  In online applications with streaming data, awareness of how far the training
or test set has shifted away from the original dataset can be crucial to the
performance of the model. However, we may not have access to historical samples
in the data stream. To cope with such situations, we propose a novel method,
Continual Density Ratio Estimation (CDRE), for estimating density ratios
between the initial and current distributions ($p/q_t$) of a data stream in an
iterative fashion without the need of storing past samples, where $q_t$ is
shifting away from $p$ over time $t$. We demonstrate that CDRE can be more
accurate than standard DRE in terms of estimating divergences between
distributions, despite not requiring samples from the original distribution.
CDRE can be applied in scenarios of online learning, such as importance
weighted covariate shift, tracing dataset changes for better decision making.
In addition, (CDRE) enables the evaluation of generative models under the
setting of continual learning. To the best of our knowledge, there is no
existing method that can evaluate generative models in continual learning
without storing samples from the original distribution.
