Graphical LASSO based Model Selection for Time Series

Jung, Alexander; Hannák, Gábor; Goertz, Norbert

doi:10.1109/lsp.2015.2425434

Cited by 50 publications

(63 citation statements)

References 22 publications

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“…An undirected edge {i, j} ∈ E of the empirical graph encodes a notion of (physical or statistical) proximity of neighbouring data points, such as profiles of befriended social network users or documents which have been co-authored by the same person. This network structure is identified with conditional independence relations within probabilistic graphical models (PGM) [21], [23], [24], [30], [31].…”

Section: Problem Settingmentioning

confidence: 99%

“…11]) whose nodes represent individual data points and whose edges connect data points which are similar in an application-specific sense. The empirical graph for a particular dataset might be obtained by (domain) expert knowledge, an intrinsic network structure (e.g., for social network data) or in a data-driven fashion by imposing smoothness constrains on observed realizations of graph signals (which serve as training data) [21], [23], [24], [27], [30], [31], [38]. Besides the graph structure, datasets carry additional information in the form of labels (e.g., class membership) associated with individual data points.…”

Section: Introductionmentioning

confidence: 99%

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On the Complexity of Sparse Label Propagation

Jung

2018

Front. Appl. Math. Stat.

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This paper investigates the computational complexity of sparse label propagation which has been proposed recently for processing network-structured data. Sparse label propagation amounts to a convex optimization problem and might be considered as an extension of basis pursuit from sparse vectors to clustered graph signals representing the label information contained in network-structured datasets. Using a standard first-order oracle model, we characterize the number of iterations for sparse label propagation to achieve a prescribed accuracy. In particular, we derive an upper bound on the number of iterations required to achieve a certain accuracy and show that this upper bound is sharp for datasets having a chain structure (e.g., time series).

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Section: Problem Settingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Complexity of Sparse Label Propagation

Jung

2018

Front. Appl. Math. Stat.

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“…This approach has been extended in various directions and applied to find a sparse dependence structure of variables. These include a 1 -penalty of an affine transformation, termed a generalized lasso [DSB + 16], estimation of the sparse vector autoregressive processes for inferring the Granger causality of time series [BVN11], joint sparse estimation of inverse covariance matrices to find a common conditional independence structure [THW + 16, MM16], and estimation of the sparse spectral density matrix to explain the conditional independence structures of time series [JHG15,SV10].…”

Section: Sparse Sem With 1 -Norm Regularizationmentioning

confidence: 99%

Convex formulation for regularized estimation of structural equation models

Pruttiakaravanich

Songsiri

2020

Signal Processing

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Path analysis is a model class of structural equation modeling (SEM), which it describes causal relations among measured variables in the form of a multiple linear regression. This paper presents two estimation formulations, one each for confirmatory and exploratory SEM, where a zero pattern of the estimated path coefficient matrix can explain a causality structure of the variables. The original nonlinear equality constraints of the model parameters were relaxed to an inequality, allowing the transformation of the original problem into a convex framework. A regularized estimation formulation was then proposed for exploratory SEM using an l1-type penalty of the path coefficient matrix. Under a condition on problem parameters, our optimal solution is low rank and provides a useful solution to the original problem. Proximal algorithms were applied to solve our convex programs in a large-scale setting. The performance of this approach was demonstrated in both simulated and real data sets, and in comparison with an existing method. When applied to two real application results (learning causality among climate variables in Thailand and examining connectivity differences in autism patients using fMRI time series from ABIDE data sets) the findings could explain known relationships among environmental variables and discern known and new brain connectivity differences, respectively.

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“…LASSO has gained wide spread popularity in signal processing and statistical learning, see [42], [43], [44]. LASSO has also been applied to forecast electricity price [20], [45], but its application to load forecasting is still a new topic.…”

Section: Sparsity In Autoregressive Modelsmentioning

confidence: 99%

A Sparse Linear Model and Significance Test for Individual Consumption Prediction

Zhang

Weng

et al. 2017

IEEE Trans. Power Syst.

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Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well.Existing prediction methods usually have high relative errors that can be larger than 30% and have difficulties accounting for heterogeneity between individual users. In this paper, we propose a method to improve prediction accuracy of individual users by adaptively exploring sparsity in historical data and leveraging predictive relationship between different users. Sparsity is captured by popular least absolute shrinkage and selection estimator, while user selection is formulated as an optimal hypothesis testing problem and solved via a covariance test. Using real world data from PG&E, we provide extensive simulation validation of the proposed method against well-known techniques such as support vector machine, principle component analysis combined with linear regression, and random forest. The results demonstrate that our proposed methods are operationally efficient because of linear nature, and achieve optimal prediction performance. Index TermsLoad forecasting, least absolute shrinkage and selection, sparse autoregressive model, significance test NOMENCLATURE y t Consumption at time t.

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Graphical LASSO based Model Selection for Time Series

Cited by 50 publications

References 22 publications

On the Complexity of Sparse Label Propagation

On the Complexity of Sparse Label Propagation

Convex formulation for regularized estimation of structural equation models

A Sparse Linear Model and Significance Test for Individual Consumption Prediction

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