  Data stream classification is an important problem in the field of machine
learning. Due to the non-stationary nature of the data where the underlying
distribution changes over time (concept drift), the model needs to continuously
adapt to new data statistics. Stream-based Active Learning (AL) approaches
address this problem by interactively querying a human expert to provide new
data labels for the most recent samples, within a limited budget. Existing AL
strategies assume that labels are immediately available, while in a real-world
scenario the expert requires time to provide a queried label (verification
latency), and by the time the requested labels arrive they may not be relevant
anymore. In this article, we investigate the influence of finite,
time-variable, and unknown verification delay, in the presence of concept drift
on AL approaches. We propose PRopagate (PR), a latency independent utility
estimator which also predicts the requested, but not yet known, labels.
Furthermore, we propose a drift-dependent dynamic budget strategy, which uses a
variable distribution of the labelling budget over time, after a detected
drift. Thorough experimental evaluation, with both synthetic and real-world
non-stationary datasets, and different settings of verification latency and
budget are conducted and analyzed. We empirically show that the proposed method
consistently outperforms the state-of-the-art. Additionally, we demonstrate
that with variable budget allocation in time, it is possible to boost the
performance of AL strategies, without increasing the overall labeling budget.
