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Mamba time series forecasting with uncertainty quantification
Pedro Pessoa1,2, Paul Campitelli1,2, Douglas P Shepherd1,2
1Center for Biological Physics, Tempe, AZ, United States of America.
Machine Learning: Science and Technology
|July 24, 2025
Summary
State space models like Mamba show promise for time series forecasting but lack accurate uncertainty quantification. Our Mamba-ProbTSF method enhances Mamba by modeling predictive uncertainty, improving forecast reliability for electricity and traffic data.
Area of Science:
- Machine Learning
- Time Series Analysis
- Probabilistic Forecasting
Background:
- State space models, including Mamba, are increasingly used for time series forecasting due to their sequence pattern recognition capabilities.
- Existing Mamba implementations show significant mean errors in electricity consumption (approx. 8%) and traffic occupancy (approx. 18%) benchmarks.
- There is a need to quantify the uncertainty in Mamba forecasts to distinguish between inaccuracy and inherent data variability.
Purpose of the Study:
- To develop a method for quantifying the predictive uncertainty of Mamba-based time series forecasts.
- To introduce a dual-network framework, Mamba-ProbTSF, for probabilistic forecasting using the Mamba architecture.
- To evaluate the performance and reliability of Mamba-ProbTSF against existing methods.
Main Methods:
- Proposed a dual-network framework integrating Mamba for probabilistic time series forecasting.
- One network generates point forecasts; a second network models predictive uncertainty by estimating variance.
- Implemented the Mamba with probabilistic TSF (Mamba-ProbTSF) tool, with code available on GitHub.
Main Results:
- Achieved reduced Kullback-Leibler divergence (10^-3 for synthetic, 10^-1 for real-world data), indicating improved probability distribution modeling.
- Validated that true trajectories fall within the predicted two-sigma uncertainty interval approximately 95% of the time for benchmark datasets.
- Demonstrated consistently lower forecast errors and more reliable uncertainty quantification compared to DeepAR and ARIMA.
Conclusions:
- Mamba-ProbTSF effectively quantifies predictive uncertainty in Mamba forecasts, enhancing reliability for time series forecasting tasks.
- The method shows superior performance over leading probabilistic forecasting models like DeepAR and ARIMA.
- The framework holds potential for application in stochastic processes, including Brownian motion and molecular dynamics.
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