System Identification Via Sparse Multiple Kernel-Based Regularization Using Sequential Convex Optimization Techniques

Chen, Tianshi; Andersen, Martin S.; Ljung, Lennart; Chiuso, Alessandro; Pillonetto, Gianluigi

doi:10.1109/tac.2014.2351851

Cited by 155 publications

(124 citation statements)

References 33 publications

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“…An alternative way is to treat σ 2 as an additional ''hyper-parameter'' contained in η, estimating it by solving (29), e.g. see Chen, Andersen, Ljung, Chiuso, and Pillonetto (2014) and MacKay (1992).…”

Section: Tuning the Regularization: Marginal Likelihood Maximizationmentioning

confidence: 99%

“…(24)) for a collection of candidate models θ 0 . This gives several advantages as described in Chen et al (2014). For example, the tuning problem (29) for (38) is a difference of convex functions programming problem, whose locally optimal solutions can be found efficiently by using sequential convex optimization techniques, (Horst & Thoai, 1999;Tao & An, 1997).…”

Section: General Predictor Models and Arx Modelsmentioning

confidence: 99%

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Kernel methods in system identification, machine learning and function estimation: A survey

et al. 2014

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a b s t r a c tMost of the currently used techniques for linear system identification are based on classical estimation paradigms coming from mathematical statistics. In particular, maximum likelihood and prediction error methods represent the mainstream approaches to identification of linear dynamic systems, with a long history of theoretical and algorithmic contributions. Parallel to this, in the machine learning community alternative techniques have been developed. Until recently, there has been little contact between these two worlds. The first aim of this survey is to make accessible to the control community the key mathematical tools and concepts as well as the computational aspects underpinning these learning techniques. In particular, we focus on kernel-based regularization and its connections with reproducing kernel Hilbert spaces and Bayesian estimation of Gaussian processes. The second aim is to demonstrate that learning techniques tailored to the specific features of dynamic systems may outperform conventional parametric approaches for identification of stable linear systems.

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Section: Tuning the Regularization: Marginal Likelihood Maximizationmentioning

confidence: 99%

Section: General Predictor Models and Arx Modelsmentioning

confidence: 99%

Kernel methods in system identification, machine learning and function estimation: A survey

et al. 2014

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“…Consequently, when the wireless traffic dataset is large, i.e., N is a large number, the time consumption of each 4 However, for multiple linear kernels, such as the ones proposed in [28], [30], [31], P 0 becomes a difference-of-convex problem and efficient algorithms exist for solving the hyper-parameters.…”

Section: ) Learning Objectivesmentioning

confidence: 99%

Wireless Traffic Prediction With Scalable Gaussian Process: Framework, Algorithms, and Verification

Yin

et al. 2019

IEEE J. Select. Areas Commun.

161

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The cloud radio access network (C-RAN) is a promising paradigm to meet the stringent requirements of the fifth generation (5G) wireless systems. Meanwhile, wireless traffic prediction is a key enabler for C-RANs to improve both the spectrum efficiency and energy efficiency through load-aware network managements. This paper proposes a scalable Gaussian process (GP) framework as a promising solution to achieve large-scale wireless traffic prediction in a cost-efficient manner. Our contribution is three-fold. First, to the best of our knowledge, this paper is the first to empower GP regression with the alternating direction method of multipliers (ADMM) for parallel hyper-parameter optimization in the training phase, where such a scalable training framework well balances the local estimation in baseband units (BBUs) and information consensus among BBUs in a principled way for large-scale executions.Second, in the prediction phase, we fuse local predictions obtained from the BBUs via a cross-validation based optimal strategy, which demonstrates itself to be reliable and robust for general regression tasks. Moreover, such a cross-validation based optimal fusion strategy is built upon a well acknowledged probabilistic model to retain the valuable closed-form GP inference properties. Third, we propose a C-RAN based scalable wireless prediction architecture, where the prediction accuracy and the time consumption can be balanced by tuning the number of the BBUs according to the real-time system demands. Experimental results show that our proposed scalable GP model can outperform the state-of-the-art approaches considerably, in terms of wireless traffic prediction performance. Index TermsC-RANs, Gaussian processes, parallel processing, ADMM, cross-validation, machine learning, wireless traffic solution to reach such ambitious goals is the adoption of cloud radio access networks (C-RANs) [2], which have attracted intense research interests from both academia and industry in recent years [3]. A C-RAN is composed of two parts: the distributed remote radio heads (RRHs) with basic radio functionalities to provide coverage over a large area, and the centralized baseband units (BBUs) pool with parallel BBUs to support joint processing and cooperative network management. The BBUs can perform dynamic resource allocation in accordance with realtime network demands based on the virtualized resources in cloud computing. One major feature for the C-RANs to enable high energy-efficient services is the fast adaptability to non-uniform traffic variations [1]-[4], e.g., the tidal effects. Consequently, wireless traffic prediction techniques stand out as the key enabler to realize such loadaware management and proactive control in C-RANs, e.g., the load-aware RRH on/off operation [4]. However, the adoption of wireless traffic prediction techniques in C-RANs must satisfy the requirements on prediction accuracy, cost-efficiency, implementability, and scalability for large-scale executions. A. Related WorksIn the literature, many statistical ti...

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“…4 When X is a subset of R and µ is the Lebesgue measure, L 2 (X, µ) will be written as L 2 (X) for simplicity. 5 If for some λ, the homogenous integral equation…”

Section: Norm and Orthonormal Basis Expansionmentioning

confidence: 99%

Continuous-time DC kernel — A stable generalized first order spline kernel

Chen

Pillonetto

Chiuso

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have been applied and studied extensively for kernel-based regularized LTI system identification. In this note, we show that similar to the derivation of the SS kernel, the continuous-time DC kernel can be derived by applying the same "stable" coordinate change to a "generalized" first-order spline kernel, and thus can be interpreted as a stable generalized first-order spline kernel. This interpretation provides new facets to understand the properties of the DC kernel. In particular, we derive a new orthonormal basis expansion of the DC kernel, and the explicit expression of the norm of the RKHS associated with the DC kernel.Moreover, for the non-uniformly sampled DC kernel, we derive its maximum entropy property and show that its kernel matrix has tridiagonal inverse.

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System Identification Via Sparse Multiple Kernel-Based Regularization Using Sequential Convex Optimization Techniques

Cited by 155 publications

References 33 publications

Kernel methods in system identification, machine learning and function estimation: A survey

Kernel methods in system identification, machine learning and function estimation: A survey

Wireless Traffic Prediction With Scalable Gaussian Process: Framework, Algorithms, and Verification

Continuous-time DC kernel — A stable generalized first order spline kernel

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