Causal inference in cue combination

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Causal inference in cue combination
Konrad Kording www.koerding.com
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Modeling Where do cues come from?
Generate
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Traditional Bayesian model
Infer
Alais Burr 04, Battaglia et al 03, Knill
Pouget 04, Ernst Banks 02, Gahramani 95, van
Beers et al, etc
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Visual Auditory combination (Ventriloquist effect)
Both cues
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What would happen now?
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Do we believe this kind of model?
Assumes there is one and only one cause!
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Alternative model
or
Kording, Beierholm, Ma, Quartz, Tenenbaum, Shams,
2007
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Calculate probability of model

• Using Bayes rule

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Independent causes where is the auditory
stimulus
Audio Visual
Best estimate
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Common cause where is the auditory stimulus
Audio Visual Combined
Best estimate
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Mean squared error estimate
Audio Visual Combine
Best estimate
Remark Knill uses virtually identical math
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Experimental test
Button common cause or two
Wallace et al 2005 Hairston et al 2004
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Measured gain
Data
Kording et al
Sato et al, in press
Wallace et al 2005 Hairston et al 2004
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How can the gain be negative?
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Predicting the variance
Worse prediction if we assume model selection
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Take home message

• Uncertainty about causal structure
• Bayesian framework is modular
• Easy to extend
• Causality problems occur in many domains

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Acknowledgements

• Ulrik Beierholm
• Wei Ji Ma
• Steven Quartz
• Joshua Tenenbaum
• Ladan Shams
• Kunlin Wei