Title: Recursive Multikernel Filters Exploiting Nonlinear Temporal Structure,
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.