Bayesian-Continuous-Time-Tucker-Decomposition

by Shikai Fang, Akil Narayan, Robert M. Kirby, Shandian Zhe

This authors' official PyTorch implementation for : Bayesian Continuous-Time Tucker Decomposition (ICML 2022 Oral paper)

See more material(slides,poster) at my page

Methods Overview:

Dynamic Tucker-core to handle the continuous-time tensor data

As shown in the figures, we assign the tucker core with Temporal-Gaussian Process priors to handle the continuous-time-varing dynamics in the tensor data.

Efficient Inference: Sequential update of SDE + Parallel update of factors

The Temporal-Gaussian Process with stationaty kernel is equivalent to linear time-invariant stochastic differential equations (LTI-SDE), which we can slove by Kalman-Filter & smoothing sequentialy. We further apply conditional moment-match to update the latent factors. The Inference Algorithm is with linear cost of time-steps.

Requirements:

The project is mainly built with pytorch 1.10.1 under python 3. Besides that, make sure to install tqdm and tensorly before running the project.

Instructions:

1. Clone this repository.
2. To play with the code quickly, we offer two notebooks at code_fang\notebook(on synthetic & real data)
3. To run the real-world datasets with scripts, run code_fang\script_BCTT.sh

Check our paper for more details.

Citation

Please cite our work if you would like it

@inproceedings{fang2022bayesian,
  title={Bayesian Continuous-Time Tucker Decomposition},
  author={Fang, Shikai and Narayan, Akil and Kirby, Robert and Zhe, Shandian},
  booktitle={International Conference on Machine Learning},
  pages={6235--6245},
  year={2022},
  organization={PMLR}
}