Initialising Kernel Adaptive Filters via Probabilistic Inference
This work addresses the challenge of improving kernel adaptive filters for nonlinear time series analysis, offering incremental advancements in probabilistic methods for adaptive filtering.
The authors tackled the problem of initializing and adapting kernel adaptive filters (KAFs) by developing a probabilistic framework that learns kernel parameters, weights, and dictionaries, achieving lower mean square error and sparser dictionaries compared to standard KAFs in nonlinear time series tasks.
We present a probabilistic framework for both (i) determining the initial settings of kernel adaptive filters (KAFs) and (ii) constructing fully-adaptive KAFs whereby in addition to weights and dictionaries, kernel parameters are learnt sequentially. This is achieved by formulating the estimator as a probabilistic model and defining dedicated prior distributions over the kernel parameters, weights and dictionary, enforcing desired properties such as sparsity. The model can then be trained using a subset of data to initialise standard KAFs or updated sequentially each time a new observation becomes available. Due to the nonlinear/non-Gaussian properties of the model, learning and inference is achieved using gradient-based maximum-a-posteriori optimisation and Markov chain Monte Carlo methods, and can be confidently used to compute predictions. The proposed framework was validated on nonlinear time series of both synthetic and real-world nature, where it outperformed standard KAFs in terms of mean square error and the sparsity of the learnt dictionaries.