# Graphical estimation of multivariate count time series

arXiv: https://arxiv.org/abs/2302.08801 · HTML: https://mlsanity.com/paper/2302.08801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 62 references that are in the map.
- First posted on arXiv 17 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)](https://mlsanity.com/paper/1704.08783/) (2017)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [High-Dimensional Poisson DAG Model Learning Using ℓ1-Regularized Regression](https://mlsanity.com/paper/1810.02501/) (2018)
- [Nonparametric graphical model for counts](https://mlsanity.com/paper/1901.00886/) (2019)
- [AR Identification of Latent-variable Graphical Models](https://mlsanity.com/paper/1405.0027/) (2014)
- [Identification of Sparse Reciprocal Graphical Models](https://mlsanity.com/paper/1806.04423/) (2018)
- [Structure learning of undirected graphical models for count data](https://mlsanity.com/paper/1810.10854/) (2018)
- [Robust Identification of "Sparse Plus Low-rank" Graphical Models: An Optimization Approach](https://mlsanity.com/paper/1901.10613/) (2019)

## Abstract (arXiv)

The problems of selecting partial correlation and causality graphs for count data are considered. A parameter driven generalized linear model is used to describe the observed multivariate time series of counts. Partial correlation and causality graphs corresponding to this model explain the dependencies between each time series of the multivariate count data. In order to estimate these graphs with tunable sparsity, an appropriate likelihood function maximization is regularized with an l1-type constraint. A novel MCEM algorithm is proposed to iteratively solve this regularized MLE. Asymptotic convergence results are proved for the sequence generated by the proposed MCEM algorithm with l1-type regularization. The algorithm is first successfully tested on simulated data. Thereafter, it is applied to observed weekly dengue disease counts from each ward of Greater Mumbai city. The interdependence of various wards in the proliferation of the disease is characterized by the edges of the inferred partial correlation graph. On the other hand, the relative roles of various wards as sources and sinks of dengue spread is quantified by the number and weights of the directed edges originating from and incident upon each ward. From these estimated graphs, it is observed that some special wards act as epicentres of dengue spread even though their disease counts are relatively low.