An Optimal Read-Out Model of Perceptual Learning: How to Measure Task Difficulty and Learning Specificity in a Principled Manner

摘要

Task difficulty is an important determinant of the amount, speed, and specificity of perceptual learning (Ahissar & Hochstein, 1997). Yet the field lacks a principled definition of "difficulty" and resorts to ceteris paribus shortcuts instead. For example, all else being equal, high-noise conditions are more difficult than low-noise conditions, high-precision discrimination is more difficult than low-precision discrimination, etc. The problem is that such ceteris paribus assumptions are violated in learning experiments because the performance improves with practice and because of the methodological necessity to manipulate at least two independent variables -- one to define difficulty levels between subjects and another to track thresholds within subjects. Which condition is more difficult: low-precision discrimination in high noise or high-precision discrimination in low noise? A principled answer to such questions must measure the information content of a given stimulus with respect to a given discrimination task. We propose an Optimal Read-Out (ORO) Model based on the Theory of Ideal Observers (TIO, Green & Swets, 1974). The main innovation is that, whereas TIO works with the conditional probability densities of the stimuli themselves, ORO works with the densities of their V1 representations under standard assumptions about the response properties of V1 neurons (Petrov, Dosher, & Lu, 2005). The optimal discrimination boundary is defined as the locus of points in representation space where the likelihood ratio equals one. The optimal d' is calculated by integrating the "hit" and "false alarm" densities on either side of the boundary. In our implementation this involves Monte Carlo integration in 200 dimensions. The efficiency of a human observer -- the squared ratio of their behavioral d' to the optimal d' -- improves with practice and can be compared across conditions. Whereas the absolute efficiency is parameter-dependent, the relative efficiency is not, and it is the latter that is theoretically relevant.