Deep Energy Estimator Networks
This addresses the challenge of density estimation in high-dimensional settings, which is a fundamental problem in statistical learning, but the approach appears incremental as it builds on existing score matching methods.
The paper tackled the problem of density estimation for complex high-dimensional data by proposing a deep energy estimator network (DEEN) built on score matching, which learns the energy and score function, and demonstrated utility in single-step denoising experiments for synthetic and high-dimensional data.
Density estimation is a fundamental problem in statistical learning. This problem is especially challenging for complex high-dimensional data due to the curse of dimensionality. A promising solution to this problem is given here in an inference-free hierarchical framework that is built on score matching. We revisit the Bayesian interpretation of the score function and the Parzen score matching, and construct a multilayer perceptron with a scalable objective for learning the energy (i.e. the unnormalized log-density), which is then optimized with stochastic gradient descent. In addition, the resulting deep energy estimator network (DEEN) is designed as products of experts. We present the utility of DEEN in learning the energy, the score function, and in single-step denoising experiments for synthetic and high-dimensional data. We also diagnose stability problems in the direct estimation of the score function that had been observed for denoising autoencoders.