AR Identification of Latent-Variable Graphical Models

Zorzi, Mattia; Sepulchre, Rodolphe

doi:10.1109/tac.2015.2491678

Cited by 69 publications

(95 citation statements)

References 24 publications

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“…In this section, we describe an estimation method which is clearly different from the one in [10]. More precisely, we generalize the Expectation-Maximization algorithm from [5], developed there for independent and identically distributed random variables, to a VAR process.…”

Section: New Algorithmmentioning

confidence: 99%

“…This step of the algorithm has a strong theoretical justification which stems from the fact that Φ −1 (ω) is the Maximum Entropy solution for a covariance extension problem (see [10] (Remark 2.1)). The number of iterations, N it , is the same as in the case of the first loop.…”

Section: Initializationmentioning

confidence: 99%

“…• A happy marriage between the approach from [4] and the use of Maximum Entropy led to the solution proposed in [10] for the identification of graphical models of autoregressive processes with latent variables. Similar to [4], the estimation is done by minimizing a cost function whose penalty term is given by a linear combination of the 1 -norm and the nuclear norm.…”

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confidence: 99%

“…The two coefficients of this linear combination are chosen by the user and they have a strong influence on the estimated model. The method introduced in [10] performs the estimation for various pairs of coefficients which yield a set of candidate models; the winner is decided by using a score function.…”

mentioning

confidence: 99%

“…In the next section, we introduce the notation and present the method from [10]. Section 3 outlines the newly proposed algorithm.…”

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confidence: 99%

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Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series

Maanan

Dumitrescu

Giurcăneanu

2018

Entropy

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This work is focused on latent-variable graphical models for multivariate time series. We show how an algorithm which was originally used for finding zeros in the inverse of the covariance matrix can be generalized such that to identify the sparsity pattern of the inverse of spectral density matrix. When applied to a given time series, the algorithm produces a set of candidate models. Various information theoretic (IT) criteria are employed for deciding the winner. A novel IT criterion, which is tailored to our model selection problem, is introduced. Some options for reducing the computational burden are proposed and tested via numerical examples. We conduct an empirical study in which the algorithm is compared with the state-of-the-art. The results are good, and the major advantage is that the subjective choices made by the user are less important than in the case of other methods.

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Section: New Algorithmmentioning

confidence: 99%

Section: Initializationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…In the next section, we introduce the notation and present the method from [10]. Section 3 outlines the newly proposed algorithm.…”

mentioning

confidence: 99%

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Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series

Maanan

Dumitrescu

Giurcăneanu

2018

Entropy

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Matrix spectral factorization for SA4 multiwavelet

Kolev

Cooklev

Keinert

2017

Multidim Syst Sign Process

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In this paper, we investigate Bauer's method for the matrix spectral factorization of an r-channel matrix product filter which is a half-band autocorrelation matrix. We regularize the resulting matrix spectral factors by an averaging approach and by multiplication by a unitary matrix. This leads to the approximate and exact orthogonal SA4 multiscaling functions. We also find the corresponding orthogonal multiwavelet functions, based on the QR decomposition.

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Regularization and Bayesian learning in dynamical systems: Past, present and future

Chiuso

2016

Annual Reviews in Control

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Regularization and Bayesian methods for system identification have been repopularized in the recent years, and proved to be competitive w.r.t. classical parametric approaches. In this paper we shall make an attempt to illustrate how the use of regularization in system identification has evolved over the years, starting from the early contributions both in the Automatic Control as well as Econometrics and Statistics literature. In particular we shall discuss some fundamental issues such as compound estimation problems and exchangeability which play and important role in regularization and Bayesian approaches, as also illustrated in early publications in Statistics. The historical and foundational issues will be given more emphasis (and space), at the expense of the more recent developments which are only briefly discussed. The main reason for such a choice is that, while the recent literature is readily available, and surveys have already been published on the subject, in the author's opinion a clear link with past work had not been completely clarified.

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AR Identification of Latent-Variable Graphical Models

Cited by 69 publications

References 24 publications

Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series

Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series

Matrix spectral factorization for SA4 multiwavelet

Regularization and Bayesian learning in dynamical systems: Past, present and future

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