Mathematics Colloquium – Modeling human decision making with probabilistic programs
Keywords: Graphical models; Decision Making; Probabilistic Programs
Abstract:
Recently, a compelling consensus has emerged on how to model decision making in nature. Across a wide range of systems and scales — from individual cells through cell populations and networks, from complex organisms up through social groups and human societies — the mathematics of probability theory, statistical inference and machine learning, game theory and control theory provide a powerful unifying toolkit for understanding how decisions can be made effectively when data are sparse, noisy, and ambiguous, and when multiple agents are competing, cooperating, or interacting in more complex ways. I will talk about how this toolkit has been used to model human decision making, but I will also talk about what it is missing: What besides the mathematics of rational inference and decision under uncertainty is needed to model distinctively human forms of thinking and acting?
I will argue that a key difference between human brains and simpler decision making systems — and arguably more complex systems as well, such as most groups of humans — is that human brains have access to powerful cognitive tools for modeling and simulating causal processes in the world, including the processes of decision-making inside other humans. I will show how we can extend the consensus toolkit to capture decision-making with these rich causal models using the formal representations of *probabilistic programs*, which can be thought of as generalizations of probabilistic graphical models in which we use computer programs rather than graphs to describe causal processes.
Instead of modeling joint distributions over a (possibly infinite) set of random variables as in traditional probabilistic models, probabilistic programs model distributions over the execution histories of programs, including programs that analyze, transform and write other programs. Probabilistic programs have allowed us to build some of the first quantitatively predictive models of core areas of human common sense, including intuitive physics and intuitive psychology (or “theory of mind”). I will show a few of these models and talk about how we test them empirically. I will also briefly mention some foundational questions that have attracted the interest of mathematicians and theoretical computer scientists.