# Partial-Multivariate Model for Forecasting

arXiv: https://arxiv.org/abs/2408.09703 · HTML: https://mlsanity.com/paper/2408.09703/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 48 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2310.08278/) (2023)
- [Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory](https://mlsanity.com/paper/1711.01244/) (2017)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [DSformer: A Double Sampling Transformer for Multivariate Time Series Long-term Prediction](https://mlsanity.com/paper/2308.03274/) (2023)
- [Generalization bounds for deep learning](https://mlsanity.com/paper/2012.04115/) (2020)
- [Learning to Embed Time Series Patches Independently](https://mlsanity.com/paper/2312.16427/) (2023)
- [PETformer: Long-term Time Series Forecasting via Placeholder-enhanced Transformer](https://mlsanity.com/paper/2308.04791/) (2023)
- [Learning Deep Time-index Models for Time Series Forecasting](https://mlsanity.com/paper/2207.06046/) (2022)

## Built on by (most cited first, 2 of 2)

- [xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories](https://mlsanity.com/paper/2410.16928/) (2024)
- [Partial multivariate transformer as a tool for cryptocurrencies time series prediction](https://mlsanity.com/paper/2512.04099/) (2025)

## Abstract (arXiv)

When solving forecasting problems including multiple time-series features, existing approaches often fall into two extreme categories, depending on whether to utilize inter-feature information: univariate and complete-multivariate models. Unlike univariate cases which ignore the information, complete-multivariate models compute relationships among a complete set of features. However, despite the potential advantage of leveraging the additional information, complete-multivariate models sometimes underperform univariate ones. Therefore, our research aims to explore a middle ground between these two by introducing what we term Partial-Multivariate models where a neural network captures only partial relationships, that is, dependencies within subsets of all features. To this end, we propose PMformer, a Transformer-based partial-multivariate model, with its training algorithm. We demonstrate that PMformer outperforms various univariate and complete-multivariate models, providing a theoretical rationale and empirical analysis for its superiority. Additionally, by proposing an inference technique for PMformer, the forecasting accuracy is further enhanced. Finally, we highlight other advantages of PMformer: efficiency and robustness under missing features.