# Recursive Multikernel Filters Exploiting Nonlinear Temporal Structure

## TL;DR

This paper introduces a recursive multikernel filtering method that adaptively combines multiple kernels to better capture nonlinear temporal structures in data, outperforming classical approaches in various tasks.

## Contribution

It proposes a novel recursive multikernel filtering approach that adaptively learns to combine kernels, capturing complex temporal dependencies more effectively than previous methods.

## Key findings

- Outperforms classical methods in artificial and real tasks
- Automatically learns to process nonlinear temporal information
- Effective in both batch and online settings

## Abstract

In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert space, giving rise to a complex model where multiple kernels operate on different temporal combinations of the input signal. In the original formulation, the kernels are then simply combined to obtain a single kernel matrix (for instance by averaging), which provides computational benefits but discards important information on the temporal structure of the signal. Inspired by works on multiple kernel learning, we overcome this drawback by considering the different kernels separately. We propose an efficient strategy to adaptively combine and select these kernels during the training phase. The resulting batch and online algorithms automatically learn to process highly nonlinear temporal information extracted from the input signal, which is implicitly encoded in the kernel values. We evaluate our proposal on several artificial and real tasks, showing that it can outperform classical approaches both in batch and online settings.