We address the problem of Bayesian structure learning for domains with
hundreds of variables by employing non-parametric bootstrap, recursively. We
propose a method that covers both model averaging and model selection in the
same framework. The proposed method deals with the main weakness of
constraint-based learning---sensitivity to errors in the independence
tests---by a novel way of combining bootstrap with constraint-based learning.
Essentially, we provide an algorithm for learning a tree, in which each node
represents a scored CPDAG for a subset of variables and the level of the node
corresponds to the maximal order of conditional independencies that are encoded
in the graph. As higher order independencies are tested in deeper recursive
calls, they benefit from more bootstrap samples, and therefore more resistant
to the curse-of-dimensionality. Moreover, the re-use of stable low order
independencies allows greater computational efficiency. We also provide an
algorithm for sampling CPDAGs efficiently from their posterior given the
learned tree. We empirically demonstrate that the proposed algorithm scales
well to hundreds of variables, and learns better MAP models and more reliable
causal relationships between variables, than other state-of-the-art-methods.

本研究提出了一种使用非参数 bootstrap 递归方法解决具有数百个变量的 Bayesian 结构学习问题的方法，该方法涵盖了模型平均和模型选择，并以一种新颖的方式将 bootstrap 与约束性学习相结合，以解决独立性检验中的错误敏感性问题，从而获得更好的 MAP 模型并建立更可靠的因果关系。

递归自助贝叶斯结构学习

Bayesian Structure Learning by Recursive Bootstrap

Constraint-based learning reduces the burden of collecting labels by having
users specify general properties of structured outputs, such as constraints
imposed by physical laws. We propose a novel framework for simultaneously
learning these constraints and using them for supervision, bypassing the
difficulty of using domain expertise to manually specify constraints. Learning
requires a black-box simulator of structured outputs, which generates valid
labels, but need not model their corresponding inputs or the input-label
relationship. At training time, we constrain the model to produce outputs that
cannot be distinguished from simulated labels by adversarial training.
Providing our framework with a small number of labeled inputs gives rise to a
new semi-supervised structured prediction model; we evaluate this model on
multiple tasks --- tracking, pose estimation and time series prediction --- and
find that it achieves high accuracy with only a small number of labeled inputs.
In some cases, no labels are required at all.

本研究提出了一种基于约束学习的半监督学习方法，利用黑盒模拟器生成未标记数据进行训练并通过对抗训练实现生成模型的训练，提高模型在多种任务上的表现。