Optimal score function estimation via derivatives constraints (opens in new tab)

We consider the problem of score function estimation via empirical risk minimization. We first start with the question of inferring the score function of a probability measure $\mu$ with density on the flat torus from a sample of distribution $\mu$. We show that constraining the hypothesis space to a Sobolev ball is sufficient to prevent overfitting and obtaining minimax estimation rates. We then consider the problem of score function estimation...