Technical appendix to "Adaptive estimation of stationary Gaussian fields"

Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior of the resulting estimator is studied. The results depend on the richness of the class of functions. Both sieve estimation and global estimation are considered. Our results apply, in particular, to estimation under shape constraints. As an example, autoregressive model fitting with a monotonic variance function is discussed in detail, including algorithmic …

从平均场稳态分布中采样

Sampling from the Mean-Field Stationary Distribution

本文通过解耦有限粒子近似与对数凹采样，提出从平均场SDE稳态分布采样的新方法，并建立关于粒子数一致的对数Sobolev不等式，改进了平均场情形下两层神经网络优化等任务的保证。

李群及其齐性空间上的平稳核与高斯过程 II：非紧对称空间

Stationary Kernels and Gaussian Processes on Lie Groups and their Homogeneous Spaces II: non-compact symmetric spaces

本研究针对非紧对称空间，开发了构建平稳高斯过程的实用技术，可实现协方差核计算与先验后验采样，让非欧高斯过程模型适配标准软件的计算方法，便于从业者使用。