Linear Regression

Linear regression, a fundamental statistical method for modeling relationships between variables, aims to find the best-fitting linear function to predict an outcome based on input features. Current research focuses on extending linear regression to handle complex scenarios, including high-dimensional data, heavy-tailed noise, and shuffled or missing data, often employing techniques like spectral matching, robust estimation methods, and regularized regression with various penalty functions (e.g., L1, L2, L∞). These advancements enhance the robustness and applicability of linear regression across diverse fields, from image registration and medical diagnosis to improving the efficiency and interpretability of machine learning models.