Considering the worst-case scenario, junction tree algorithm remains the most efficient and general solution for exact MAP inference on discrete graphical models. Unfortunately, its main tractability assumption requires the treewidth of a corresponding MRF to be bounded strongly limiting the range of admissible applications. In fact, many practical problems in the area of structured prediction require modelling of global dependencies by either directly introducing global factors or enforcing global constraints on the prediction variables. This, however, always results in a fully-connected graph making exact inference by means of this algorithm intractable. Nevertheless, depending on the structure of the global factors, we can further relax the conditions for an efficient inference. In this paper we reformulate the work in [1] and present a better way to establish the theory also extending the set of handleable problem instances for free - since it requires only a simple modification of the originally presented algorithm. To demonstrate that this extension is not of a purely theoretical interest we identify one further use case in the context of generalisation bounds for structured learning which cannot be handled by the previous formulation. Finally, we accordingly adjust the theoretical guarantees that the modified algorithm always finds an optimal solution in polynomial time.

翻译：考虑到最坏的情况,接合树算法仍然是离散图形模型精确MAP推断的最有效和一般的解决办法。不幸的是,它的主要可移植性假设要求相应的MRF的树边严格地限制可受理申请的范围。事实上,结构化预测领域的许多实际问题要求通过直接引入全球因素或通过对预测变量施加全球限制来模拟全球依赖性。然而,这总是导致一个完全连通的图表,通过这种算法难以处理,得出准确的推论。然而,根据全球因素的结构,我们可以进一步放宽有效推断的条件。在本文中,我们重新拟订[1]的工作,并提供一个更好的方法来建立理论,同时扩大可免费处理的一系列问题案例的范围,因为它只需要简单修改最初提出的算法。为了证明这一扩展不是纯粹的理论利益,我们确定一个在一般化界限的背景下进一步使用一个案例,以便进行结构化学习,而以前的措辞无法处理。最后,我们调整了理论保障,即修改的算法总是在聚氨时间找到最佳解决办法。