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DanWaxman authored Oct 16, 2024
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Expand Up @@ -22,9 +22,11 @@ @article{waxman2024obs
@article{butler2024tangent,
selected = {true},
bibtex_show = {false},
author = {Butler, Kurt and Waxman, Daniel and Djurić, Petar {M.}},
author = {Butler, Kurt˟ and Waxman, Daniel˟ and Djurić, Petar {M.}},
title = {Tangent Space Causal Inference: Leveraging Vector Fields for Causal Discovery in Dynamical Systems},
note = {Submitted.},
note = {Advances in Neural Information Processing Systems (NeurIPS) 2024},
abbr = {NeurIPS '24},
code = {https://github.com/KurtButler/tangentspaces},
year = {2024},
abstract = {Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamic systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields. The TSCI approach is model-agnostic and can be used as a drop-in replacement for CCM and its generalizations. We present both a basic TSCI algorithm, which is lightweight and more effective than the basic CCM algorithm, as well as augmented versions of TSCI that leverage the expressive power of latent variable models and deep learning. We validate our theory on standard systems, and we demonstrate improved causal inference performance across a number of benchmarks.}
}
Expand All @@ -39,6 +41,7 @@ @inproceedings{waxman2024online
year = {2024},
code = {https://github.com/DanWaxman/Lintel},
arxiv = {http://arxiv.org/abs/2406.00570},
pdf = {https://ieeexplore.ieee.org/document/10706404},
abstract = {Online prediction of time series under regime switching is a widely studied problem in the literature, with many celebrated approaches. Using the non-parametric flexibility of Gaussian processes, the recently proposed INTEL algorithm provides a product of experts approach to online prediction of time series under possible regime switching, including the special case of outliers. This is achieved by adaptively combining several candidate models, each reporting their predictive distribution at time t. However, the INTEL algorithm uses a finite context window approximation to the predictive distribution, the computation of which scales cubically with the maximum lag, or otherwise scales quartically with exact predictive distributions. We introduce LINTEL, which uses the exact filtering distribution at time t with constant-time updates, making the time complexity of the streaming algorithm optimal. We additionally note that the weighting mechanism of INTEL is better suited to a mixture of experts approach, and propose a fusion policy based on arithmetic averaging for LINTEL. We show experimentally that our proposed approach is over five times faster than INTEL under reasonable settings with better quality predictions.}
}

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