  Regression models, which are widely used from engineering applications to
financial forecasting, are vulnerable to targeted malicious attacks such as
training data poisoning, through which adversaries can manipulate their
predictions. Previous works that attempt to address this problem rely on
assumptions about the nature of the attack/attacker or overestimate the
knowledge of the learner, making them impractical. We introduce a novel Local
Intrinsic Dimensionality (LID) based measure called N-LID that measures the
local deviation of a given data point's LID with respect to its neighbors. We
then show that N-LID can distinguish poisoned samples from normal samples and
propose an N-LID based defense approach that makes no assumptions of the
attacker. Through extensive numerical experiments with benchmark datasets, we
show that the proposed defense mechanism outperforms the state of the art
defenses in terms of prediction accuracy (up to 76% lower MSE compared to an
undefended ridge model) and running time.
