Mixtures of Gaussian process experts is a class of models that can
simultaneously address two of the key limitations inherent in standard Gaussian
processes: scalability and predictive performance. In particular, models that
use Dirichlet processes as gating functions permit straightforward
interpretation and automatic selection of the number of experts in a mixture.
While the existing models are intuitive and capable of capturing
non-stationarity, multi-modality and heteroskedasticity, the simplicity of
their gating functions may limit the predictive performance when applied to
complex data-generating processes. Capitalising on the recent advancement in
the dependent Dirichlet processes literature, we propose a new mixture model of
Gaussian process experts based on kernel stick-breaking processes. Our model
maintains the intuitive appeal yet improve the performance of the existing
models. To make it practical, we design a sampler for posterior computation
based on the slice sampling. The model behaviour and improved predictive
performance are demonstrated in experiments using six datasets.

提出了一个基于核棍强过程的高斯过程专家混合模型，具有直观吸引力和改进的预测性能，可通过基于切片采样的后验计算器进行实际操作。

基于核棒法的高斯过程专家混合模型

Mixtures of Gaussian process experts based on kernel stick-breaking  processes

Bayesian models are a powerful tool for studying complex data, allowing the
analyst to encode rich hierarchical dependencies and leverage prior
information. Most importantly, they facilitate a complete characterization of
uncertainty through the posterior distribution. Practical posterior computation
is commonly performed via MCMC, which can be computationally infeasible for
high dimensional models with many observations. In this article we discuss the
potential to improve posterior computation using ideas from machine learning.
Concrete future directions are explored in vignettes on normalizing flows,
Bayesian coresets, distributed Bayesian inference, and variational inference.

概述：本文使用贝叶斯模型解决了复杂数据的建模问题，提出了通过机器学习的方法来改善后验计算的潜力，并探讨了正则化流、贝叶斯核平衡、分布式贝叶斯推理和变分推理等未来的具体发展方向。

机器学习与贝叶斯计算的未来

Machine Learning and the Future of Bayesian Computation

Penalized regression methods, such as $L_1$ regularization, are routinely
used in high-dimensional applications, and there is a rich literature on
optimality properties under sparsity assumptions. In the Bayesian paradigm,
sparsity is routinely induced through two-component mixture priors having a
probability mass at zero, but such priors encounter daunting computational
problems in high dimensions. This has motivated an amazing variety of
continuous shrinkage priors, which can be expressed as global-local scale
mixtures of Gaussians, facilitating computation. In sharp contrast to the
frequentist literature, little is known about the properties of such priors and
the convergence and concentration of the corresponding posterior distribution.
In this article, we propose a new class of Dirichlet--Laplace (DL) priors,
which possess optimal posterior concentration and lead to efficient posterior
computation exploiting results from normalized random measure theory. Finite
sample performance of Dirichlet--Laplace priors relative to alternatives is
assessed in simulated and real data examples.

通过引入一类新的 Dirichlet-Laplace 先验，文章探讨在 Bayesian 范例下连续收缩先验的特点及性质，并对使用该先验进行的后验计算进行了评估。