Causal inference in cue combination

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

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

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

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

Causal inference in cue combination

Causal inference in cue combination

Presentation Transcript

Causal Inference in Epidemiology

Causal Inference

CAUSAL INFERENCE IN STATISTICS

Impact Evaluation Methods: Causal Inference

Causal Inference with Multiple Treatments

Synthesis: Causal Inference

Causal Inference and Ambiguous Manipulations

Clash of Causal Inference Techniques

Causal Inference

Causal inference

Depth cue combination

Causal Inference

Causality and causal inference

Causal inference

Causal Inference

CAUSAL INFERENCE

Causal Inference