# Optimizing accuracy and diversity: a multi-task approach to forecast combinations

arXiv: https://arxiv.org/abs/2310.20545 · HTML: https://mlsanity.com/paper/2310.20545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 74 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [A Survey of Convolutional Neural Networks: Analysis, Applications, and Prospects](https://mlsanity.com/paper/2004.02806/) (2020)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Forecast combinations: an over 50-year review](https://mlsanity.com/paper/2205.04216/) (2022)
- [A machine learning approach for forecasting hierarchical time series](https://mlsanity.com/paper/2006.00630/) (2020)
- [Deep learning in business analytics and operations research: Models, applications and managerial implications](https://mlsanity.com/paper/1806.10897/) (2018)
- [Forecasting with time series imaging](https://mlsanity.com/paper/1904.08064/) (2019)
- [Optimization Problems for Machine Learning: A Survey](https://mlsanity.com/paper/1901.05331/) (2019)
- [Forecast with Forecasts: Diversity Matters](https://mlsanity.com/paper/2012.01643/) (2020)

## Abstract (arXiv)

We present a multi-task optimization approach based on a deep learning architecture for time series forecasting. We leverage large collections of time series to identify the weights of forecasting models that can be combined to produce forecasts for each series. This method jointly addresses two tasks: the selection of different forecasting models, and their effective combination. In doing so, it keeps into account, in an original way, both the accuracy and diversity of the forecasting methods. For a given time series, the model combination module extracts features and uses them to optimize the weights of the forecasting methods. Simultaneously, the model selection module extracts other features to identify the subset of methods to be used for the prediction. This selection process is framed as a classification problem, with the labels representing the set of models to be used for a series. These labels are determined by solving an auxiliary optimization problem that identifies accurate and diverse methods for each time series. The outputs of the two modules are then combined and the entire neural network is jointly trained by minimizing a custom loss function via gradient descent optimization. Experimental results on a large set of series from the M4 competition dataset and from real road traffic data show that our proposal enhances point forecast accuracy compared to state-of-the-art methods.