Similarity as Likelihood Ratio: Coupling Representations from Machine Learning (and Other Sources) With Cognitive Models

Similarity lies at the core of theories of memory and perception. To understand similarity relations among complex items like text and images, researchers often rely on machine learning to derive high-dimensional vector representations of those items. To use these representations to explain and predict human performance, a cognitive model must establish a relationship between vector similarity and the psychological construct of similarity. To that end, I introduce SALR (``similarity as likelihood ratio''), a mathematical transformation of the similarity between vector representations, operationalized as the cosine of the angle between them, into a ratio of the relative likelihood that the two representations encode the same versus different items. The likelihood ratio operationalizes similarity in a manner that is motivated by theories of perception and memory while also being readily ``plugged in'' to existing cognitive models. Three example applications show how SALR can be used to compute drift rates of a diffusion decision model based on similarity information derived from machine learning models, thereby accounting for the speed and accuracy with which individual participants respond to individual items. SALR enables inferences regarding how different people represent items, how much information they encode about each item, and how that information is affected by experimental manipulations. SALR serves both the practical purpose of making it easier to incorporate representations from machine learning---indeed, any method in which similarity is operationalized as a cosine---into cognitive models and the theoretical purpose of allowing cognitive models to grant insight into how people process the increasingly complex, naturalistic items to which machine learning models are applied.