What is representer theorem?

The representer theorem is a key result in machine learning and optimization theory. It states that under certain conditions, the solution to a regularized empirical risk minimization problem can be represented in terms of the training data points.

In other words, instead of optimizing over the entire input space, the solution is determined by a linear combination of the training data points. This reduces the computational complexity of the optimization problem and makes it easier to interpret the final model.

The representer theorem is particularly useful in the context of regularization techniques such as ridge regression and support vector machines, where a penalty term is added to the loss function to prevent overfitting. By providing a concise and data-driven representation of the solution, the representer theorem helps in understanding and analyzing the learned model.

Overall, the representer theorem is a powerful tool in machine learning theory that provides insights into the structure of the solutions to optimization problems and allows for efficient and interpretable model learning.