Initialising Kernel Adaptive Filters via Probabilistic Inference

TL;DR

This paper introduces a probabilistic framework for initializing and adaptively learning kernel adaptive filters, improving their performance and sparsity through Bayesian inference and sequential updates.

Contribution

It proposes a novel probabilistic approach for initializing and fully adapting kernel adaptive filters with learned kernel parameters and dictionaries.

Findings

Outperforms standard KAFs in mean square error

Achieves sparser learned dictionaries

Enables sequential updates with new data

Abstract

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.