Isotonic and Convex Regression: A Review of Theory, Algorithms, and Applications (www.mdpi.com)

A recent review titled "Isotonic and Convex Regression: A Review of Theory, Algorithms, and Applications" offers an in-depth exploration of the theoretical underpinnings, algorithmic approaches, and practical applications related to isotonic and convex regression methods. With a focus on quadratic programming (QP) formulations, the study highlights statistical properties, computational algorithms, and the distinct challenges posed by non-smoothness and overfitting in both regression types. These insights are crucial for researchers and practitioners seeking to implement these methods effectively in machine learning tasks. The significance of this review lies in its connections to contemporary machine learning, as the authors propose future directions to address critical challenges such as developing scalable algorithms for large-scale data and refining methods for multivariate isotonic regression. By emphasizing the need for penalized approaches and theoretical frameworks to mitigate overfitting, this work not only advances the statistical understanding of these techniques but also informs their potential integration into machine learning models. The findings serve as a valuable resource for enhancing the robustness and applicability of isotonic and convex regression in various data-driven fields.