1 research outputs found
Sparse Partially Linear Additive Models
The generalized partially linear additive model (GPLAM) is a flexible and
interpretable approach to building predictive models. It combines features in
an additive manner, allowing each to have either a linear or nonlinear effect
on the response. However, the choice of which features to treat as linear or
nonlinear is typically assumed known. Thus, to make a GPLAM a viable approach
in situations in which little is known about the features, one must
overcome two primary model selection challenges: deciding which features to
include in the model and determining which of these features to treat
nonlinearly. We introduce the sparse partially linear additive model (SPLAM),
which combines model fitting and of these model selection challenges
into a single convex optimization problem. SPLAM provides a bridge between the
lasso and sparse additive models. Through a statistical oracle inequality and
thorough simulation, we demonstrate that SPLAM can outperform other methods
across a broad spectrum of statistical regimes, including the high-dimensional
() setting. We develop efficient algorithms that are applied to real
data sets with half a million samples and over 45,000 features with excellent
predictive performance.Comment: Corrected typo