Causal inference in cue combination Konrad Kording www.koerding.com.

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Presentation transcript:

Causal inference in cue combination Konrad Kording

Modeling: Where do cues come from? Generate

Traditional Bayesian model Infer Alais & Burr 04, Battaglia et al 03, Knill & Pouget 04, Ernst & Banks 02, Gahramani 95, van Beers et al, etc

Visual Auditory combination (Ventriloquist effect) Both cues

What would happen now?

Do we believe this kind of model? Assumes there is one and only one cause!

Alternative model or Kording, Beierholm, Ma, Quartz, Tenenbaum, Shams, 2007

Calculate probability of model Using Bayes rule:

Independent causes: where is the auditory stimulus Audio Visual Best estimate

Common cause: where is the auditory stimulus Audio Visual Combined Best estimate

Mean squared error estimate Audio Visual Combine Best estimate Remark: Knill uses virtually identical math

Experimental test Wallace et al 2005 Hairston et al 2004 Button: common cause or two

Measured gain Wallace et al 2005 Hairston et al 2004 Data Kording et alSato et al, in press

How can the gain be negative?

Predicting the variance Worse prediction if we assume model selection

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

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