Mind Reading by Machine Learning: A Doubly Bayesian Method for Inferring Mental Representations

Mind Reading by Machine Learning: A Doubly Bayesian Method for Inferring Mental Representations Ferenc Husz´ ar (fh277@eng.cam.ac.uk ) Computational and Biological Learning Lab, Dept Engineering, U Cambridge, Cambridge CB2 1PZ, UK Uta Noppeney (uta.noppeney@tuebingen.mpi.de) Max Planck Institute for Biological Cybernetics, Spemannstrasse 41, T¨ ubingen 72076, Germany M´ at´ e Lengyel (m.lengyel@eng.cam.ac.uk) Computational and Biological Learning Lab, Dept Engineering, U Cambridge, Cambridge CB2 1PZ, UK Abstract A central challenge in cognitive science is to measure and quantify the mental representations humans develop – in other words, to ‘read’ subject’s minds. In order to elimi- nate potential biases in reporting mental contents due to verbal elaboration, subjects’ responses in experiments are often limited to binary decisions or discrete choices that do not require conscious reflection upon their mental contents. However, it is unclear what such impoverished data can tell us about the potential richness and dy- namics of subjects’ mental representations. To address this problem, we used ideal observer models that for- malise choice behaviour as (quasi-)Bayes-optimal, given subjects’ representations in long-term memory, acquired through prior learning, and the stimuli currently avail- able to them. Bayesian inversion of such ideal observer models allowed us to infer subjects’ mental representation from their choice behaviour in a variety of psychophysical tasks. The inferred mental representations also allowed us to predict future choices of subjects with reasonable accuracy, even in tasks that were different from those in which the representations were estimated. These results demonstrate a significant potential in standard binary decision tasks to recover detailed information about sub- jects’ mental representations. Introduction Cognitive science studies the mental representations hu- mans (and other animals) develop and the way these representations are used to perform particular tasks. A central challenge is to measure and quantify such men- tal representations experimentally – in other words, to ‘read’ subjects’ minds. A classical approach to this is to ask subjects directly to report their mental contents verbally. Unfortunately, this procedure is prone to intro- ducing biases arising from verbal processing, and from the educational and cultural backgrounds of subjects (Ericsson & Simon, 1980; Russo et al., 1989). In order to eliminate these biases, an alternative approach is to limit subjects’ responses to simple binary decisions or discrete choices that do not require conscious reflection upon their mental contents. However, it is unclear what such impoverished data can tell us about the potential richness and dynamics of subjects’ mental contents. A powerful computational framework formalises the goal of learning as estimating the probability distribution or density of stimuli (Hinton & Sejnowski, 1986; Dayan & Abbott, 2001). This motivates many formal theories of human learning and cognition to model the relevant mental content of a subject either implicitly or explicitly as a ‘subjective’ distribution over possible stimuli (Chater et al., 2006; Sanborn & Griffiths, 2008). In this study we adopted this representation, and our goal was to estimate subjects’ subjective distributions solely from their responses in simple binary decision tasks without making any assumptions about the process by which those subjective distributions were acquired, i. e. learning. Ideal observer models are widely used for explaining human behaviour in various psychophysics tasks (Geisler, 2003). They formalise (quasi-)optimal decision making strategies given the information available to subjects and their background knowledge about the task, which in our case includes their subjective distributions. While previous studies mostly used ideal observer models to de- termine optimal performance in particular tasks to which human performance could then be compared, we treat them as stochastic models formalising the link between subjective distributions (the unobserved variable), and test stimuli and responses (the observed variables). Our main observation is that such models can be used to provide the likelihood in a Bayesian statistical analysis of subjective distributions, thus enabling one to infer mental contents from task responses in a principled way. We term our approach doubly Bayesian, as we assume that subjects act as quasi-ideal observers, which entails Bayesian inference on their side; and then we use these ideal-observer models in a Bayesian framework to infer a posterior distribution of possible subjective distributions. Inferring subjective distributions The graphical model (Koller & Friedman, 2009) in Fig. 1A describes our model of a subject’s behaviour in a session of a psychophysics experiment. We assume that the sub- ject entertains a subjective distribution P over possible stimuli, and that this distribution does not change over the analysed session. In trial i of the experiment, the subject is presented a set of test stimuli S i and gives a re- sponse r i . The value of r i depends on the current stimuli S i , the subjective distribution P, and ‘link’ parameters Θ O describing further aspects of observation and decision making, such as attention, perceptual noise, etc.