We focus on a stochastic learning model where the learner observes a finite
set of training examples and the output of the learning process is a
data-dependent distribution over a space of hypotheses. The learned
data-dependent distribution is then used to make randomized predictions, and
the high-level theme addressed here is guaranteeing the quality of predictions
on examples that were not seen during training, i.e. generalization. In this
setting the unknown quantity of interest is the expected risk of the
data-dependent randomized predictor, for which upper bounds can be derived via
a PAC-Bayes analysis, leading to PAC-Bayes bounds.
Specifically, we present a basic PAC-Bayes inequality for stochastic kernels,
from which one may derive extensions of various known PAC-Bayes bounds as well
as novel bounds. We clarify the role of the requirements of fixed 'data-free'
priors, bounded losses, and i.i.d. data. We highlight that those requirements
were used to upper-bound an exponential moment term, while the basic PAC-Bayes
theorem remains valid without those restrictions. We present three bounds that
illustrate the use of data-dependent priors, including one for the unbounded
square loss.

该研究探讨了基于数据相关分布的随机预测模型在训练后的泛化能力以及基于 PAC-Bayes 分析的上界推导方法，同时研究了使用数据相关先验分布的应用，包括针对无界方差的损失函数的一种新颖的边界推导方法。