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Winner-takes-all for Multivariate Probabilistic Time Series Forecasting

ICML 2025 · Time series › Causal and generative time series · approach: Probabilistic and conformal forecasting · 0 citations (OpenAlex)

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Proposes TimeMCL, a multi-head winner-takes-all (multiple choice learning) autoregressive forecaster that produces K diverse plausible multivariate futures in one forward pass, with a theoretical link to functional quantization.

Problem

Probabilistic multivariate time series forecasting must represent multimodal future distributions, but diffusion and flow models are computationally expensive at inference and lack explicit diversity guarantees among hypotheses.

Approach

Adapt Multiple Choice Learning with a winner-takes-all loss to autoregressive time-series forecasters: K heads share a recurrent backbone, only the best head per window is trained, score heads estimate each head's winning probability, and the training is interpreted as conditional functional quantization (centroidal Voronoi tessellation).

Key results

• On Solar with 16 hypotheses, TimeMCL (relaxed) reaches distortion 280.03 versus 360.6 for TimeGrad and 358.01 for Tactis2.
• On Traffic, TimeMCL (relaxed) achieves total variation 5.766 vs 12.991 for TimeGrad; smoother trajectories across datasets.
• TimeMCL inference costs 8.83e6 FLOPs and 1.12 s run-time at K=16 on Exchange, versus 3.05e9 FLOPs and 241.57 s for TimeGrad.

Measured effects reported in the paper

Surprising findings

• Performance improvement with the number of hypotheses is not strictly monotonic for TimeMCL, which the authors attribute partly to the mean scaling choice.
• TimeMCL does not beat TimeGrad on CRPS and RMSE for most datasets; the authors say TimeGrad outperforms other baselines on those metrics, and Tactis2 is better on Exchange.

Limitations

• Performance depends on the data scaler; mean scaling may bias which hypotheses get used.
• The number of hypotheses K must be fixed in advance; adding hypotheses requires retraining.
• Only an RNN (LSTM) backbone is evaluated; transformer or larger-scale backbones are left for future work.

Experimental setup

Datasets: Solar Electricity Exchange Traffic Taxi Wikipedia Brownian motion (synthetic) Brownian bridge (synthetic) AR(5) (synthetic) cryptocurrency prices (YahooFinance)

Benchmarks: Solar Electricity Exchange Traffic Taxi Wikipedia

Metrics: distortion RMSE CRPS total variation FLOPs run-time

Baselines: ETS Tactis2 DeepAR TempFlow TimeGrad Trf.TempFlow Relaxed-WTA aMCL

Builds on: Multiple Choice Learning Relaxed Winner-Takes-All TimeGrad DeepAR TempFlow

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• Annealed Multiple Choice Learning: Overcoming limitations of Winner-takes-all with annealing (NeurIPS 2024 · similarity 0.86)
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