# SLOTH: Structured Learning and Task-based Optimization for Time Series Forecasting on Hierarchies

arXiv: https://arxiv.org/abs/2302.05650 · HTML: https://mlsanity.com/paper/2302.05650/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 11 Feb 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [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)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [Tree-structured Attention with Hierarchical Accumulation](https://mlsanity.com/paper/2002.08046/) (2020)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [Bellman Meets Hawkes: Model-Based Reinforcement Learning via Temporal Point Processes](https://mlsanity.com/paper/2201.12569/) (2022)
- [A Meta Reinforcement Learning Approach for Predictive Autoscaling in the Cloud](https://mlsanity.com/paper/2205.15795/) (2022)
- [Convolutional Neural Networks over Tree Structures for Programming Language Processing](https://mlsanity.com/paper/1409.5718/) (2014)
- [Reconciliation of probabilistic forecasts with an application to wind power](https://mlsanity.com/paper/1808.02635/) (2018)

## Built on by (most cited first, 5 of 5)

- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [GinAR: An End-To-End Multivariate Time Series Forecasting Model Suitable for Variable Missing](https://mlsanity.com/paper/2405.11333/) (2024)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [Revisiting Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2509.23494/) (2025)
- [Hierarchical Time Series Forecasting with Operator-Valued Kernels](https://mlsanity.com/paper/2610.18196/) (2026)

## Abstract (arXiv)

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS) forecasting includes two sub-tasks, i.e., forecasting and reconciliation. In the previous works, hierarchical information is only integrated in the reconciliation step to maintain coherency, but not in forecasting step for accuracy improvement. In this paper, we propose two novel tree-based feature integration mechanisms, i.e., top-down convolution and bottom-up attention to leverage the information of the hierarchical structure to improve the forecasting performance. Moreover, unlike most previous reconciliation methods which either rely on strong assumptions or focus on coherent constraints only,we utilize deep neural optimization networks, which not only achieve coherency without any assumptions, but also allow more flexible and realistic constraints to achieve task-based targets, e.g., lower under-estimation penalty and meaningful decision-making loss to facilitate the subsequent downstream tasks. Experiments on real-world datasets demonstrate that our tree-based feature integration mechanism achieves superior performances on hierarchical forecasting tasks compared to the state-of-the-art methods, and our neural optimization networks can be applied to real-world tasks effectively without any additional effort under coherence and task-based constraints