# Network Inference via the Time-Varying Graphical Lasso

@article{Hallac2017NetworkIV, title={Network Inference via the Time-Varying Graphical Lasso}, author={David Hallac and Youngsuk Park and Stephen P. Boyd and Jure Leskovec}, journal={Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining}, year={2017} }

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of such data, it is essential to understand the relationships between the different entities and how these relationships evolve over time. In this paper, we introduce the time-varying graphical lasso (TVGL), a method of inferring time-varying networks from raw time…

## 126 Citations

### Efficient Variational Bayesian Structure Learning of Dynamic Graphical Models

- Computer ScienceArXiv
- 2020

BADGE can be extended to learning frequency-varying inverse spectral density matrices, and yields graphical models for multivariate stationary time series and is more efficient than the existing methods, especially for high-dimensional cases.

### Latent Variable Time-varying Network Inference

- Computer ScienceKDD
- 2018

This work presents latent variable time-varying graphical lasso (LTGL), a method for multivariate time-series graphical modelling that considers the influence of hidden or unmeasurable factors, and develops a scalable and efficient implementation which exploits proximity operators in closed form.

### Estimating Time-Varying Graphical Models

- Computer ScienceJournal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
- 2020

A new model, LOcal Group Graphical Lasso Estimation (loggle), under the assumption that the graph topology changes gradually over time is proposed, which uses a novel local group-lasso type penalty to efficiently incorporate information from neighboring time points and to impose structural smoothness of the graphs.

### Segment-Wise Time-Varying Dynamic Bayesian Network with Graph Regularization

- Computer ScienceACM Trans. Knowl. Discov. Data
- 2022

This article constructs a TVDBN model that adopts a vector autoregressive (VAR) model to describe inter-slice and intra-slice relations between variables, and uses the alternating direction method of multipliers with L-BFGS-B algorithm for optimal structure learning.

### Temporal Pattern Detection in Time-Varying Graphical Models

- Computer Science2020 25th International Conference on Pattern Recognition (ICPR)
- 2021

This work proposes a dynamical network inference model that leverages on kernels to consider general temporal patterns (such as circadian rhythms or seasonality) and shows how this approach may be exploited when the recurrent patterns are unknown, by coupling the network inference with a clustering procedure that detects possibly non-consecutive similar networks.

### DYNAMIC NETWORK IDENTIFICATION FROM NON-STATIONARY VECTOR AUTOREGRESSIVE TIME SERIES

- Computer Science2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
- 2018

An estimation criterion and a solver are developed to learn the parameters of a time-varying vector autoregressive model supported on a network of time series and the notion of local breakpoint is proposed to accommodate changes at individual edges.

### Structural inference of time‐varying mixed graphical models

- Computer ScienceStat
- 2021

Joint structural estimation of time‐varying mixed graphical models based on multivariate data over a series of time points using an accelerated alternating direction method of multipliers (ADMM)‐based algorithm exploiting the block diagonal structure to adapt the problem for large sparse networks.

### Time-Varying Graph Learning for Node-Wise Anomaly Detection

- Computer Science2022 IEEE/CIC International Conference on Communications in China (ICCC)
- 2022

A perturbed-node time-varying graph learning (PNTVGL) method is proposed to solve a graph-based signal model where the hidden graph smoothly varies most of the time but there exists a sudden change of graph disrupted by node perturbations.

### Learning Time-Varying Graphs From Online Data

- Computer ScienceIEEE Open Journal of Signal Processing
- 2022

This work proposes an algorithmic framework to learn time-varying graphs from online data that is model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then instantiated under a variety of model-dependent graph learning problems.

### Time Adaptive Gaussian Model

- Computer ScienceArXiv
- 2021

This work proposes a novel method that leverages on Hidden Markov Models and Gaussian Graphical Models — Time Adaptive Gaussian Model (TAGM) that performs pattern recognition by clustering data points in time and finds probabilistic relationships among the observed variables.

## References

SHOWING 1-10 OF 37 REFERENCES

### Recovering time-varying networks of dependencies in social and biological studies

- Computer ScienceProceedings of the National Academy of Sciences
- 2009

A machine learning method called TESLA is presented, which builds on a temporally smoothed l1-regularized logistic regression formalism that can be cast as a standard convex-optimization problem and solved efficiently by using generic solvers scalable to large networks.

### On the Convexity of Latent Social Network Inference

- Computer ScienceNIPS
- 2010

This work considers contagions propagating over the edges of an unobserved social network, and presents a maximum likelihood approach based on convex programming with a l1-like penalty term that encourages sparsity to identify the optimal network that best explains the observed data.

### Structured Learning of Gaussian Graphical Models

- Computer ScienceNIPS
- 2012

This work proposes to solve the perturbed-node joint graphical lasso, a convex optimization problem that is based upon the use of a row-column overlap norm penalty, and solves the convex problem using an alternating directions method of multipliers algorithm.

### Network Lasso: Clustering and Optimization in Large Graphs

- Computer ScienceKDD
- 2015

The network lasso is introduced, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs and an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner.

### Node-based learning of multiple Gaussian graphical models

- Computer ScienceJ. Mach. Learn. Res.
- 2014

This work takes a node-based approach to estimation of high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions, and derives a set of necessary and sufficient conditions that allows the problem to decompose into independent subproblems so that the algorithm can be scaled to high- dimensional settings.

### Time varying undirected graphs

- MathematicsMachine Learning
- 2010

A nonparametric method for estimating time varying graphical structure for multivariate Gaussian distributions using an ℓ1 regularization method is developed and it is shown that, as long as the covariances change smoothly over time, the covariance matrix well (in predictive risk) even when p is large.

### Estimating time-varying brain connectivity networks from functional MRI time series

- Biology, PsychologyNeuroImage
- 2014

### Inferring slowly-changing dynamic gene-regulatory networks

- Computer ScienceBMC Bioinformatics
- 2015

A new model for estimating slow changes in dynamic gene-regulatory networks, suitable for high-dimensional data, e.g. time-course microarray data is introduced, based on the penalized likelihood with ℓ1-norm, that penalizes conditional dependencies between genes as well as differences between conditional independence elements across time points.

### Fused Multiple Graphical Lasso

- Computer ScienceSIAM J. Optim.
- 2015

This paper considers the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures, and presents a simple screening rule, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) sub graphs, dramatically reducing the computational cost.

### Sparse inverse covariance estimation with the graphical lasso.

- Computer ScienceBiostatistics
- 2008

Using a coordinate descent procedure for the lasso, a simple algorithm is developed that solves a 1000-node problem in at most a minute and is 30-4000 times faster than competing methods.