Trajectory prediction combining forward models and historical knowledge
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1
University of Oxford, FMRIB Centre, United Kingdom
To interact effectively with the environment, brains need to extract predictive information from their environment. Prediction can involve different computational processes. In motor control, forward models are important for extrapolating the results of motor commands. In other situations, (e.g. foraging) the goal may to extract the statistical properties of the environment, a process well modelled by reinforcement learning algorithms. How are these computationally different types of prediction, which may be associated with distinct brain structures, combined to optimise behaviour? We designed a paradigm in which participants must combine historical, probabilistic knowledge with online forward modelling to resolve uncertainty in prediction. In this paradigm, participants must predict the endpoint of a visually observed trajectory (the flight-path of a ’space invader’) - a forward modelling/extrapolation task. However, probabilistic historical information is also informative - the trajectory-endpoints follow a Gaussian distribution so that the ’space invaders’ are most likely to land in one part of the screen. The contributions of forward modelling (extrapolation of the current trajectory) and historical/probabilistic knowledge depend on how informative each is. We manipulated the informativeness of trajectory data (by adding white noise to the trajectory seen by the participant) and the historical distribution (by changing its variance) over the course of the experiment. When the observed trajectory was noisy, participants chose endpoints closer to the historical mean - i.e. they used historical knowledge to resolve uncertain predictions from a forward model. In Bayesian terms, on each trial the participant has both a PRIOR expectation of the endpoint (from historical knowledge), and observed DATA (from forward modelling of the current trajectory). These are combined to give a POSTERIOR distribution from which we hypothesise the prediction about the endpoint is made. Using data from 19 human participants, we found that responses were indeed distributed about the posterior mean. We modelled the endpoints selected by the humans as having a Gaussian distribution about either the posterior mean, prior mean or trajectory endpoints. Using maximum-likelihood estimates for the standard deviation of each distribution, the log likelihood of the posterior model was significantly higher than for the trajectory-only model (Bayes factor 35) or the prior-only model (BF:130). This indicated that human participants really do combine forward-modelling and historical knowledge in a perceptual prediction task. The historical prior must be learnt over many trials. We modelled this process using a Bayesian ’computer participant’ which estimated the mean and variance of the historical distribution at each trial t plus the parameters of a transitional Beta distribution, through which the prior for t+1 was generated. Estimates of the historical distribution taken from the Bayesian learner predicted human responses better than a baseline model which assumed knowledge of the historical distribution without accounting for learning. We are collecting fMRI data using this paradigm. By modelling the contributions of prior knowledge and forward modelling to endpoint prediction on each trial, we hope to find out which brain structures are involved in each computational mode of prediction, and where the two types of information are combined.
Conference:
Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010.
Presentation Type:
Poster Presentation
Topic:
Poster session I
Citation:
O'Reilly
J and
Behrens
T
(2010). Trajectory prediction combining forward models and historical knowledge.
Front. Neurosci.
Conference Abstract:
Computational and Systems Neuroscience 2010.
doi: 10.3389/conf.fnins.2010.03.00014
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Received:
17 Feb 2010;
Published Online:
17 Feb 2010.
*
Correspondence:
Jill O'Reilly, University of Oxford, FMRIB Centre, Oxford, United Kingdom, joreilly@fmrib.ox.ac.uk