SG-PALM: a Fast Physically Interpretable Tensor Graphical Model

Abstract

We propose a new graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly (i.e., geometric convergence rate) to a global optimum of its objective function. We demonstrate the scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data.

arXiv commentAccepted in ICML 2021

References in corpus (10)

• Nearly unbiased variable selection under minimax concave penalty
• A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees
• Identifying Solar Flare Precursors Using Time Series of SDO/HMI Images and SHARP Parameters
• Convergence Properties of Kronecker Graphical Lasso Algorithms
• Iterative Thresholding Algorithm for Sparse Inverse Covariance Estimation
• Solar Flare Intensity Prediction with Machine Learning Models
• Optimization Methods for Sparse Pseudo-Likelihood Graphical Model Selection
• Generalized subdifferentials of spectral functions over Euclidean Jordan algebras
• Non-separable covariance models for spatio-temporal data, with applications to neural encoding analysis
• Interpreting LSTM Prediction on Solar Flare Eruption with Time-series Clustering