\Ell_p$ Regression

$\ell_p$ regression aims to find the best fit line (or hyperplane) to a dataset by minimizing the sum of the $p$-th powers of the errors. Current research focuses on developing efficient algorithms for large datasets, including coreset constructions and sensitivity sampling, to reduce computational complexity and improve approximation guarantees, particularly for high-dimensional data and multiple response variables. These advancements are significant for improving the scalability and accuracy of regression analysis across diverse applications, such as machine learning, data analysis, and scientific modeling, especially in scenarios with privacy constraints or limited computational resources. Furthermore, research explores optimal sampling strategies and the impact of different values of *p* on the regression's robustness and efficiency.