Robust averaging during perceptual choice Vincent de Gardelle and Christopher Summerfield [email protected] http://sites.google.com/site/vincentdegardelle/

Robust averaging

Background: SDT and diffusion

using multiple logistic regression we assessed the weight of evidence for each element, as a function of its rank in the array.

Signal detection theory (SDT) as a model for perceptual choices

Accumulation models using SDT in time

LPR model

Robust averaging: variance effect

Questions: how do we integrate multiple elements? process the mean and variance of the evidence?

within participants

across participants

1 stimulus rank

1.5

Multi-element averaging paradigm RT(s)

beta reduction

beta

inlying outlying

0.5

1

0.5

0

Errors(%) −0.5

decision relevant

30

0.7

15 0.6 0

fixation

low mean |μ|=1 high mean |μ|=2

stimulus

30

0.7 feedback

15 0.6

σ x>0

low mid high variance

0

low

med

0

high

bars: human data, lines: LPR model

40

80

120

160

variance cost on RT (ms)

variance

dots: individual subjects, line: regression

Robust averaging: within trial 1. we computed separately the weighting profiles for the two categories of trials... 1.2

within-trial discarding: separate profiles

1

low mid high variance

0.8

beta

μ x<0

decision irrelevant

response is the average more red or blue?

0

2. Control experiment: testing different regions of the color space, discarding was related to the decision value, not to the color itself.

0.6 0.4 0.2

μ<0 μ>0

0 −0.2

DV(t+1) = DV(t) + inc + noise predicted

simple average inc = μ

signal over noise inc = μ/σ

probabilistic averaging inc = mean(LPR(x))

fitted

−0.2

0

0.2

value space

between-trials discarding: global profile across categories

Conlusions When combining several pieces of evidence, subjects exhibit a robust averaging behaviour, and discard the elements that contribute extreme values in the pool. In the present study, this behaviour can be captured by a model accumulating probabilistic information across the array to make its choice.

de Gardelle, V., and Summerfield, C., (2011) Robust averaging during perceptual judgment, PNAS 108 (32) 13341-13346