Fast Estimation of Information Theoretic Learning Descriptors using Explicit Inner Product Spaces
This work addresses scalability problems in signal processing and machine learning for large datasets, though it is incremental as it builds on existing no-trick kernel methods.
The paper tackles the computational scalability issues of Information Theoretic Learning (ITL) by extending no-trick kernel methods to ITL, resulting in fast and accurate estimators that maintain performance without compromising scalability.
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of a kernel function, leading to scalability issues for large datasets due to its linear and superlinear growth with respect to the training data. Recently, we proposed \emph{no-trick} (NT) kernel adaptive filtering (KAF) that leverages explicit feature space mappings using data-independent basis with constant complexity. The inner product defined by the feature mapping corresponds to a positive-definite finite-rank kernel that induces a finite-dimensional reproducing kernel Hilbert space (RKHS). Information theoretic learning (ITL) is a framework where information theory descriptors based on non-parametric estimator of Renyi entropy replace conventional second-order statistics for the design of adaptive systems. An RKHS for ITL defined on a space of probability density functions simplifies statistical inference for supervised or unsupervised learning. ITL criteria take into account the higher-order statistical behavior of the systems and signals as desired. However, this comes at a cost of increased computational complexity. In this paper, we extend the NT kernel concept to ITL for improved information extraction from the signal without compromising scalability. Specifically, we focus on a family of fast, scalable, and accurate estimators for ITL using explicit inner product space (EIPS) kernels. We demonstrate the superior performance of EIPS-ITL estimators and combined NT-KAF using EIPS-ITL cost functions through experiments.