@conference {471,
	title = {On The Relationship Between Online Gaussian Process Regression And Kernel Least Mean Squares Algorithms},
	booktitle = {2016 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2016)},
	year = {2016},
	month = {September},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Salerno, Italy},
	abstract = {We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover that their operation corresponds to the assumption of a fixed posterior covariance that follows a simple parametric model. Interestingly, several well-known KLMS algorithms correspond to specific cases of this model. The probabilistic perspective allows us to understand how each of them handles uncertainty, which could explain some of their performance differences.},
	keywords = {gaussian processes, kernel adaptive filtering, KLMS},
	author = {Van Vaerenbergh, Steven and Fern{\'a}ndez-Bes, Jes{\'u}s and Elvira, Victor}
}
@conference {393,
	title = {Probabilistic Kernel Least Mean Squares Algorithms},
	booktitle = {2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
	year = {2014},
	month = {05/2014},
	abstract = {The kernel least mean squares (KLMS) algorithm is a computationally efficient nonlinear adaptive filtering method that "kernelizes" the celebrated (linear) least mean squares algorithm. We demonstrate that the least mean squares algorithm is closely related to the Kalman filtering, and thus, the KLMS can be interpreted as an approximate Bayesian filtering method. This allows us to systematically develop extensions of the KLMS by modifying the underlying state-space and observation models. The resulting extensions introduce many desirable properties such as "forgetting", and the ability to learn from discrete data, while retaining the computational simplicity and time complexity of the original algorithm.},
	keywords = {kernel adaptive filtering, KLMS, sequential Bayesian learning, state-space model},
	isbn = {978-1-4799-2892-7},
	author = {Park, Il Memming and Seth, Sohan and Van Vaerenbergh, Steven}
}
@inbook {423,
	title = {Online Regression with Kernels},
	booktitle = {Regularization, Optimization, Kernels, and Support Vector Machines},
	number = {Machine Learning \& Pattern Recognition Series},
	year = {2014},
	pages = {477-501},
	publisher = {Chapman and Hall/CRC},
	organization = {Chapman and Hall/CRC},
	chapter = {21},
	address = {New York},
	abstract = {Online machine learning algorithms are designed to learn from one data instance at a time. They are typically used in real-time scenarios, such as prediction or tracking problems, where data arrive sequentially and instant decisions must be made. The real-time nature of these settings implies that shortly after the decision is made, the true label will be made available, which allows the learning algorithm to adjust its solution before a new datum is received.

Online kernel methods extend the nonlinear learning capabilities of standard batch kernel methods to online environments. Especially important for these techniques is that they maintain their computational load moderate during each iteration, in order to perform fast updates in real time. Ideally, they should not only be able to learn in a stationary environment but also in non-stationary settings, where they must forget outdated information and adapt their solution to respond to changes in time. Online kernel methods also find use in batch scenarios where the amount of data is too high to fit in the machine{\textquoteright}s memory, and one or several passes over the data are to be performed.

In this chapter we focus on the problem of online regression. We will give an overview of the most important kernel-based methods for this problem, which have been developed over the span of the last decade. We start by formulating the online solution to the kernel ridge regression problem, and we point out different strategies to overcome the bottlenecks associated to using kernels in online methods. The discussed techniques are often referred to as kernel adaptive filtering algorithms, due to their close relationship with classical adaptive filters from the signal processing literature. After reviewing the most relevant algorithms in this area, we introduce an evaluation framework that allows us to compare their performance. We finish the discussion with a brief overview of the recent and future research directions.},
	keywords = {KLMS, KRLS},
	isbn = {9781482241396},
	url = {http://www.crcpress.com/product/isbn/9781482241396},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
