The relevance of the research is due to the growing need for fast and accurate tools for building mathematical models. This paper discusses approaches to building adaptive quantile regression because selecting the optimal quantile during the training process can save a large amount of researcher's time. The correct choice of quantile can significantly improve the performance of the model on test datasets and, as a consequence, obtain more reliable predictions when such a mathematical model is actually used. The developed approach is a combination of modified quantile regression and gradient descent, which improves the adaptation of the model to different data. A detailed description of the developed algorithm is given. The paper also presents a comparison of the performance accuracy of the proposed model with traditional quantile regression and gradient descent along with their combinations. It also analyzes the training time of the models, including the number of training epochs. Experiments show that adaptive quantile regression exhibits improved accuracy with reduced training time. The results emphasize the effectiveness of this method in data analysis and prediction, opening new perspectives for more efficient and faster machine learning models.
1. Zheng Qi, Limin Peng, Xuming He. Globally adaptive quantile regression with ultra-high dimensional data. The Annals of Statistics. 2015;43(5):2225–2258. DOI: 10.1214/15-AOS1340.
2. Barrodale I., Roberts F.D.K. An improved algorithm for discrete L1 linear approximation. SIAM Journal on Numerical Analysis. 1973;10(5):839–848. DOI: 10.1137/0710069.
3. Chen C. An Adaptive Algorithm for Quantile Regression. In: Theory and Applications of Recent Robust Methods by ICORS2003: International Conference on Robust Statistics – 2003, 13–18 July 2003, Antwerp, Belgium. Basel: Springer Basel AG; 2004. p. 39–48.
4. Chen C. A Finite Smoothing Algorithm for Quantile Regression. Journal of Computational and Graphical Statistics. 2007;16(1):136–164. DOI: 10.1198/106186007X180336.
5. Behl P., Claeskens G., Dette H. Focused model selection in quantile regression. Statistica Sinica. 2014;24(2):601–624. DOI: 10.5705/ss.2012.097.
6. Wang K., Wang H.J. Optimally combined estimation for tail quantile regression. Statistica Sinica. 2016;26(1):295–311. DOI: 10.5705/ss.2014.051.
7. Zheng S. Gradient descent algorithms for quantile regression with smooth approximation. International Journal of Machine Learning and Cybernetics. 2011;2:191–207. DOI: 10.1007/s13042-011-0031-2.
8. Li Y., Zhu J. L1-norm quantile regression. Journal of Computational and Graphical Statistics. 2008;17(1):1–23. DOI: 10.1198/106186008X289155.
9. Wang B., Hu T., Yin H. Quantile regression with Gaussian Kernels. Contemporary Experimental Design, Multivariate Analysis and Data Mining. 2020;373–386.
10. Tyurin A.S., Saraev P.V. Construction of quantile regression using natural gradient descent. Prikladnaya matematika i voprosy upravleniya = Applied Mathematics and Control Sciences. 2023;(2):43–52. (In Russ.).
