  Supervised learning models are one of the most fundamental classes of models.
Viewing supervised learning from a probabilistic perspective, the set of
training data to which the model is fitted is usually assumed to follow a
stationary distribution. However, this stationarity assumption is often
violated in a phenomenon called concept drift, which refers to changes over
time in the predictive relationship between covariates $\mathbf{X}$ and a
response variable $Y$ and can render trained models suboptimal or obsolete. We
develop a comprehensive and computationally efficient framework for detecting,
monitoring, and diagnosing concept drift. Specifically, we monitor the Fisher
score vector, defined as the gradient of the log-likelihood for the fitted
model, using a form of multivariate exponentially weighted moving average,
which monitors for general changes in the mean of a random vector. In spite of
the substantial performance advantages that we demonstrate over popular
error-based methods, a score-based approach has not been previously considered
for concept drift monitoring. Advantages of the proposed score-based framework
include applicability to any parametric model, more powerful detection of
changes as shown in theory and experiments, and inherent diagnostic
capabilities for helping to identify the nature of the changes.
