Local Dependence Graphs for Discrete Time Processes

Wojciech Niemiro, Łukasz Rajkowski
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:772-790, 2023.

Abstract

Local dependence graphs for discrete time processes encapsulate information concerning the dependence relationships between the past of the multidimensional process and its present state and as such can represent feedback loops. Even in the discrete time setting some natural questions relating the conditional (in)dependence statements in the stochastic process to separation properties of the underlying local dependence graph are scattered throughout the literature. We provide an unifying view and fill in certain gaps. In this paper we examine graphical characteristics for two kinds of conditional independences: those occurring in Markov chains under the stationary regime and independences between the past of one subprocess and the future of another given the past of the third subprocess.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-niemiro23a, title = {Local Dependence Graphs for Discrete Time Processes}, author = {Niemiro, Wojciech and Rajkowski, {\L}ukasz}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {772--790}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/niemiro23a/niemiro23a.pdf}, url = {https://proceedings.mlr.press/v213/niemiro23a.html}, abstract = {Local dependence graphs for discrete time processes encapsulate information concerning the dependence relationships between the past of the multidimensional process and its present state and as such can represent feedback loops. Even in the discrete time setting some natural questions relating the conditional (in)dependence statements in the stochastic process to separation properties of the underlying local dependence graph are scattered throughout the literature. We provide an unifying view and fill in certain gaps. In this paper we examine graphical characteristics for two kinds of conditional independences: those occurring in Markov chains under the stationary regime and independences between the past of one subprocess and the future of another given the past of the third subprocess. } }
Endnote
%0 Conference Paper %T Local Dependence Graphs for Discrete Time Processes %A Wojciech Niemiro %A Łukasz Rajkowski %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-niemiro23a %I PMLR %P 772--790 %U https://proceedings.mlr.press/v213/niemiro23a.html %V 213 %X Local dependence graphs for discrete time processes encapsulate information concerning the dependence relationships between the past of the multidimensional process and its present state and as such can represent feedback loops. Even in the discrete time setting some natural questions relating the conditional (in)dependence statements in the stochastic process to separation properties of the underlying local dependence graph are scattered throughout the literature. We provide an unifying view and fill in certain gaps. In this paper we examine graphical characteristics for two kinds of conditional independences: those occurring in Markov chains under the stationary regime and independences between the past of one subprocess and the future of another given the past of the third subprocess.
APA
Niemiro, W. & Rajkowski, Ł.. (2023). Local Dependence Graphs for Discrete Time Processes. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:772-790 Available from https://proceedings.mlr.press/v213/niemiro23a.html.

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