# SG-PALM: a Fast Physically Interpretable Tensor Graphical Model

arXiv: https://arxiv.org/abs/2105.12271 · HTML: https://mlsanity.com/paper/2105.12271/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 26 May 2021.

## Builds on (most cited first, 13 of 13)

- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Calculus of the exponent of Kurdyka-Lojasiewicz inequality and its applications to linear convergence of first-order methods](https://mlsanity.com/paper/1602.02915/) (2016)
- [A Machine Learning Dataset Prepared From the NASA Solar Dynamics Observatory Mission](https://mlsanity.com/paper/1903.04538/) (2019)
- [Tensor Graphical Lasso (TeraLasso)](https://mlsanity.com/paper/1705.03983/) (2017)
- [A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees](https://mlsanity.com/paper/1307.5381/) (2013)
- [The Sylvester Graphical Lasso (SyGlasso)](https://mlsanity.com/paper/2002.00288/) (2020)
- [Optimization Methods for Sparse Pseudo-Likelihood Graphical Model Selection](https://mlsanity.com/paper/1409.3768/) (2014)
- [G-AMA: Sparse Gaussian graphical model estimation via alternating minimization](https://mlsanity.com/paper/1405.3034/) (2014)
- [New Analysis of Linear Convergence of Gradient-type Methods via Unifying Error Bound Conditions](https://mlsanity.com/paper/1606.00269/) (2016)
- [Errors-in-variables models with dependent measurements](https://mlsanity.com/paper/1611.04701/) (2016)
- [Non-separable covariance models for spatio-temporal data, with applications to neural encoding analysis](https://mlsanity.com/paper/1705.05265/) (2017)
- [Generalized subdifferentials of spectral functions over Euclidean Jordan algebras](https://mlsanity.com/paper/1902.05270/) (2019)
- [Interpreting LSTM Prediction on Solar Flare Eruption with Time-series Clustering](https://mlsanity.com/paper/1912.12360/) (2019)

## Built on by (most cited first, 3 of 3)

- [GmGM: a Fast Multi-Axis Gaussian Graphical Model](https://mlsanity.com/paper/2211.02920/) (2022)
- [Multiway Ensemble Kalman Filter](https://mlsanity.com/paper/2112.04322/) (2021)
- [Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes](https://mlsanity.com/paper/2301.06021/) (2023)

## Abstract (arXiv)

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.