Regularized joint estimation of related vector autoregressive models

Skripnikov, Andrey; Michailidis, George

doi:10.1016/j.csda.2019.05.007

Cited by 16 publications

(9 citation statements)

References 34 publications

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“…Thus, ignoring the information of other groups may lead to suboptimal solutions (Danaher et al, 2014;Lee and Liu, 2015). Moreover, joint estimation of graphical models has been applied successfully in a number of problems, including metabolite experiments (Tan et al, 2017), cancer networks (Mohan et al, 2012;Peterson et al, 2015;Lee and Liu, 2015;Saegusa and Shojaie, 2016;Hao et al, 2018), biomedical data (Yajima et al, 2014;Kling et al, 2015;Pierson et al, 2015), gene expression (Chun et al, 2015;), text processing (Guo et al, 2011), climate data (Ma and Michailidis, 2016), and fMRI (Qiu et al, 2016;Colclough et al, 2018;Skripnikov and Michailidis, 2019;Lukemire et al, 2020). In all of these problems, data are heterogeneous, but the graphs share similarities.…”

Section: Joint Gaussian Graphical Modelsmentioning

confidence: 99%

“…A variety of applications have illustrated the value of graphical models for analyzing scientific phenomena (Felsenstein, 1981;Schäfer and Strimmer, 2005;Friedman et al, 2000;Chan et al, 2017;Dondelinger et al, 2013). Specifically, graphical models have proven useful for elucidating the mechanisms of brain function (Foti and Fox, 2019;Manning et al, 2018;Schwab et al, 2018;Greenewald et al, 2017;Colclough et al, 2018;Qiu et al, 2016;Skripnikov and Michailidis, 2019). This manuscript outlines joint graphical models, an extension to standard graphical models that are useful for jointly analyzing data from multiple sources, e.g., neurological data measured at multiple timescales, or joint neurological, genetic and phenotypic data.…”

Section: Introductionmentioning

confidence: 99%

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Joint Gaussian Graphical Model Estimation: A Survey

Tsai¹,

Koyejo²,

Kolar³

2021

Preprint

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Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific discoveries or clinical diagnoses. Furthermore, growing evidence shows that the shared structure across domains boosts the estimation power of graphs, particularly for high-dimensional data. However, building a joint estimator to extract the common structure may be more complicated than it seems, most often due to data heterogeneity across sources. This manuscript surveys recent work on statistical inference of joint Gaussian graphical models, identifying model structures that fit various data generation processes. Simulations under different data generation processes are implemented with detailed discussions on the choice of models.

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Section: Joint Gaussian Graphical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Joint Gaussian Graphical Model Estimation: A Survey

Tsai¹,

Koyejo²,

Kolar³

2021

Preprint

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“…In the so-called high-dimensional setting, where the model dimension becomes comparable to or even exceeds the sample size, regularization schemes are employed to guard against over-fitting. These schemes include Tikonov regularization [56], [57], ℓ 1 -regularization or the LASSO [30]- [33], smoothly clipped absolute deviation [58], [59], Elastic-Net [60], and their variants, and have particularly proven useful in MVAR estimation [21]- [24], [28], [29]. Among these techniques, the LASSO has been widely used and studied in the high-dimensional sparse MVAR setting, under fairly general assumptions [22]- [24].…”

Section: B Lasso-based Causal Inference In the High-dimensional Settingmentioning

confidence: 99%

Non-Asymptotic Guarantees for Robust Identification of Granger Causality via the LASSO

Das,

Babadi

2021

Preprint

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Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this methodology are: 1) over-fitting as a result of limited data duration, and 2) correlated process noise as a confounding factor, both leading to errors in identifying the causal influences. Sparse estimation via the LASSO has successfully addressed these challenges for parameter estimation. However, the classical statistical tests for Granger causality resort to asymptotic analysis of ordinary least squares, which require long data durations to be useful and are not immune to confounding effects. In this work, we close this gap by introducing a LASSO-based statistic and studying its non-asymptotic properties under the assumption that the true models admit sparse autoregressive representations. We establish that the sufficient conditions of LASSO also suffice for robust identification of Granger causal influences. We also characterize the false positive error probability of a simple thresholding rule for identifying Granger causal effects. We present simulation studies and application to real data to compare the performance of the ordinary least squares and LASSO in detecting Granger causal influences, which corroborate our theoretical results.

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“…• Skrip19b: a two-stage approach [SM19b] that first estimated the parameters of the common network using a group lasso (like our CGN) and then estimated the individual components based on the resulting common network. This approach does not guarantee a global optimal solution as the parameters were estimated in sequential steps, not being optimized in batch.…”

Section: Common and Differential Gcmentioning

confidence: 99%

Joint learning of multiple Granger causal networks via non-convex regularizations: Inference of group-level brain connectivity

Manomaisaowapak¹,

Songsiri²

2021

Preprint

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This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain connectivity inferences from a homogeneous group of subjects or discovering network differences among groups of signals collected under heterogenous conditions. By recognizing that the GC of a single multivariate time series can be characterized by common zeros of vector autoregressive (VAR) lag coefficients, a group sparse prior is included in joint regularized least-squares estimations of multiple VAR models. Group-norm regularizations based on group-and fusedlasso penalties encourage a decomposition of multiple networks into a common GC structure, with other remaining parts defined in individual-specific networks. Prior information about sparseness and sparsity patterns of desired GC networks are incorporated as relative weights, while a non-convex group norm in the penalty is proposed to enhance the accuracy of network estimation in low-sample settings. Extensive numerical results on simulations illustrated our method's improvements over existing sparse estimation approaches on GC network sparsity recovery. Our methods were also applied to available resting-state fMRI time series from the ADHD-200 data sets to learn the differences of causality mechanisms, called effective brain connectivity, between adolescents with ADHD and typically developing children. Our analysis revealed that parts of the causality differences between the two groups often resided in the orbitofrontal region and areas associated with the limbic system, which agreed with clinical findings and data-driven results in previous studies.

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Regularized joint estimation of related vector autoregressive models

Cited by 16 publications

References 34 publications

Joint Gaussian Graphical Model Estimation: A Survey

Joint Gaussian Graphical Model Estimation: A Survey

Non-Asymptotic Guarantees for Robust Identification of Granger Causality via the LASSO

Joint learning of multiple Granger causal networks via non-convex regularizations: Inference of group-level brain connectivity

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