# MixSeq: Connecting Macroscopic Time Series Forecasting with Microscopic Time Series Data

arXiv: https://arxiv.org/abs/2110.14354 · HTML: https://mlsanity.com/paper/2110.14354/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 27 Oct 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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [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)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Deep Transformer Models for Time Series Forecasting: The Influenza Prevalence Case](https://mlsanity.com/paper/2001.08317/) (2020)
- [Deep Temporal Clustering : Fully Unsupervised Learning of Time-Domain Features](https://mlsanity.com/paper/1802.01059/) (2018)
- [Long-term Forecasting using Higher Order Tensor RNNs](https://mlsanity.com/paper/1711.00073/) (2017)
- [Unsupervised Discrete Sentence Representation Learning for Interpretable Neural Dialog Generation](https://mlsanity.com/paper/1804.08069/) (2018)
- [Deep Factors with Gaussian Processes for Forecasting](https://mlsanity.com/paper/1812.00098/) (2018)
- [Temporal Convolutional Attention-based Network For Sequence Modeling](https://mlsanity.com/paper/2002.12530/) (2020)
- [How Much Can A Retailer Sell? Sales Forecasting on Tmall](https://mlsanity.com/paper/2002.11940/) (2020)
- [Radflow: A Recurrent, Aggregated, and Decomposable Model for Networks of Time Series](https://mlsanity.com/paper/2102.07289/) (2021)

## Built on by (most cited first, 9 of 9)

- [Multi-Modality Spatio-Temporal Forecasting via Self-Supervised Learning](https://mlsanity.com/paper/2405.03255/) (2024)
- [Learning Differential Operators for Interpretable Time Series Modeling](https://mlsanity.com/paper/2209.01491/) (2022)
- [SutraNets: Sub-series Autoregressive Networks for Long-Sequence, Probabilistic Forecasting](https://mlsanity.com/paper/2312.14880/) (2023)
- [Learning Gaussian Mixture Representations for Tensor Time Series Forecasting](https://mlsanity.com/paper/2306.00390/) (2023)
- [Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data](https://mlsanity.com/paper/2306.10275/) (2023)
- [OptScaler: A Collaborative Framework for Robust Autoscaling in the Cloud](https://mlsanity.com/paper/2311.12864/) (2023)
- [C2FAR: Coarse-to-Fine Autoregressive Networks for Precise Probabilistic Forecasting](https://mlsanity.com/paper/2312.15002/) (2023)
- [ALT: An Automatic System for Long Tail Scenario Modeling](https://mlsanity.com/paper/2305.11390/) (2023)
- [Frequency-Domain Multi-Modality Transportation Modeling](https://mlsanity.com/paper/2607.08475/) (2026)

## Abstract (arXiv)

Time series forecasting is widely used in business intelligence, e.g., forecast stock market price, sales, and help the analysis of data trend. Most time series of interest are macroscopic time series that are aggregated from microscopic data. However, instead of directly modeling the macroscopic time series, rare literature studied the forecasting of macroscopic time series by leveraging data on the microscopic level. In this paper, we assume that the microscopic time series follow some unknown mixture probabilistic distributions. We theoretically show that as we identify the ground truth latent mixture components, the estimation of time series from each component could be improved because of lower variance, thus benefitting the estimation of macroscopic time series as well. Inspired by the power of Seq2seq and its variants on the modeling of time series data, we propose Mixture of Seq2seq (MixSeq), an end2end mixture model to cluster microscopic time series, where all the components come from a family of Seq2seq models parameterized by different parameters. Extensive experiments on both synthetic and real-world data show the superiority of our approach.