  Often machine learning and statistical models will attempt to describe the
majority of the data. However, there may be situations where only a fraction of
the data can be fit well by a linear regression model. Here, we are interested
in a case where such inliers can be identified by a Disjunctive Normal Form
(DNF) formula. We give a polynomial time algorithm for the conditional linear
regression task, which identifies a DNF condition together with the linear
predictor on the corresponding portion of the data. In this work, we improve on
previous algorithms by removing a requirement that the covariances of the data
satisfying each of the terms of the condition have to all be very similar in
spectral norm to the covariance of the overall condition.
