# Better Batch for Deep Probabilistic Time Series Forecasting

arXiv: https://arxiv.org/abs/2305.17028 · HTML: https://mlsanity.com/paper/2305.17028/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 13 of 13)

- [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)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [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)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [Neural networks for geospatial data](https://mlsanity.com/paper/2304.09157/) (2023)
- [Probabilistic Traffic Forecasting with Dynamic Regression](https://mlsanity.com/paper/2301.06650/) (2023)

## Built on by (most cited first, 5 of 5)

- [Multivariate Probabilistic Time Series Forecasting with Correlated Errors](https://mlsanity.com/paper/2402.01000/) (2024)
- [MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecasting](https://mlsanity.com/paper/2410.09133/) (2024)
- [When Context Is Not Enough: Modeling Unexplained Variability in Car-Following Behavior](https://mlsanity.com/paper/2507.07012/) (2025)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2605.23402/) (2026)

## Abstract (arXiv)

Deep probabilistic time series forecasting has gained attention for its ability to provide nonlinear approximation and valuable uncertainty quantification for decision-making. However, existing models often oversimplify the problem by assuming a time-independent error process and overlooking serial correlation. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to enhance probabilistic forecasting accuracy. Our method constructs a mini-batch as a collection of D consecutive time series segments for model training. It explicitly learns a time-varying covariance matrix over each mini-batch, encoding error correlation among adjacent time steps. The learned covariance matrix can be used to improve prediction accuracy and enhance uncertainty quantification. We evaluate our method on two different neural forecasting models and multiple public datasets. Experimental results confirm the effectiveness of the proposed approach in improving the performance of both models across a range of datasets, resulting in notable improvements in predictive accuracy.