Speaker: Fernando Andrés Quintana
Title: A Projection Approach to Local Regression with Variable-Dimension Covariates
Abstract:
Incomplete covariate vectors are known to be problematic for estimation and inferences
on model parameters, but their impact on prediction performance is less
understood. We develop an imputation-free method that builds on a random partition
model admitting variable-dimension covariates. Cluster-specific response models
further incorporate covariates via linear predictors, facilitating estimation of smooth
prediction surfaces with relatively few clusters. Component kernels exploit marginalization
techniques to analytically project response distributions according to any
pattern of missing covariates, yielding a local regression with internally consistent
uncertainty propagation that utilizes only one set of coefficients per cluster. Aggressive
shrinkage of these coefficients regulates uncertainty due to missing covariates.
The method allows in- and out-of-sample prediction for any missingness pattern,
even if the pattern in a new subject’s incomplete covariate vector was not seen in
the training data. We develop an MCMC algorithm for posterior sampling that improves
a computationally expensive update for latent cluster allocation. Finally, we
demonstrate the model’s effectiveness for nonlinear point and density prediction under
various circumstances by comparing with other recent methods for regression of
variable dimensions on synthetic and real data.
Note: Seminars are free and open to the public.
