# Deep Factors for Forecasting

arXiv: https://arxiv.org/abs/1905.12417 · HTML: https://mlsanity.com/paper/1905.12417/

## Key facts

- Cited by 86 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 30 of 86)

- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Domain Adaptation for Time Series Forecasting via Attention Sharing](https://mlsanity.com/paper/2102.06828/) (2021)
- [Criteria for Classifying Forecasting Methods](https://mlsanity.com/paper/2212.03523/) (2022)
- [Retrieval Augmented Time Series Forecasting](https://mlsanity.com/paper/2411.08249/) (2024)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)
- [Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting](https://mlsanity.com/paper/2111.06581/) (2021)
- [DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting](https://mlsanity.com/paper/2203.07681/) (2022)
- [A Multi-view Multi-task Learning Framework for Multi-variate Time Series Forecasting](https://mlsanity.com/paper/2109.01657/) (2021)
- [Multivariate Time Series Forecasting with Latent Graph Inference](https://mlsanity.com/paper/2203.03423/) (2022)
- [Disentangling Structured Components: Towards Adaptive, Interpretable and Scalable Time Series Forecasting](https://mlsanity.com/paper/2305.13036/) (2023)
- [Decoupling Local and Global Representations of Time Series](https://mlsanity.com/paper/2202.02262/) (2022)
- [RNN with Particle Flow for Probabilistic Spatio-temporal Forecasting](https://mlsanity.com/paper/2106.06064/) (2021)
- [SSDNet: State Space Decomposition Neural Network for Time Series Forecasting](https://mlsanity.com/paper/2112.10251/) (2021)
- [Robust Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.11910/) (2022)
- [Variance Reduced Training with Stratified Sampling for Forecasting Models](https://mlsanity.com/paper/2103.02062/) (2021)
- [Topological Attention for Time Series Forecasting](https://mlsanity.com/paper/2107.09031/) (2021)
- [A Transformer-based Diffusion Probabilistic Model for Heart Rate and Blood Pressure Forecasting in Intensive Care Unit](https://mlsanity.com/paper/2301.06625/) (2023)
- [From Values to Tokens: An LLM-Driven Framework for Context-aware Time Series Forecasting via Symbolic Discretization](https://mlsanity.com/paper/2508.09191/) (2025)
- [Cast-R1: Learning Tool-Augmented Sequential Decision Policies for Time Series Forecasting](https://mlsanity.com/paper/2602.13802/) (2026)
- [Hierarchically Regularized Deep Forecasting](https://mlsanity.com/paper/2106.07630/) (2021)
- [Deep Autoregressive Models with Spectral Attention](https://mlsanity.com/paper/2107.05984/) (2021)
- [Instance-Based Uncertainty Estimation for Gradient-Boosted Regression Trees](https://mlsanity.com/paper/2205.11412/) (2022)
- [MemCast: Memory-Driven Time Series Forecasting with Experience-Conditioned Reasoning](https://mlsanity.com/paper/2602.03164/) (2026)
- [Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features](https://mlsanity.com/paper/2106.05960/) (2021)

## Abstract (arXiv)

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically relevant and challenging task. Classical time series models fail to capture complex patterns in the data, and multivariate techniques struggle to scale to large problem sizes. Their reliance on strong structural assumptions makes them data-efficient, and allows them to provide uncertainty estimates. The converse is true for models based on deep neural networks, which can learn complex patterns and dependencies given enough data. In this paper, we propose a hybrid model that incorporates the benefits of both approaches. Our new method is data-driven and scalable via a latent, global, deep component. It also handles uncertainty through a local classical model. We provide both theoretical and empirical evidence for the soundness of our approach through a necessary and sufficient decomposition of exchangeable time series into a global and a local part. Our experiments demonstrate the advantages of our model both in term of data efficiency, accuracy and computational complexity.