Single Index Model

Single-index models represent a class of regression problems where the response variable depends on a linear projection of the input features through a potentially unknown non-linear function. Current research focuses on developing efficient algorithms, including those based on neural networks and gradient descent methods, to learn this projection and the link function, often addressing challenges like high dimensionality, agnostic learning settings (where the link function is unknown and potentially noisy), and computational complexity. These models are valuable for their interpretability and ability to capture non-linear relationships in high-dimensional data, finding applications in diverse fields such as scientific machine learning and signal processing. Recent advancements aim to improve sample efficiency and robustness, bridging the gap between statistical and computational limits.