Kalman Filter for Online Classification of Non-Stationary Data
Michalis K. Titsias Alexandre Galashov Amal Rannen-Triki Razvan Pascanu Yee Whye Teh Jorg Bornschein
In Online Continual Learning (OCL) a learning system receives a stream of
data and sequentially performs prediction and training steps. Important
challenges in OCL are concerned with automatic adaptation to the particular
non-stationary structure of the data, and with quantification of predictive
uncertainty. Motivated by these challenges we introduce a probabilistic
Bayesian online learning model by using a (possibly pretrained) neural
representation and a state space model over the linear predictor weights.
Non-stationarity over the linear predictor weights is modelled using a
parameter drift transition density, parametrized by a coefficient that
quantifies forgetting. Inference in the model is implemented with efficient
Kalman filter recursions which track the posterior distribution over the linear
weights, while online SGD updates over the transition dynamics coefficient
allows to adapt to the non-stationarity seen in data. While the framework is
developed assuming a linear Gaussian model, we also extend it to deal with
classification problems and for fine-tuning the deep learning representation.
In a set of experiments in multi-class classification using data sets such as
CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its
flexibility to capture non-stationarity.