Sequential Indeterminate Probability Theory for Multivariate Time Series Forecasting
Keywords: Indeterminate Probability Theory, Continuous Random Variable, Analytical Solution, MTS
TL;DR: We propose a new probabilistic method for MTS forecasting that does not rely on any neural models. Experimental results show that our method outperforms LSTM models and also some transformer-based models.
Abstract: Currently, there is no mathematical analytical form for a general posterior, however, Indeterminate Probability Theory has now discovered a way to address this issue. This is a big discovery in the field of probability and it is also applicable to multivariate time series (MTS) forecasting. Deep models, particularly transformer-based models, have shown better performance for MTS forecasting than traditional statistical models, however, deep models are black-boxes for human. In this paper, we propose a new probabilistic method for MTS forecasting that does not rely on any neural models, and this method does not require any training process. We formulate MTS forecasting problem as a complex posterior and consider the MTS value as an indeterminate probability distribution. Based on the indeterminate probability theory, the posterior becomes analytical tractable, even in the presence of a thousand-dimensional latent space. Experimental results show that our method outperforms LSTM models as well as some transformer-based models.
Supplementary Material: zip
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 2271
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