# Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes

arXiv: https://arxiv.org/abs/2301.06021 · HTML: https://mlsanity.com/paper/2301.06021/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 245 references that are in the map.
- First posted on arXiv 15 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [A Computational Approach to Understanding Empathy Expressed in Text-Based Mental Health Support](https://mlsanity.com/paper/2009.08441/) (2020)
- [Autoencoding Variational Inference For Topic Models](https://mlsanity.com/paper/1703.01488/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sources](https://mlsanity.com/paper/2103.06261/) (2021)
- [The Sylvester Graphical Lasso (SyGlasso)](https://mlsanity.com/paper/2002.00288/) (2020)
- [Bayesian Graphical Models for Multivariate Functional Data](https://mlsanity.com/paper/1411.4158/) (2014)
- [Integrating Machine Learning with Physics-Based Modeling](https://mlsanity.com/paper/2006.02619/) (2020)
- [Dynamic topic modeling of the COVID-19 Twitter narrative among U.S. governors and cabinet executives](https://mlsanity.com/paper/2004.11692/) (2020)
- [Double Machine Learning Methods for Estimating Average Treatment Effects: A Comparative Study](https://mlsanity.com/paper/2204.10969/) (2022)
- [Non-separable covariance models for spatio-temporal data, with applications to neural encoding analysis](https://mlsanity.com/paper/1705.05265/) (2017)
- [Identifying Principal Stratum Causal Effects Conditional on a Post-treatment Intermediate Response](https://mlsanity.com/paper/2103.04175/) (2021)
- [SG-PALM: a Fast Physically Interpretable Tensor Graphical Model](https://mlsanity.com/paper/2105.12271/) (2021)
- [RISE: Robust Individualized Decision Learning with Sensitive Variables](https://mlsanity.com/paper/2211.06569/) (2022)
- [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)
- [Convergence of cyclic coordinatewise l1 minimization](https://mlsanity.com/paper/1404.5100/) (2014)
- [Addressing selection bias and measurement error in COVID-19 case count data using auxiliary information](https://mlsanity.com/paper/2005.10425/) (2020)
- [Multiway Ensemble Kalman Filter](https://mlsanity.com/paper/2112.04322/) (2021)

## Built on by (most cited first, 1 of 1)

- [Cluster-Segregate-Perturb (CSP): A Model-agnostic Explainability Pipeline for Spatiotemporal Land Surface Forecasting Models](https://mlsanity.com/paper/2408.05916/) (2024)

## Abstract (arXiv)

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical models for tensor-variate data and summarization of complex time-varying texts using topic models. This work advances the state-of-the-art in several directions. First, it introduces a new class of tensor-variate Gaussian graphical models via the Sylvester tensor equation. Second, it develops an optimization technique based on a fast-converging proximal alternating linearized minimization method, which scales tensor-variate Gaussian graphical model estimations to modern big-data settings. Third, it connects Kronecker-structured (inverse) covariance models with spatio-temporal partial differential equations (PDEs) and introduces a new framework for ensemble Kalman filtering that is capable of tracking chaotic physical systems. Fourth, it proposes a modular and interpretable framework for unsupervised and weakly-supervised probabilistic topic modeling of time-varying data that combines generative statistical models with computational geometric methods. Throughout, practical applications of the methodology are considered using real datasets. This includes brain-connectivity analysis using EEG data, space weather forecasting using solar imaging data, longitudinal analysis of public opinions using Twitter data, and mining of mental health related issues using TalkLife data. We show in each case that the graphical modeling framework introduced here leads to improved interpretability, accuracy, and scalability.