# Winner-takes-all for Multivariate Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2506.05515 · HTML: https://mlsanity.com/paper/2506.05515/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 5 Jun 2025.

## Builds on (most cited first, 25 of 25)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinforcement Learning](https://mlsanity.com/paper/2010.13303/) (2020)
- [DMCL: Distillation Multiple Choice Learning for Multimodal Action Recognition](https://mlsanity.com/paper/1912.10982/) (2019)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Confident Multiple Choice Learning](https://mlsanity.com/paper/1706.03475/) (2017)
- [Resilient Multiple Choice Learning: A learned scoring scheme with application to audio scene analysis](https://mlsanity.com/paper/2311.01052/) (2023)
- [Annealed Multiple Choice Learning: Overcoming limitations of Winner-takes-all with annealing](https://mlsanity.com/paper/2407.15580/) (2024)
- [Winner-takes-all learners are geometry-aware conditional density estimators](https://mlsanity.com/paper/2406.04706/) (2024)

## Built on by (most cited first, 4 of 4)

- [From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting](https://mlsanity.com/paper/2509.19975/) (2025)
- [TimePre: Bridging Accuracy, Efficiency, and Stability in Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2511.18539/) (2025)
- [PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation](https://mlsanity.com/paper/2605.28867/) (2026)
- [Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting](https://mlsanity.com/paper/2602.10182/) (2026)

## Abstract (arXiv)

We introduce TimeMCL, a method leveraging the Multiple Choice Learning (MCL) paradigm to forecast multiple plausible time series futures. Our approach employs a neural network with multiple heads and utilizes the Winner-Takes-All (WTA) loss to promote diversity among predictions. MCL has recently gained attention due to its simplicity and ability to address ill-posed and ambiguous tasks. We propose an adaptation of this framework for time-series forecasting, presenting it as an efficient method to predict diverse futures, which we relate to its implicit quantization objective. We provide insights into our approach using synthetic data and evaluate it on real-world time series, demonstrating its promising performance at a light computational cost.