This work establishes a novel link between the problem of PAC-learning high-dimensional graphical models and the task of (efficient) counting and sampling of graph structures, using an online learning framework. We observe that if we apply the exponentially weighted average (EWA) or randomized weighted majority (RWM) forecasters on a sequence of samples from a distribution P using the log loss function, the average regret incurred by the forecaster's predictions can be used to bound the expected KL divergence between P and the predictions. Known regret bounds for EWA and RWM then yield new sample complexity bounds for learning Bayes nets. Moreover, these algorithms can be made computationally efficient for several interesting classes of Bayes nets. Specifically, we give a new sample-optimal and polynomial time learning algorithm with respect to trees of unknown structure and the first polynomial sample and time algorithm for learning with respect to Bayes nets over a given chordal skeleton.

翻译：本工作建立了一个新颖的链接，将PAC学习高维图模型的问题与图结构（高效）计数和采样的任务联系起来，采用在线学习框架。我们观察到，如果对来自分布P的样本序列应用指数加权平均（EWA）或随机加权多数（RWM）预测器，并使用对数损失函数，则预测器预测产生的平均遗憾可用于界定P与预测之间期望的KL散度。EWA和RWM的已知遗憾界进而为学习贝叶斯网络提供了新的样本复杂度界。此外，对于若干有趣的贝叶斯网络类别，这些算法可以变得计算高效。具体来说，我们针对未知结构的树给出了一个新的样本最优且多项式时间的学习算法，并首次给出了针对给定弦骨架上的贝叶斯网络学习的多项式样本与时间算法。