Density Estimation in Infinite Dimensional Exponential Families

1 code implementation • 12 Dec 2013 • Bharath Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Aapo Hyvärinen, Revant Kumar

When $p_0\in\mathcal{P}$, we show that the proposed estimator is consistent, and provide a convergence rate of $n^{-\min\left\{\frac{2}{3},\frac{2\beta+1}{2\beta+2}\right\}}$ in Fisher divergence under the smoothness assumption that $\log p_0\in\mathcal{R}(C^\beta)$ for some $\beta\ge 0$, where $C$ is a certain Hilbert-Schmidt operator on $H$ and $\mathcal{R}(C^\beta)$ denotes the image of $C^\beta$.

Density Estimation