In this talk I will describe two scientific collaborations where high-dimensional linear regression has proven useful.
In the first part, we discuss adjustments of treatment effect estimates in randomized experiments using the lasso (l1 penalized linear regression). Randomization ensures that the difference in mean outcomes between treatment and control groups is an unbiased estimate of the average causal effect of the treatment. However, investigators often use regression to correct for covariate imbalances, with the aim of reducing the variance of the estimated treatment effect. If there are a large number of covariates relative to the number of observations, the Lasso can be used for both variable selection and adjustment. We study the resulting treatment effect estimator under the nonparametric Neyman-Rubin model of randomized experiments, which does not assume the data comes from a generative linear model. We derive conditions under which the adjusted estimator enjoys favorable asymptotic properties compared to the unadjusted estimator, even under this flexible model.

In the second part, we study the properties of extrastriate regions in the mammalian visual cortex by building encoding models of natural stimuli. We focus on area MT (middle temporal), which is involved in perception of motion and object tracking. We develop and compare predictive models of spiking neurons in area MT using several image and video descriptors, including spatiotemporal Gabor wavelets and patch-based methods using sparse coding. Though MT is often thought to behave like area V1, but with larger receptive fields, we find evidence of sensitivity of MT neurons to complex visual features beyond the outputs of standard V1-type filters.