Kernel-based system identification from noisy and incomplete input-output data

Risuleo, Riccardo Sven; Bottegal, Giulio; Hjalmarsson, Håkan

doi:10.1109/cdc.2016.7798567

Cited by 5 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tracing the proof of Theorem 3, we have that q (j+1) w is a Gaussian distribution with covariance matrix and mean given by (41) where the expectations are taken with respect to q Similarly, q (j+1) g is a Gaussian distribution with covariance matrix and mean given by (42), where the expectations are taken with respect to q Plugging these expectations into (42) and (41) we obtain (35).…”

Section: A4 Proof Of Corollarymentioning

confidence: 98%

“…Alternatively, we could estimate all samples of the input signal with the choice [µ w (ρ)] i = θ i and [K w (ρ)] = 0, even though this may lead to nonidentifiability of the model [43,51,42].…”

Section: Errors-in-variables System Identificationmentioning

confidence: 99%

“…Similarly, q (j+1) g is a Gaussian distribution with covariance matrix and mean given by (42), where the expectations are taken with respect to q (j+1) w . We have that…”

Section: A3 Proof Of Theoremmentioning

confidence: 99%

“…Similar to blind problems are the problems of system identification with missing data. In these cases, the missing data are estimated, together with a description of the system, by making hypotheses on the mechanism that generated the missing data [47,26,34,42,23].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modeling and identification of uncertain-input systems

2019

Self Cite

View full text Add to dashboard Cite

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about the input or the linear system, we use Gaussian-process models. We estimate the model from data using the empirical Bayes approach: the input and the impulse responses of the linear system are estimated using the posterior means of the Gaussian-process models given the data, and the hyperparameters that characterize the Gaussian-process models are estimated from the marginal likelihood of the data. We propose an iterative algorithm to find the hyperparameters that relies on the EM method and results in simple update steps. In the most general formulation, neither the marginal likelihood nor the posterior distribution of the unknowns is tractable. Therefore, we propose two approximation approaches, one based on Markov-chain Monte Carlo techniques and one based on variational Bayes approximation. We also show special model structures for which the distributions are treatable exactly. Through numerical simulations, we study the application of the uncertain-input model to the identification of Hammerstein systems and cascaded linear systems. As part of the contribution of the paper, we show that this model structure encompasses many classical problems in system identification such as classical PEM, Hammerstein models, errors-in-variables problems, blind system identification, and cascaded linear systems. This allows us to build a systematic procedure to apply the algorithms proposed in this work to a wide class of classical problems.

show abstract

Section: A4 Proof Of Corollarymentioning

confidence: 98%

Section: Errors-in-variables System Identificationmentioning

confidence: 99%

“…Similarly, q (j+1) g is a Gaussian distribution with covariance matrix and mean given by (42), where the expectations are taken with respect to q (j+1) w . We have that…”

Section: A3 Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling and identification of uncertain-input systems

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…They have been further developed to infer the so-called sparse plus low rank networks where it is assumed that the majority of nodes can be described by a few other components that are not accessible for observation [37]. In addition, system identification of a variety of model classes have been considered: the models include NFI, NARX, NARMAX, linear parameter-varying (LPV) Box-Jenkins models, Hammerstein models, and cascaded linear systems [11,25,27,28]. System dynamics and network topology are controlled by the hyperparameters of kernel functions.…”

Section: Introductionmentioning

confidence: 99%

High Precision Variational Bayesian Inference of Sparse Linear Networks

Jin¹,

Yuan²

2019

Preprint

View full text Add to dashboard Cite

Sparse networks can be found in a wide range of applications, such as biological and communication networks. Inference of such networks from data has been receiving considerable attention lately, mainly driven by the need to understand and control internal working mechanisms. However, while most available methods have been successful at predicting many correct links, they also tend to infer many incorrect links. Precision is the ratio between the number of correctly inferred links and all inferred links, and should ideally be close to 100%. For example, 50% precision means that half of inferred links are incorrect, and there is only a 50% chance of picking a correct one. In contrast, this paper infers links of discrete-time linear networks with very high precision, based on variational Bayesian inference and Gaussian processes. Our method can handle limited datasets, does not require full-state measurements and effectively promotes both system stability and network sparsity. On several of examples, Monte Carlo simulations illustrate that our method consistently has 100% or nearly 100% precision, even in the presence of noise and hidden nodes, outperforming several state-of-the-art methods. The method should be applicable to a wide range of network inference contexts, including biological networks and power systems.

show abstract

Impulse Response Estimation of Linear Time-Invariant Systems Using Convolved Gaussian Processes and Laguerre Functions

Guarnizo

López

2018

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

View full text Add to dashboard Cite

Kernel-based system identification from noisy and incomplete input-output data

Cited by 5 publications

References 34 publications

Modeling and identification of uncertain-input systems

Modeling and identification of uncertain-input systems

High Precision Variational Bayesian Inference of Sparse Linear Networks

Impulse Response Estimation of Linear Time-Invariant Systems Using Convolved Gaussian Processes and Laguerre Functions

Contact Info

Product

Resources

About