A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting (2211.02989v1)

Abstract: 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.

• The paper provides a systematic evaluation of 14 regression-based loss functions for time series forecasting.
• It compares performance on four diverse datasets using metrics such as P10, P50, and P90 to identify optimal use cases.
• The study highlights that selecting the appropriate loss function based on dataset characteristics enhances model accuracy and convergence.

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

In the paper entitled "A Comprehensive Survey of Regression Based Loss Functions for Time Series Forecasting," the authors Aryan Jadon, Avinash Patil, and Shruti Jadon present a systematic exploration of the various loss functions employed in time series forecasting. This paper serves as an indispensable reference for researchers looking to understand the nuances and applications of different regression-based loss functions.

The paper explores 14 prevalent regression loss functions, leaving no stone unturned in its quest to highlight how each function performs under various conditions and data distributions. These loss functions, such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and Huber Loss, among others, are crucial in guiding the convergence of forecasting models across a multitude of applications like anomaly detection and predictive maintenance.

A significant contribution of this research is its systematic analysis and the performance comparison of these loss functions on four diverse datasets, ranging from electricity consumption data to financial volatility indices. For each dataset, the paper introduces performance metrics like P10, P50, and P90, providing a robust framework for evaluating forecasting accuracy. Observations from such analyses reveal, for instance, that Quantile Loss, MSE, and Relative Root Mean Squared Error (RRMSE) demonstrate superior performance on the electricity dataset, whereas Log Cosh Loss performs better in traffic prediction scenarios.

Furthermore, the paper does not shy from speculating on the theoretical implications of loss function selection in forecasting tasks. Training machine learning models with different loss functions can affect the models' sensitivity to outliers, convergence rates, and computational efficiency. The paper suggests that researchers must tailor the choice of loss functions to align precisely with the characteristics of their specific datasets. For example, when dealing with datasets susceptible to outliers, adopting MSE can lead to better model accuracy due to its quadratic penalization of errors. Conversely, Quantile Loss can be pivotal when forecast reliability across percentiles is more salient.

The paper concludes by emphasizing that no single loss function holds universal superiority; rather, the function's effectiveness hinges on the context and objectives of the forecasting task. Looking forward, the paper recommends utilizing this comprehensive evaluation as a foundation for further research into adaptive loss function selection for AI models in time series forecasting. This work not only advances current understanding but also sets the stage for more adaptive and context-aware machine learning solutions in the future.