NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge

Xiangyu Sun, Oliver Schulte, Guiliang Liu, Pascal Poupart
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:1942-1964, 2023.

Abstract

We describe NTS-NOTEARS, a score-based structure learning method for time-series data to learn dynamic Bayesian networks (DBNs) that captures nonlinear, lagged (inter-slice) and instantaneous (intra-slice) relations among variables. NTS-NOTEARS utilizes 1D convolutional neural networks (CNNs) to model the dependence of child variables on their parents; 1D CNN is a neural function approximation model well-suited for sequential data. DBN-CNN structure learning is formulated as a continuous optimization problem with an acyclicity constraint, following the NOTEARS DAG learning approach (Zheng et al., 2018, 2020). We show how prior knowledge of dependencies (e.g., forbidden and required edges) can be included as additional optimization constraints. Empirical evaluation on simulated and benchmark data shows that NTS-NOTEARS achieves state-of-the-art DAG structure quality compared to both parametric and nonparametric baseline methods, with improvement in the range of 10-20$%$ on the F1-score. We also evaluate NTS-NOTEARS on complex real-world data acquired from professional ice hockey games that contain a mixture of continuous and discrete variables. The code is available online.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-sun23c, title = {NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge}, author = {Sun, Xiangyu and Schulte, Oliver and Liu, Guiliang and Poupart, Pascal}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {1942--1964}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/sun23c/sun23c.pdf}, url = {https://proceedings.mlr.press/v206/sun23c.html}, abstract = {We describe NTS-NOTEARS, a score-based structure learning method for time-series data to learn dynamic Bayesian networks (DBNs) that captures nonlinear, lagged (inter-slice) and instantaneous (intra-slice) relations among variables. NTS-NOTEARS utilizes 1D convolutional neural networks (CNNs) to model the dependence of child variables on their parents; 1D CNN is a neural function approximation model well-suited for sequential data. DBN-CNN structure learning is formulated as a continuous optimization problem with an acyclicity constraint, following the NOTEARS DAG learning approach (Zheng et al., 2018, 2020). We show how prior knowledge of dependencies (e.g., forbidden and required edges) can be included as additional optimization constraints. Empirical evaluation on simulated and benchmark data shows that NTS-NOTEARS achieves state-of-the-art DAG structure quality compared to both parametric and nonparametric baseline methods, with improvement in the range of 10-20$%$ on the F1-score. We also evaluate NTS-NOTEARS on complex real-world data acquired from professional ice hockey games that contain a mixture of continuous and discrete variables. The code is available online.} }
Endnote
%0 Conference Paper %T NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge %A Xiangyu Sun %A Oliver Schulte %A Guiliang Liu %A Pascal Poupart %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-sun23c %I PMLR %P 1942--1964 %U https://proceedings.mlr.press/v206/sun23c.html %V 206 %X We describe NTS-NOTEARS, a score-based structure learning method for time-series data to learn dynamic Bayesian networks (DBNs) that captures nonlinear, lagged (inter-slice) and instantaneous (intra-slice) relations among variables. NTS-NOTEARS utilizes 1D convolutional neural networks (CNNs) to model the dependence of child variables on their parents; 1D CNN is a neural function approximation model well-suited for sequential data. DBN-CNN structure learning is formulated as a continuous optimization problem with an acyclicity constraint, following the NOTEARS DAG learning approach (Zheng et al., 2018, 2020). We show how prior knowledge of dependencies (e.g., forbidden and required edges) can be included as additional optimization constraints. Empirical evaluation on simulated and benchmark data shows that NTS-NOTEARS achieves state-of-the-art DAG structure quality compared to both parametric and nonparametric baseline methods, with improvement in the range of 10-20$%$ on the F1-score. We also evaluate NTS-NOTEARS on complex real-world data acquired from professional ice hockey games that contain a mixture of continuous and discrete variables. The code is available online.
APA
Sun, X., Schulte, O., Liu, G. & Poupart, P.. (2023). NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:1942-1964 Available from https://proceedings.mlr.press/v206/sun23c.html.

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