Interpreting Big, Dense, Scary Linear Models Along Predictor Groups for Studying Visual Area V4

• Activity Number: 301
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yuval Benjamini*+ and Julien Mairal and Bin Yu
• Companies: Stanford University and INRIA and University of California, Berkeley
• Keywords: high-dimensional linear models ; interpretation ; predictor-groups ; prediction models ; cortical area V4 ; neuroscience

Abstract

Predictive linear models are getting big: researchers can add thousands of predictors to their model to improve prediction accuracy. Dense model, such as those obtained using ridge-regression, often achieve better prediction than sparse alternatives by adding together many small effects creating a stable prediction rule. Alas, they are much harder to interpret, and often remain black-boxes.

We encounter this problem in modeling the firing rates of neurons in the V4 cortical area in response to a sequence of natural images. Accurate models for these require dense linear combination of features, but it is hard to extract scientific insight from such dense models.

We therefore propose a method for summarizing models along pre-specified predictor groups. We take into account the covariance structure of the design to summarize the impact of each group predictor variables on the predictions. Using this method, we can generate insights regarding the fitted models and develop new hypotheses for function of these neurons. This work was done in collaboration with Jack Gallant's vision lab at UC Berkeley.