  Medical studies frequently require to extract the relationship between each
covariate and the outcome with statistical confidence measures. To do this,
simple parametric models are frequently used (e.g. coefficients of linear
regression) but usually fitted on the whole dataset. However, it is common that
the covariates may not have a uniform effect over the whole population and thus
a unified simple model can miss the heterogeneous signal. For example, a linear
model may be able to explain a subset of the data but fail on the rest due to
the nonlinearity and heterogeneity in the data. In this paper, we propose
DDGroup (data-driven group discovery), a data-driven method to effectively
identify subgroups in the data with a uniform linear relationship between the
features and the label. DDGroup outputs an interpretable region in which the
linear model is expected to hold. It is simple to implement and computationally
tractable for use. We show theoretically that, given a large enough sample,
DDGroup recovers a region where a single linear model with low variance is
well-specified (if one exists), and experiments on real-world medical datasets
confirm that it can discover regions where a local linear model has improved
performance. Our experiments also show that DDGroup can uncover subgroups with
qualitatively different relationships which are missed by simply applying
parametric approaches to the whole dataset.
