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This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
Controlling nonlinear systems, especially when data are being used to offset uncertainties in the model, is hard. A natural approach when dealing with the challenges of nonlinear control is to reduce the system to a linear one via change of…
The paper is a follow-up of the recently introduced kernel-based framework to identify nonlinear input-output systems regularized by desirable input-output incremental properties. Assuming that the system has fading memory, we propose to…
In this paper we aim at increasing the descriptive power of the covariance matrix, limited in capturing linear mutual dependencies between variables only. We present a rigorous and principled mathematical pipeline to recover the kernel…
The possible methodologies to handle the uncertain parameter are reviewed. The core idea of the desensitized Kalman filter is introduced. A new cost function consisting of a posterior covariance trace and trace of a weighted norm of the…
This paper addresses the problem of filtering with a state-space model. Standard approaches for filtering assume that a probabilistic model for observations (i.e. the observation model) is given explicitly or at least parametrically. We…
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…
In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…
There is a great need for robust techniques in data mining and machine learning contexts where many standard techniques such as principal component analysis and linear discriminant analysis are inherently susceptible to outliers.…
Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model…
A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of…