On Prediction Feature Assignment in the Heckman Selection Model
Huy Mai Xintao Wu
Under missing-not-at-random (MNAR) sample selection bias, the performance of
a prediction model is often degraded. This paper focuses on one classic
instance of MNAR sample selection bias where a subset of samples have
non-randomly missing outcomes. The Heckman selection model and its variants
have commonly been used to handle this type of sample selection bias. The
Heckman model uses two separate equations to model the prediction and selection
of samples, where the selection features include all prediction features. When
using the Heckman model, the prediction features must be properly chosen from
the set of selection features. However, choosing the proper prediction features
is a challenging task for the Heckman model. This is especially the case when
the number of selection features is large. Existing approaches that use the
Heckman model often provide a manually chosen set of prediction features. In
this paper, we propose Heckman-FA as a novel data-driven framework for
obtaining prediction features for the Heckman model. Heckman-FA first trains an
assignment function that determines whether or not a selection feature is
assigned as a prediction feature. Using the parameters of the trained function,
the framework extracts a suitable set of prediction features based on the
goodness-of-fit of the prediction model given the chosen prediction features
and the correlation between noise terms of the prediction and selection
equations. Experimental results on real-world datasets show that Heckman-FA
produces a robust regression model under MNAR sample selection bias.