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January 24, 2004
Probabilistic Sensorimotor Learning
Chris Genovese has done an interesting and informative analysis of a paper by Konrad P. Körding and Daniel M. Wolpert of the Institute of Neurology, University College London, that suggests, in Chris' words, "the brain's motor system can effectively manage uncertainty". Chris not only explains the significance of the research with the insight of a statistician, he supports the analysis with links to explanatory material so that we unwashed readers can improve our understanding of the relevant theories. The research paper uses the game of tennis to present the idea that the sensory feedback needed to perform such precision tasks, to judge the flight of a ball and strike it well in return, exceeds the ability of humans, especially under adverse conditions such as inadequate light or gusting wind. Prior knowledge, experience with such conditions, can be integrated with sensory feedback by the human sensorimotor system to allow improved performance. According to bayesian theory, an optimal estimate results from combining information about the distribution of velocities — the prior — with evidence from sensory feedback. As uncertainty increases, when playing in fog or at dusk, the system should increasingly rely on prior knowledge. To use a bayesian strategy, the brain would need to represent the prior distribution and the level of uncertainty in the sensory feedback. Here we control the statistical variations of a new sensorimotor task and manipulate the uncertainty of the sensory feedback. We show that subjects internally represent both the statistical distribution of the task and their sensory uncertainty, combining them in a manner consistent with a performance-optimizing bayesian process. The central nervous system therefore employs probabilistic models during sensorimotor learning.Chris points out that this does not mean, as has been claimed in some over hyped news articles, that we are all "hard wired Bayesian with a subconscious grasp of deep mathematics". If we are then so is my dog who can catch things thrown at him pretty well, even in windy conditions. Chris adds: As to whether this study reveals the Bayesian within, I'd submit that the question is not really well defined here. A frequentist modeler with the same information in the study would behave consistently with what was observed. Why? Because Bayes' rule is a probabilistic device, not an exclusively Bayesian one. The posterior mean which minimizes mean-squared error is an optimal (suitably qualified) frequentist procedure as well as a natural Bayesian predictor. The practical distinction between a Bayesian and frequentist lies in the tools they use, how they interpret their inferences, and how they incorporate unmodeled prior information, especially in cases where the data do not dominate. This task paradigm does not exercise these differences.Ok, so were not wired for math and it's not obviously Bayesian, but the "hard-wired" bit intrigues me. Something subconscious is happening. fMRI studies of brains indicate that our brains "decide" and react before we become consciously aware of having made a decision. Thinking about complex, speedy physical tasks as you are doing them seems to degrade performance. "Use the force Luke". Once we have learned the basic skills of some activity by paying attention it seems as if the skill and knowledge is in our bodies rather than our conscious minds, that our hands know what to do. Some of us are very much more talented than others though not obviously smarter in the usual sense of the term. Better sensory equipment can explain part of this difference, a ball player with exceptional vision has a distinct advantage, but it doesn't explain everything. "Fast twitch" muscle fibers can explain part of the difference, and someone with both great sensory and great motor equipment has a huge advantage. But there still seems to be more, something not explained by sensorimotor differences. We may not be conscious of decision making but we do decide and so there's a mental component, even if it is somehow a distributed mentality that includes the nervous system as well as the brain. This brings to mind the speculations of William Calvin about the evolution of human brains. Calvin seizes on the action-at-a-distance skills humans developed; throwing in the simplest case. To hit a rabbit from a car length away, you need to let go of the rock within a time equal to the time the shutter of a camera stays open when set at 1/200 second. And if the rabbit is twice as far away, your launch window shrinks eightfold. There aren't too many cameras around that operate at 1/1600 second. But your brain can time things that precisely, letting the rock slip at just the right fraction of a millisecond, over a throwing time of many hundreds of milliseconds. Somehow. It has to, if you can hit such a target. So saith Newtonian physics...Precise timing in organic systems seems to depend on synchronization of a large number of cells, none of which are individually precise but when together influence one another. The more the better. Neurons are notably noisy things and great precision is not their forte. But more are better. Heart cells in isolation will beat, but somewhat irregularly. Clump a few together, and they'll exchange currents so as to all beat together--and the beat will be more regular. Forty cells linked together are even more rhythmic, ticking along like a clock. The timing precision depends on the square root of the number of cells, something called the Law of Large Numbers.I wonder if Chris, a statistician with a background in biochemistry and an inquiring mind, can illuminate this subject further? |
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Comments
(Appropriate disclaimer: Although I absorb a good amount of neuroscience as part of my research, I'm not an expert; take this as you will.) There's a classic experiment on motor learning and transfer (I forget the reference offhand) where participants were trained to throw an object to hit an underwater target. The target was then moved to a different depth. In one condition, participants were briefly instructed about refraction of the object to give them a conceptual model; in the other condition, participants received no such instruction. The result was that the instructed group trained up at the new depth much faster; in fact, many in the non-instructed group had persistent difficulty. Having a high-level conceptual model thus significantly improved transfer of motor performance between tasks. This goes to the point you raised about variations in sensory equipment or fast muscle speed not being sufficient to explain individual differences in performance. The network governing motor learning and transfer involves many different “skills” (and also brain areas), including planning, prediction, eye movement, and focusing of attention. Altering execution of any of these can sharply affect performance, leaving a wide scope for individual variation. Once we have learned the basic skills of some activity by paying attention it seems as if the skill and knowledge is in our bodies rather than our conscious minds, that our hands know what to do. You're right. Automatization of practiced motor tasks is very effective, which is why it can be so difficult to slowly demonstrate a well-practiced maneuver and why it's so easy to choke on a high pressure shot. (As you suggest, there is a lot of evidence generally that experts at a motor-skill have problems when they think about their actions.) Precise timing in organic systems seems to depend on synchronization of a large number of cells, none of which are individually precise but when together influence one another. The more the better. Precise direction, too. There's an old study on monkeys from the 1980s where it was shown that large groups of neurons in primary motor cortex encode movement direction. Each individual neuron is tuned to a rather broad range of preferred directions, and many neurons have similar preferred ranges. But in encoding the movement direction they average together vector-like, and thus achieve greater precision than any one neuron can alone. (I'm sure there's been much more work on this of late.) This is consistent with the larger cortical representation in the primary motor area (the so-called homunculus) associated with parts of the body requiring precise control. A similar averaging probably also enables precise timing, though the specifics seem more complex to me. For a complex movement like hitting a moving target from a distance, the fastest response times to stimuli, even under the best conditions, are larger than the differences in timing between success and failure. Preparation and planning are also required and can take more time than the response itself. Thus, the movement must be initiated substantially before the throw. I can imagine (though this is only speculation) a population of neurons with varying timing windows; inputs related to target prediction and from feedback received during practice strengthen a subset of these whose combined firing averages out to a particular timing. As practice accrues, some parts of the task presumably become automatized. I'm not sure this implies that more is better, however, at least beyond some point of diminishing returns. For instance, there are some inherent constraints on precision (e.g., stochasticity in neural firing, muscular response) below which it does not pay to go. And there is a trade-off between the cost of supporting that precision (in energy needs, opportunity cost, etc.) and the survival value of the task. Without taking too hard an adaptationist line, I'd guess that brain size is rather well tuned to this trade off in most species. The example of the chickadee comes to mind: every fall, it's brain volume increases by 30% through the addition of new neurons, only to decrease again in the spring. One working model is that this change is related to its increased need for spatial memory in the winter to find it's many caches of food that it makes in the fall. That the brain volume decreases again in the spring may suggest that its extra metabolic cost is not worth the added survival value during that period. Thanks for the interesting comments. Hi Chris, It seems true; brains are as big as they need to be and no bigger. The sea squirt, a relative of ours that shares a remarkable number of features with us, no longer needs its cerebral ganglion once past the larval stage so it goes away. I'm sure you've heard all the jokes. It's not clear what survival advantage in the EEA would have been served by an even bigger brain for humans. The price would have been high not only in the cost of running it but in the skeletal changes to carry it around. It would have been pretty hard on mothers too unless the trend to delayed maturity and neoteny also increased. That's not cheap either. I'll think about this more, sleep on it, and maybe say something useful. Thanks for your help. Posted by: back40 at January 25, 2004 11:53 PMPost a comment
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