Vector-Valued Kernel Ridge Regression for the Modeling of High-Speed Links

Soleimani, Nastaran; Trinchero, Riccardo; Canavero, Flavio

doi:10.1109/nemo51452.2022.10038963

Cited by 4 publications

(6 citation statements)

References 11 publications

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“…As a tradeoff between the uncoupled and mixed kernel function, this article presents a separable kernel structure based on the product of standard radial basis function (RBF) kernels [29], such as…”

Section: B Coupled Multioutput Kernel Matrixmentioning

confidence: 99%

“…Specifically, the proposed modeling framework implements the conjugate gradient method [43], which provides an efficient version of the above algorithm tailored for semidefinite matrices, as the matrix A [29]. Such implementation allows reducing the computational complexity of the training phase from O(L 3 D 3 ) to O(K L 2 D 2 ), where K is the number of iterations required by the GD algorithm to converge.…”

Section: B Coupled Multioutput Kernel Matrixmentioning

confidence: 99%

“…It is important to stress that the obtained speedup is mitigated by the relatively fast simulation time required by the ADS circuital solver when it is used in a small-signal analysis. Moreover, unlike the ADS optimizer, the obtained model turns out to be independent of the optimization constraints and therefore can be suitably adopted as it is to meet different optimization constraints, as well as for the stochastic analysis within the uncertainty quantification scenario [13], [29].…”

Section: Application Example: Doherty Amplifiermentioning

confidence: 99%

“…Such a technique exploits the statistical correlations among the different components of the output dimensions. Due to its statistical nature, it provides extremely accurate results in the uncertainty quantification scenario [12], [27], [29]. On the contrary, if the number of components in the compressed representation is not carefully tuned, the obtained model can have a limited generalization capability on unseen data, thus leading to possible lack of accuracy for the case of deterministic parametric models (e.g., the ones used for optimization purposes) [29].…”

Section: Introductionmentioning

confidence: 99%

“…This article makes use of a vector-valued formulation of the kernel ridge regression (KRR) able to deal with multioutput regression problems. The proposed methodology is based on a generalized definition of the reproducing kernel Hilbert space (RKHS) and kernel functions in the case of vector-valued learning problem presented in [26], [30], [31], and [32] and extends the preliminary implementation briefly presented in [29]. The proposed multioutput KRR aims at reducing the gap between kernel-based regressions and multioutput ANN structures.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Bridging the Gap Between Artificial Neural Networks and Kernel Regressions for Vector-Valued Problems in Microwave Applications

Soleimani

Trinchero

Canavero

2023

IEEE Trans. Microwave Theory Techn.

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Thanks to their convex formulation, kernel regressions have shown an improved accuracy with respect to artificial neural network (ANN) structures in regression problems where a reduced set of training samples are available. However, despite the above interesting features, kernel regressions are inherently less flexible than ANN structures since their implementations are usually limited to scalar-output regression problems. This article presents a vector-valued (multioutput) formulation of the kernel ridge regression (KRR) aimed at bridging the gap between multioutput ANN structures and scalar kernel-based approaches. The proposed vector-valued KRR relies on a generalized definition of the reproducing kernel Hilbert space (RKHS) and on a new multioutput kernel structure. The mathematical background of the proposed vector-valued formulation is extensively discussed together with different matrix kernel functions and training schemes. Moreover, a compression strategy based on the Nystrom approximation is presented to reduce the computational complexity of the model training. The effectiveness and the performance of the proposed vector-valued KRR are discussed on an illustrative example consisting of a high-speed link and on the optimization of a Doherty amplifier.

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Section: B Coupled Multioutput Kernel Matrixmentioning

confidence: 99%

Section: B Coupled Multioutput Kernel Matrixmentioning

confidence: 99%

Section: Application Example: Doherty Amplifiermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Bridging the Gap Between Artificial Neural Networks and Kernel Regressions for Vector-Valued Problems in Microwave Applications

Soleimani

Trinchero

Canavero

2023

IEEE Trans. Microwave Theory Techn.

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Efficient Implementation of the Vector-Valued Kernel Ridge Regression for the Uncertainty Quantification of the Scattering Parameters of a 2-GHz Low-Noise Amplifier

Soleimani,

Manfredi,

Trinchero

2023

2023 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO)

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Stochastic Time-Domain Mapping for Comprehensive Uncertainty Assessment in Eye Diagrams

Telescu,

Trinchero,

Soleimani

et al. 2023

IEEE Trans. Electromagn. Compat.

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The eye diagram is one of the most common tools used for quality assessment in high-speed links. This article proposes a method of predicting the shape of the inner eye for a link subject to uncertainties. The approach relies on machine learning regression and is tested on the very challenging example of flexible link for smart textiles. Several sources of uncertainties are taken into account related to both manufacturing tolerances and physical deformation. The resulting model is fast and accurate. It is also extremely versatile: rather than focusing on a specific metric derived from the eye diagram, its aim is to fully reconstruct the inner eye and enable designers to use it as they see fit. This article investigates the features and convergence of three alternative machine learning algorithms, including the single-output support vector machine regression, together with its least squares variant, and the vector-valued kernel ridge regression. The latter method is arguably the most promising, resulting in an accurate, fast and robust tool enabling a complete parametric stochastic map of the eye.

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Vector-Valued Kernel Ridge Regression for the Modeling of High-Speed Links

Cited by 4 publications

References 11 publications

Bridging the Gap Between Artificial Neural Networks and Kernel Regressions for Vector-Valued Problems in Microwave Applications

Bridging the Gap Between Artificial Neural Networks and Kernel Regressions for Vector-Valued Problems in Microwave Applications

Efficient Implementation of the Vector-Valued Kernel Ridge Regression for the Uncertainty Quantification of the Scattering Parameters of a 2-GHz Low-Noise Amplifier

Stochastic Time-Domain Mapping for Comprehensive Uncertainty Assessment in Eye Diagrams

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