Human Movement Science 26 2007 511 524 www elsevier com locate humov Probabilistic models in human sensorimotor control Daniel M Wolpert Computational and Biological Learning Group Department of Engineering University of Cambridge Trumpington Street Cambridge CB2 1PZ Cambridge UK Available online 12 July 2007 Abstract Sensory and motor uncertainty form a fundamental constraint on human sensorimotor control Bayesian decision theory BDT has emerged as a unifying framework to understand how the central nervous system performs optimal estimation and control in the face of such uncertainty BDT has two components Bayesian statistics and decision theory Here we review Bayesian statistics and show how it applies to estimating the state of the world and our own body Recent results suggest that when learning novel tasks we are able to learn the statistical properties of both the world and our own sensory apparatus so as to perform estimation using Bayesian statistics We review studies which suggest that humans can combine multiple sources of information to form maximum likelihood estimates can incorporate prior beliefs about possible states of the world so as to generate maximum a posteriori estimates and can use Kalman lter based processes to estimate time varying states Finally we review Bayesian decision theory in motor control and how the central nervous system processes errors to determine loss functions and select optimal actions We review results that suggest we plan movements based on statistics of our actions that result from signal dependent noise on our motor outputs Taken together these studies provide a statistical framework for how the motor system performs in the presence of uncertainty 2007 Elsevier B V All rights reserved PsycINFO classi cation 2330 Keywords Motor control Motor learning Bayesian processes Computational models E mail address wolpert eng cam ac uk 0167 9457 see front matter 2007 Elsevier B V All rights reserved doi 10 1016 j humov 2007 05 005 512 D M Wolpert Human Movement Science 26 2007 511 524 1 Introduction With over a century of intensive research on the control of human movement it is illuminating to ask how well we are doing elucidating the principles that govern movement One way to assess progress is to examine how well we can build machines that emulate human skills Taking the game of chess we can pit a grandmaster against the best chess computers in the world and usually the computer will win In fact if the computer were to play the entire population of the world perhaps only a handful of people would be able to ever win a single game Therefore when compared to the majority of players this problem is e ectively solved However if we consider the skills of dexterously manipulating a chess piece it is clear that if we pit the best robots of today against the skills of a young child there is no competition The child exhibits manipulation skills that outstrip any robot Why is choosing where to move a chess piece so much easier than actually moving it The answer may lie in the algorithms required to achieve each task In the case of determining which piece to move where the algorithm is obvious even to a child look at all possible moves to the end of the game and choose the one that ensures you win While the algorithm is clear its implementation is far from straightforward The number of moves clearly exceeds the ability of any computer to enumerate However with the dramatic increases in computer speed and some shortcuts it has been possible to approximate such an algorithm However when it comes to the problem of skilled movement the algorithm is simply not known Unlike the game of chess where the state of the board and the consequences of each move are known the control of movement requires interaction with a variable and ever changing world The signals which the brain has access to when perceiving the world and acting upon it are not discrete signals such as the location of a pawn on the chess board but analogue signals which the brain represents with its digital code This transformation from analogue to a digital code limits resolution and in addition many of the properties of neural transduction and synaptic interaction add a great deal of noise to these signals Barlow Kaushal Hawken Parker 1987 This noise that is unwanted disturbance on the signal makes the problems of perception and action computationally di cult For example if we bought a motor for a robot with the noise properties of our motor system coe cient of variance of around 6 Hamilton Jones Wolpert 2004 we would send it back saying it is too noisy for our use To what extent will solution to robotics come from hardware or from software We would argue that it will be software For example on the sensory side even people who have lost all their proprioceptive sense while being far from as skilled as normal participants are nevertheless able to control movements in a feedforward manner better than robotic devices Cole 1995 While there are many factors that make motor control hard in a noise free system such as nonlinearities and long time delays noise is one area in which there have been signi cant advances in our understanding of how the brain may deal with noise and underlying principles have recently begun to emerge In this review we will focus on the issue of how the brain may minimize the negative features of noise within the framework of Bayesian decision theory Bayesian theory is named after an 18th century English Presbyterian minister named Thomas Bayes During his lifetime he published two works of which only one dealt with mathematics in which he defended the logical foundation of Isaac Newton s methods However after Bayes death his friend Richard Price found a mathematical proof among Bayes papers and sent it to the Editor of the Philosophical Transactions of the Royal Soci D M Wolpert Human Movement Science 26 2007 511 524 513 ety stating I now send you an essay which I have found among the papers of our deceased friend Mr Bayes and which in my opinion has great merit The paper was published posthumously in 1764 as Essay towards solving a problem in the doctrine of chances In the latter half of the 20th century Bayesian approaches have become a mainstay of statistics and a more general framework has now emerged termed Bayesian decision theory BDT Cox 1946 Freedman 1995 Jaynes 1995 MacKay 2003 The application of BDT to neuroscience has provided a framework for how the brain deals
View Full Document
Unlocking...