# Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2101.10460 · HTML: https://mlsanity.com/paper/2101.10460/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 70 references that are in the map.
- First posted on arXiv 25 Jan 2021.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [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)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (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)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems](https://mlsanity.com/paper/1808.08798/) (2018)
- [LSTM-MSNet: Leveraging Forecasts on Sets of Related Time Series with Multiple Seasonal Patterns](https://mlsanity.com/paper/1909.04293/) (2019)
- [Towards Better Forecasting by Fusing Near and Distant Future Visions](https://mlsanity.com/paper/1912.05122/) (2019)
- [R2N2: Residual Recurrent Neural Networks for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1709.03159/) (2017)

## Built on by (most cited first, 30 of 32)

- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Temporal Data Meets LLM -- Explainable Financial Time Series Forecasting](https://mlsanity.com/paper/2306.11025/) (2023)
- [Learning the Evolutionary and Multi-scale Graph Structure for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.13816/) (2022)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Decoupling Local and Global Representations of Time Series](https://mlsanity.com/paper/2202.02262/) (2022)
- [Federated Learning for 5G Base Station Traffic Forecasting](https://mlsanity.com/paper/2211.15220/) (2022)
- [Towards Long-Term Time-Series Forecasting: Feature, Pattern, and Distribution](https://mlsanity.com/paper/2301.02068/) (2023)
- [Self-Supervised Learning of Time Series Representation via Diffusion Process and Imputation-Interpolation-Forecasting Mask](https://mlsanity.com/paper/2405.05959/) (2024)
- [Distributional Drift Adaptation with Temporal Conditional Variational Autoencoder for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2209.00654/) (2022)
- [Regions of Reliability in the Evaluation of Multivariate Probabilistic Forecasts](https://mlsanity.com/paper/2304.09836/) (2023)
- [Probabilistic Decomposition Transformer for Time Series Forecasting](https://mlsanity.com/paper/2210.17393/) (2022)
- [Deep Coupling Network For Multivariate Time Series Forecasting](https://mlsanity.com/paper/2402.15134/) (2024)
- [Deep Evidential Learning for Bayesian Quantile Regression](https://mlsanity.com/paper/2308.10650/) (2023)
- [A Survey of Transformer Enabled Time Series Synthesis](https://mlsanity.com/paper/2406.02322/) (2024)
- [Probabilistic forecasts of wind power generation in regions with complex topography using deep learning methods: An Arctic case](https://mlsanity.com/paper/2203.07080/) (2022)
- [Latent Temporal Flows for Multivariate Analysis of Wearables Data](https://mlsanity.com/paper/2210.07475/) (2022)
- [Non-parametric Probabilistic Time Series Forecasting via Innovations Representation](https://mlsanity.com/paper/2306.03782/) (2023)
- [Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction](https://mlsanity.com/paper/2506.04542/) (2025)
- [DynaConF: Dynamic Forecasting of Non-Stationary Time Series](https://mlsanity.com/paper/2209.08411/) (2022)
- [Generative Probabilistic Time Series Forecasting and Applications in Grid Operations](https://mlsanity.com/paper/2402.13870/) (2024)
- [How to Unlock Time Series Editing? Diffusion-Driven Approach with Multi-Grained Control](https://mlsanity.com/paper/2506.05276/) (2025)
- [PRISM: A hierarchical multiscale approach for time series forecasting](https://mlsanity.com/paper/2512.24898/) (2025)
- [OrcoDCS: An IoT-Edge Orchestrated Online Deep Compressed Sensing Framework](https://mlsanity.com/paper/2308.05757/) (2023)
- [Encoding Seasonal Climate Predictions for Demand Forecasting with Modular Neural Network](https://mlsanity.com/paper/2309.02248/) (2023)
- [Unsupervised Representation Learning of Complex Time Series for Maneuverability State Identification in Smart Mobility](https://mlsanity.com/paper/2409.06718/) (2024)
- [The Roles of Generative Artificial Intelligence in Internet of Electric Vehicles](https://mlsanity.com/paper/2409.15750/) (2024)
- [CoRe: Coherency Regularization for Hierarchical Time Series](https://mlsanity.com/paper/2502.15983/) (2025)

## Abstract (arXiv)

Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or abandons modeling cross-series correlations. A promising line of work exploits scalable matrix factorization for latent-space forecasting, but is limited to linear embeddings, unable to model distributions, and not trainable end-to-end when using deep learning forecasting. We introduce a novel temporal latent auto-encoder method which enables nonlinear factorization of multivariate time series, learned end-to-end with a temporal deep learning latent space forecast model. By imposing a probabilistic latent space model, complex distributions of the input series are modeled via the decoder. Extensive experiments demonstrate that our model achieves state-of-the-art performance on many popular multivariate datasets, with gains sometimes as high as 50% for several standard metrics.