# Dynamic Gaussian Mixture based Deep Generative Model For Robust Forecasting on Sparse Multivariate Time Series

arXiv: https://arxiv.org/abs/2103.02164 · HTML: https://mlsanity.com/paper/2103.02164/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 3 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [RETAIN: An Interpretable Predictive Model for Healthcare using Reverse Time Attention Mechanism](https://mlsanity.com/paper/1608.05745/) (2016)
- [Multitask learning and benchmarking with clinical time series data](https://mlsanity.com/paper/1703.07771/) (2017)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data](https://mlsanity.com/paper/1811.08055/) (2018)
- [Interpolation-Prediction Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/1909.07782/) (2019)
- [Joint Modeling of Local and Global Temporal Dynamics for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/1911.10273/) (2019)
- [Autoregressive Convolutional Neural Networks for Asynchronous Time Series](https://mlsanity.com/paper/1703.04122/) (2017)

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

- [Graph-Guided Network for Irregularly Sampled Multivariate Time Series](https://mlsanity.com/paper/2110.05357/) (2021)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [Time Series as Images: Vision Transformer for Irregularly Sampled Time Series](https://mlsanity.com/paper/2303.12799/) (2023)
- [Asynchrony-Robust Collaborative Perception via Bird's Eye View Flow](https://mlsanity.com/paper/2309.16940/) (2023)
- [Improving Medical Predictions by Irregular Multimodal Electronic Health Records Modeling](https://mlsanity.com/paper/2210.12156/) (2022)
- [RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomalies](https://mlsanity.com/paper/2402.02032/) (2024)
- [FECAM: Frequency Enhanced Channel Attention Mechanism for Time Series Forecasting](https://mlsanity.com/paper/2212.01209/) (2022)
- [Towards Long-Term Time-Series Forecasting: Feature, Pattern, and Distribution](https://mlsanity.com/paper/2301.02068/) (2023)
- [A Systematic Review for Transformer-based Long-term Series Forecasting](https://mlsanity.com/paper/2310.20218/) (2023)
- [Unleashing The Power of Pre-Trained Language Models for Irregularly Sampled Time Series](https://mlsanity.com/paper/2408.08328/) (2024)
- [Distributional Drift Adaptation with Temporal Conditional Variational Autoencoder for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2209.00654/) (2022)
- [CTPD: Cross-Modal Temporal Pattern Discovery for Enhanced Multimodal Electronic Health Records Analysis](https://mlsanity.com/paper/2411.00696/) (2024)
- [Irregularity-Informed Time Series Analysis: Adaptive Modelling of Spatial and Temporal Dynamics](https://mlsanity.com/paper/2410.12257/) (2024)
- [Gaussian Process Latent Variable Modeling for Few-shot Time Series Forecasting](https://mlsanity.com/paper/2212.10306/) (2022)
- [Disentangling Imperfect: A Wavelet-Infused Multilevel Heterogeneous Network for Human Activity Recognition in Flawed Wearable Sensor Data](https://mlsanity.com/paper/2402.09434/) (2024)
- [DeepExpress: Heterogeneous and Coupled Sequence Modeling for Express Delivery Prediction](https://mlsanity.com/paper/2108.08170/) (2021)
- [Compatible Transformer for Irregularly Sampled Multivariate Time Series](https://mlsanity.com/paper/2310.11022/) (2023)
- [Channel-Aware Throughput Maximization for Cooperative Data Fusion in CAV](https://mlsanity.com/paper/2410.04320/) (2024)
- [Mind the Missing: Variable-Aware Representation Learning for Irregular EHR Time Series using Large Language Models](https://mlsanity.com/paper/2509.22121/) (2025)
- [Towards Learning in Grey Spatiotemporal Systems: A Prophet to Non-consecutive Spatiotemporal Dynamics](https://mlsanity.com/paper/2208.08878/) (2022)
- [WaveGNN: Integrating Graph Neural Networks and Transformers for Decay-Aware Classification of Irregular Clinical Time-Series](https://mlsanity.com/paper/2412.10621/) (2024)
- [Beyond Observations: Reconstruction Error-Guided Irregularly Sampled Time Series Representation Learning](https://mlsanity.com/paper/2511.06854/) (2025)
- [Comparative study of clustering models for multivariate time series from connected medical devices](https://mlsanity.com/paper/2312.17286/) (2023)
- [MuSiCNet: A Gradual Coarse-to-Fine Framework for Irregularly Sampled Multivariate Time Series Analysis](https://mlsanity.com/paper/2412.01063/) (2024)
- [SuperMAN: Interpretable and Expressive Networks over Temporally Sparse Heterogeneous Data](https://mlsanity.com/paper/2505.19193/) (2025)
- [Graph Mixing Additive Networks](https://mlsanity.com/paper/2509.23923/) (2025)
- [A Statistical Approach for Modeling Irregular Multivariate Time Series with Missing Observations](https://mlsanity.com/paper/2602.19531/) (2026)
- [DBGL: Decay-aware Bipartite Graph Learning for Irregular Medical Time Series Classification](https://mlsanity.com/paper/2604.11842/) (2026)
- [ForecastCompass: Guiding Agentic Forecasting with Adaptive Factor Memory](https://mlsanity.com/paper/2605.30858/) (2026)
- [Multimodal Prompt Learning with Irregular EHRs for Robust Monitoring of Critical Care Patients](https://mlsanity.com/paper/2608.21941/) (2026)

## Abstract (arXiv)

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.