# Distributional Drift Adaptation with Temporal Conditional Variational Autoencoder for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2209.00654 · HTML: https://mlsanity.com/paper/2209.00654/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 99 references that are in the map.
- First posted on arXiv 1 Sep 2022.

## Builds on (most cited first, 30 of 42)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Conditional Variational Autoencoder with Adversarial Learning for End-to-End Text-to-Speech](https://mlsanity.com/paper/2106.06103/) (2021)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Learning Discourse-level Diversity for Neural Dialog Models using Conditional Variational Autoencoders](https://mlsanity.com/paper/1703.10960/) (2017)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [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)
- [TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generation](https://mlsanity.com/paper/2111.08095/) (2021)
- [Temporal Pattern Attention for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1809.04206/) (2018)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Constrained Generation of Semantically Valid Graphs via Regularizing Variational Autoencoders](https://mlsanity.com/paper/1809.02630/) (2018)
- [VideoFlow: A Conditional Flow-Based Model for Stochastic Video Generation](https://mlsanity.com/paper/1903.01434/) (2019)
- [SOM-VAE: Interpretable Discrete Representation Learning on Time Series](https://mlsanity.com/paper/1806.02199/) (2018)
- [Towards Spatio-Temporal Aware Traffic Time Series Forecasting--Full Version](https://mlsanity.com/paper/2203.15737/) (2022)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis](https://mlsanity.com/paper/1712.00975/) (2017)
- [DialogWAE: Multimodal Response Generation with Conditional Wasserstein Auto-Encoder](https://mlsanity.com/paper/1805.12352/) (2018)
- [DDG-DA: Data Distribution Generation for Predictable Concept Drift Adaptation](https://mlsanity.com/paper/2201.04038/) (2022)

## Built on by (most cited first, 7 of 7)

- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Learning Informative Representation for Fairness-aware Multivariate Time-series Forecasting: A Group-based Perspective](https://mlsanity.com/paper/2301.11535/) (2023)
- [SEMPO: Lightweight Foundation Models for Time Series Forecasting](https://mlsanity.com/paper/2510.19710/) (2025)
- [Nearest Neighbor Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.11625/) (2025)
- [Robust Multivariate Time Series Forecasting against Intra- and Inter-Series Transitional Shift](https://mlsanity.com/paper/2407.13194/) (2024)
- [Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch](https://mlsanity.com/paper/2607.05830/) (2026)
- [Assessing Low Back Movement with Motion Tape Sensor Data Through Deep Learning](https://mlsanity.com/paper/2602.11465/) (2026)

## Abstract (arXiv)

Due to the non-stationary nature, the distribution of real-world multivariate time series (MTS) changes over time, which is known as distribution drift. Most existing MTS forecasting models greatly suffer from distribution drift and degrade the forecasting performance over time. Existing methods address distribution drift via adapting to the latest arrived data or self-correcting per the meta knowledge derived from future data. Despite their great success in MTS forecasting, these methods hardly capture the intrinsic distribution changes, especially from a distributional perspective. Accordingly, we propose a novel framework temporal conditional variational autoencoder (TCVAE) to model the dynamic distributional dependencies over time between historical observations and future data in MTSs and infer the dependencies as a temporal conditional distribution to leverage latent variables. Specifically, a novel temporal Hawkes attention mechanism represents temporal factors subsequently fed into feed-forward networks to estimate the prior Gaussian distribution of latent variables. The representation of temporal factors further dynamically adjusts the structures of Transformer-based encoder and decoder to distribution changes by leveraging a gated attention mechanism. Moreover, we introduce conditional continuous normalization flow to transform the prior Gaussian to a complex and form-free distribution to facilitate flexible inference of the temporal conditional distribution. Extensive experiments conducted on six real-world MTS datasets demonstrate the TCVAE's superior robustness and effectiveness over the state-of-the-art MTS forecasting baselines. We further illustrate the TCVAE applicability through multifaceted case studies and visualization in real-world scenarios.