to introduce key ideas and examples of probabilistic modeling. A Church program rep- resents a probabilistic model, and hence inferences that can be drawn from this model, without committing to a process level implementation of inference. This will allow us to focus the tutorial on structured representations and probabilistic inference phenomena without worrying about the details of inference algorithms (such as Markov chain Monte Carlo) that tutorials on Bayesian modeling often become bogged down in. On the other hand, because there are existing inference tools for Church (e.g. Wingate, Stuhlm¨uller, & Goodman, 2011), students will get hands-on experience with performing inference over different probabilistic models. Tutorial format This full-day tutorial aims to introduce students to key ideas of, and new tools for constructing, structured probabilistic models. We will assume only basic familiarity with proba- bility and with programming (i.e. minimal mathematical or statistical background). The tutorial will thus be appropriate for a general Cognitive Science audience, as well for practi- tioners of bayesian modeling who want to learn about proba- bilistic programming. We will teach this tutorial drawing on a combination of in- frastructure and materials that we have developed over the last five years, teaching graduate classes (at Stanford and MIT) and short tutorials around the world. The online book “Proba- bilistic Models of Cognition” (http://probmods.org) gives a systematic introduction to modern Bayesian modeling using Church for model representation. It integrates an easy to use but powerful implementation of Church that allows students to explore these modeling tools without the need to install special software. It contains extensive examples, including intuitive physics based on forward-simulation and theory-of- mind based on recursive probabilistic conditioning. We will use the morning session to introduce the ideas of probabilistic modeling and the Church language, to illustrate basic ideas (such as explaining away, and hierarchical mod- els), and to provide hands-on exercises using Church to create models. The afternoon session will be devoted to case studies of more sophisticated applications of these ideas to cognition, including studies from vision, language, and reasoning. The afternoon session will be structured around a series of exam- ples and exercises building more and more complex intuitive theories of a simple domain: reasoning about ping-pong.