Braiding: A scheme for resolving hazards in kernel adaptive filters

Computational cost presents a barrier in the application of machine learning algorithms to large-scale real-time learning problems. Kernel adaptive filters (KAFs) have low computational cost with the ability to learn online and are hence favoured for such applications. Unfortunately, dependencies of the outputs on the weight updates prohibit pipelining. This paper introduces a combination of parallel execution and conditional forwarding, called braiding, which overcomes dependencies by expressing the output as a combination of the earlier state and other examples in the pipeline. To demonstrate its utility, braiding is applied to the implementation of classification, regression and novelty detection algorithms based on the Naive Online regularised Risk Minimization Algorithm (NORMA). Fixed point, open source implementations are described which can achieve data rates of around 130 MSamples/s with a latency of 10 to 13 clock cycles. This constitutes a two orders of magnitude increase in throughput and one order of magnitude decrease in latency compared to a single core CPU implementation.