The literature on provable robustness in machine learning has primarily
focused on static prediction problems, such as image classification, in which
input samples are assumed to be independent and model performance is measured
as an expectation over the input distribution. Robustness certificates are
derived for individual input instances with the assumption that the model is
evaluated on each instance separately. However, in many deep learning
applications such as online content recommendation and stock market analysis,
models use historical data to make predictions. Robustness certificates based
on the assumption of independent input samples are not directly applicable in
such scenarios. In this work, we focus on the provable robustness of machine
learning models in the context of data streams, where inputs are presented as a
sequence of potentially correlated items. We derive robustness certificates for
models that use a fixed-size sliding window over the input stream. Our
guarantees hold for the average model performance across the entire stream and
are independent of stream size, making them suitable for large data streams. We
perform experiments on speech detection and human activity recognition tasks
and show that our certificates can produce meaningful performance guarantees
against adversarial perturbations