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1. Delay Embedding for Matrix Graphical Model Learning from Dependent Data

   https://doi.org/10.1109/ICASSP48485.2024.10447097  

   Tugnait, Jitendra K (April 2024, IEEE)

   We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. The correlation function of the matrix series is Kronecker-decomposable. Unlike most past work on matrix graphical models, where independent and identically distributed (i.i.d.) observations of matrix-variate are assumed to be available, we allow time-dependent observations. We follow a time-delay embedding approach where with each matrix node, we associate a random vector consisting of a scalar series component and its time-delayed copies. A group-lasso penalized negative pseudo log-likelihood (NPLL) objective function is formulated to estimate a Kronecker-decomposable covariance matrix which allows for inference of the underlying CIG. The NPLL function is bi-convex and the Kronecker-decomposable covariance matrix is estimated via flip-flop optimization of the NPLL function. Each iteration of flip-flop optimization is solved via an alternating direction method of multipliers (ADMM) approach. Numerical results illustrate the proposed approach which outperforms an existing i.i.d. modeling based approach as well as an existing frequency-domain approach for dependent data, in correctly detecting the graph edges. 

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2. Multi-view spectral graph convolution with consistent edge attention for molecular modeling

   https://doi.org/https://doi.org/10.1016/j.neucom.2021.02.025  

   Shang, C; Liu, Q; Tong, Q; Sun, J; Song, M; Bi, J (July 2021, Neurocomputing)

   null (Ed.)

   Although graph convolutional networks (GCNs) that extend the convolution operation from images to graphs have led to competitive performance, the existing GCNs are still difficult to handle a variety of applications, especially cheminformatics problems. Recently multiple GCNs are applied to chemical compound structures which are represented by the hydrogen-depleted molecular graphs of different size. GCNs built for a binary adjacency matrix that reflects the connectivity among nodes in a graph do not account for the edge consistency in multiple molecular graphs, that is, chemical bonds (edges) in different molecular graphs can be similar due to the similar enthalpy and interatomic distance. In this paper, we propose a variant of GCN where a molecular graph is first decomposed into multiple views of the graph, each comprising a specific type of edges. In each view, an edge consistency constraint is enforced so that similar edges in different graphs can receive similar attention weights when passing information. Similarly to prior work, we prove that in each layer, our method corresponds to a spectral filter derived by the first order Chebyshev approximation of graph Laplacian. Extensive experiments demonstrate the substantial advantages of the proposed technique in quantitative structure-activity relationship prediction. 

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3. Graph Learning From Multivariate Dependent Time Series Via A Multi-Attribute Formulation

   https://doi.org/10.1109/ICASSP43922.2022.9746603  

   Tugnait, Jitendra K. (May 2022, ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges. 

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4. Discrete Graph Structure Learning for Forecasting Multiple Time Series

   Chao Shang, Jie Chen (April 2021, Proceedings of International Conference on Learning Representations)

   null (Ed.)

   Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based. 

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5. Benchmarking of Data-Driven Causality Discovery Approaches in the Interactions of Arctic Sea Ice and Atmosphere

   https://doi.org/10.3389/fdata.2021.642182  

   Huang, Yiyi; Kleindessner, Matthäus; Munishkin, Alexey; Varshney, Debvrat; Guo, Pei; Wang, Jianwu (August 2021, Frontiers in Big Data)

   null (Ed.)

   The Arctic sea ice has retreated rapidly in the past few decades, which is believed to be driven by various dynamic and thermodynamic processes in the atmosphere. The newly open water resulted from sea ice decline in turn exerts large influence on the atmosphere. Therefore, this study aims to investigate the causality between multiple atmospheric processes and sea ice variations using three distinct data-driven causality approaches that have been proposed recently: Temporal Causality Discovery Framework Non-combinatorial Optimization via Trace Exponential and Augmented lagrangian for Structure learning (NOTEARS) and Directed Acyclic Graph-Graph Neural Networks (DAG-GNN). We apply these three algorithms to 39 years of historical time-series data sets, which include 11 atmospheric variables from ERA-5 reanalysis product and passive microwave satellite retrieved sea ice extent. By comparing the causality graph results of these approaches with what we summarized from the literature, it shows that the static graphs produced by NOTEARS and DAG-GNN are relatively reasonable. The results from NOTEARS indicate that relative humidity and precipitation dominate sea ice changes among all variables, while the results from DAG-GNN suggest that the horizontal and meridional wind are more important for driving sea ice variations. However, both approaches produce some unrealistic cause-effect relationships. Additionally, these three methods cannot well detect the delayed impact of one variable on another in the Arctic. It also turns out that the results are rather sensitive to the choice of hyperparameters of the three methods. As a pioneer study, this work paves the way to disentangle the complex causal relationships in the Earth system, by taking the advantage of cutting-edge Artificial Intelligence technologies. 

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