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Probabilistic Sequential Matrix Factorization

This repository contains the code to reproduce the experiments in:

Akyildiz, van den Burg, Damoulas, Steel - Probabilistic Sequential Matrix Factorization (2021)

Work that uses the methods described in the paper or the code in this repository should cite the paper, for instance using the following BibTeX entry:

@inproceedings{akyildiz2021probabilistic,
    title={Probabilistic Sequential Matrix Factorization},
    author={{\"O}mer Deniz Akyildiz and Gerrit J. J. {van den Burg} and Theodoros Damoulas and Mark F. J. Steel},
    booktitle={Proceedings of the 24th International Conference on Artificial Intelligence and Statistics},
    editor={Banerjee, Arindam and Fukumizu, Kenji},
    pages={3484--3492},
    volume={130},
    year={2021},
    series={Proceedings of Machine Learning Research},
    publisher={PMLR},
}

If you encounter a problem when using this repository or simply want to ask a question, please don't hesitate to open an issue on GitHub or send an email to odakyildiz at turing dot ac dot uk and/or gertjanvandenburg at gmail dot com.

Introduction

Our Probabilistic Sequential Matrix Factorization (PSMF) method allows you to model high-dimensional timeseries data that exhibits non-stationary dynamics. We also propose a robust variant of the model, called rPSMF, that handles model misspecification and outliers.

See the paper for further details.

Illustration of fitting 
  rPSMF to a multidimensional time series that contains outliers

Illustration of using rPSMF to model a 20-dimensional time series with non-linear dynamics and t-distributed outliers. Blue lines are the observed data and yellow lines are unobserved future data. The red dashed line shows the predictions from our model.

Usage

The code in this repository is organized by experiment. The Convergence directory contains the code for the convergence experiment in the appendix of the paper.

The accompanying Makefile can be used to reproduce the experiments by simply running

$ make ExperimentSynthetic   # or ExperimentBeijing, or ExperimentImpute, or ExperimentRecursive

These experiments will be run through a Python virtual environment that will be automatically created with the required dependencies. For the imputation experiment the results are captured in LaTeX tables that are automatically generated as well.

The code for the change point detection Experiment and the convergence experiment are written in Matlab, so require a Matlab installation to reproduce. See the readme files in the corresponding directories for more information.

Notes

The code is licensed under the MIT license unless otherwise noted, see the LICENSE file for further details.