# A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting

arXiv: https://arxiv.org/abs/2211.02989 · HTML: https://mlsanity.com/paper/2211.02989/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 5 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [A survey of loss functions for semantic segmentation](https://mlsanity.com/paper/2006.14822/) (2020)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Mean Absolute Percentage Error for regression models](https://mlsanity.com/paper/1605.02541/) (2016)
- [An Alternative Probabilistic Interpretation of the Huber Loss](https://mlsanity.com/paper/1911.02088/) (2019)
- [On Mean Absolute Error for Deep Neural Network Based Vector-to-Vector Regression](https://mlsanity.com/paper/2008.07281/) (2020)
- [Statistical Properties of the log-cosh Loss Function Used in Machine Learning](https://mlsanity.com/paper/2208.04564/) (2022)

## Built on by (most cited first, 30 of 33)

- [A Comprehensive Survey of Evaluation Techniques for Recommendation Systems](https://mlsanity.com/paper/2312.16015/) (2023)
- [Convergence Rate Analysis of LION](https://mlsanity.com/paper/2411.07724/) (2024)
- [A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions](https://mlsanity.com/paper/2502.06026/) (2025)
- [Leveraging Generative AI Models for Synthetic Data Generation in Healthcare: Balancing Research and Privacy](https://mlsanity.com/paper/2305.05247/) (2023)
- [Modeling Temporal Dependencies within the Target for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2406.04777/) (2024)
- [TINED: GNNs-to-MLPs by Teacher Injection and Dirichlet Energy Distillation](https://mlsanity.com/paper/2412.11180/) (2024)
- [Towards Better Long-range Time Series Forecasting using Generative Forecasting](https://mlsanity.com/paper/2212.06142/) (2022)
- [A Comparative Study of Text Embedding Models for Semantic Text Similarity in Bug Reports](https://mlsanity.com/paper/2308.09193/) (2023)
- [Enhancing Risk Assessment in Transformers with Loss-at-Risk Functions](https://mlsanity.com/paper/2411.02558/) (2024)
- [Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions](https://mlsanity.com/paper/2503.12354/) (2025)
- [Task-based Loss Functions in Computer Vision: A Comprehensive Review](https://mlsanity.com/paper/2504.04242/) (2025)
- [To See Far, Look Close: Evolutionary Forecasting for Long-term Time Series](https://mlsanity.com/paper/2601.23114/) (2026)
- [Reshaping Action Error Distributions for Reliable Vision-Language-Action Models](https://mlsanity.com/paper/2602.04228/) (2026)
- [Reviving Error Correction in Modern Deep Time-Series Forecasting](https://mlsanity.com/paper/2605.21088/) (2026)
- [KLAS: Using Similarity to Stitch Neural Networks for Improved Accuracy-Efficiency Tradeoffs](https://mlsanity.com/paper/2605.29259/) (2026)
- [Hybrid Imbalanced Regression Through Unified Data-Level and Algorithm-Level Balancing](https://mlsanity.com/paper/2606.01221/) (2026)
- [Automated Measurement of Vascular Calcification in Femoral Endarterectomy Patients Using Deep Learning](https://mlsanity.com/paper/2311.16001/) (2023)
- [Use of Deep Neural Networks for Uncertain Stress Functions with Extensions to Impact Mechanics](https://mlsanity.com/paper/2311.16135/) (2023)
- [Bond Graphs for multi-physics informed Neural Networks for multi-variate time series](https://mlsanity.com/paper/2405.13586/) (2024)
- [Enhancing Solar Driver Forecasting with Multivariate Transformers](https://mlsanity.com/paper/2406.15847/) (2024)
- [How to warm-start your unfolding network](https://mlsanity.com/paper/2502.01854/) (2025)
- [DeepSeasons: a Deep Learning scale-selecting approach to Seasonal Forecasts](https://mlsanity.com/paper/2509.10494/) (2025)
- [A study of Universal ODE approaches to predicting soil organic carbon](https://mlsanity.com/paper/2509.24306/) (2025)
- [Early wind turbine alarm prediction based on machine learning: AlarmForecasting](https://mlsanity.com/paper/2510.06831/) (2025)
- [Real-Time Long Horizon Air Quality Forecasting via Group-Relative Policy Optimization](https://mlsanity.com/paper/2511.22169/) (2025)
- [Robust Outlier Detection and Low-Latency Concept Drift Adaptation for Data Stream Regression: A Dual-Channel Architecture](https://mlsanity.com/paper/2512.12289/) (2025)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Generalizing Dynamics Modeling More Easily from Representation Perspective](https://mlsanity.com/paper/2603.22655/) (2026)
- [Ratio-based Loss Functions](https://mlsanity.com/paper/2605.05808/) (2026)
- [IstGPT: LLM-based Anomaly Detection for Spatial-Temporal Graph in Industrial Systems](https://mlsanity.com/paper/2606.01691/) (2026)

## Abstract (arXiv)

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.