Tractable Conditional Density Estimation using Logistic Gaussian Process

Music City Center 

Conditional density estimation in high dimensional data has been studied extensively inrecent times. In this talk, we propose a model to estimate the conditional density of responses which varies spatially given a covariate vector and a specific location. By utilizing a variation of logspline models, we nonparametrically approximate the unknown link using a triangular basis expansion and assuming a Gaussian prior on the coefficients. We show that the posterior contracts to the true density at a minimax optimal (upto a logarithmic constant) rate. We evaluate the performance of our method with numerous simulations, and compare the results with related high dimensional density estimation techniques. We illustrate our method on a summary measure, namely, the Fractional Anisotropy, collected from 213 subjects at 83 brain locations in a dataset generated by the Alzheimer's Disease Neuroimaging Initiative to identify the functional relationship between the various covariatesand the response with the various locations.

Density estimation

Posterior Contraction

Spline

Scalable approximation 

Biometrics Section