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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Optimal score estimation via empirical Bayes smoothing
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If you have a question about this talk, please contact nobody. DMLW01 - International workshop on diffusions in machine learning: foundations, generative models, and optimisation We study the problem of estimating the score function of an unknown probability distribution $\rho$ from $n$ independent and identically distributed observations in $d$ dimensions. Assuming that $\rho$ is subgaussian and has a Lipschitz-continuous score function $s$, we establish the optimal rate of $\tilde \Theta(n{-\frac{2}{d+4}})$ for this estimation problem under the loss function $\|\hat s – s\|2_{L2(\rho*)}$ that is commonly used in the score matching literature, highlighting the curse of dimensionality where sample complexity for accurate score estimation grows exponentially with the dimension $d$. Leveraging key insights in empirical Bayes theory as well as a new convergence rate of smoothed empirical distribution in Hellinger distance, we show that a regularized score estimator based on a Gaussian kernel attains this rate, shown optimal by a matching minimax lower bound. We also discuss the implication of our theory on the sample complexity of score-based generative models. Joint work with Yihong Wu and Kaylee Yang. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:
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