CausalX：因果解释与块多线性因子分析
CausalX: Causal Explanations and Block Multilinear Factor Analysis
AI总结：
本文提出CausalX框架，通过统一多线性模型和分层块多线性因子分解（M-mode Block SVD）解耦因果因子，并引入增量计算方法提升效率，使物体识别对遮挡更具鲁棒性。
摘要：
遵循“没有操纵（处理、干预）就没有因果关系”这一格言，因果数据分析通过因果因子的变化来表示观测数据中的变化。当由于当前技术限制或伦理考量，因果因子在现实世界中无法进行主动操纵时，反事实方法会对数据生成模型进行干预。在物体表示或活动（时间物体）表示的情况下，改变物体各部分通常是不可行的，无论它们是空间和/或时间上的。多线性代数作为高阶张量的代数，是解耦数据生成因果因子的合适且透明的框架。在多线性框架中学习基于部分的内在因果因子表示，需要对基于部分的多线性模型应用一系列干预。我们提出了一个整体与部分的统一多线性模型。我们推导出一种分层块多线性因子分解方法，即M-mode Block SVD，该方法通过在整个物体层级上同时进行优化，计算出因果因子的解耦表示。考虑到计算效率，我们引入了一种增量自底向上的计算替代方案，即Incremental M-mode Block SVD，它采用较低层级的抽象（部分表示）来表示较高层级的抽象（父级整体）。当数据增量可用时，这种增量计算方法也可用于更新因果模型参数。由此产生的物体表示是内在因果因子表示的可解释组合选择，它与物体整体和部分的递归层级相关，从而使物体识别对遮挡具有鲁棒性并减少了训练数据需求。
英文摘要：
By adhering to the dictum, "No causation without manipulation (treatment, intervention)", cause and effect data analysis represents changes in observed data in terms of changes in the causal factors. When causal factors are not amenable for active manipulation in the real world due to current technological limitations or ethical considerations, a counterfactual approach performs an intervention on the model of data formation. In the case of object representation or activity (temporal object) representation, varying object parts is generally unfeasible whether they be spatial and/or temporal. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for disentangling the causal factors of data formation. Learning a part-based intrinsic causal factor representations in a multilinear framework requires applying a set of interventions on a part-based multilinear model. We propose a unified multilinear model of wholes and parts. We derive a hierarchical block multilinear factorization, the M-mode Block SVD, that computes a disentangled representation of the causal factors by optimizing simultaneously across the entire object hierarchy. Given computational efficiency considerations, we introduce an incremental bottom-up computational alternative, the Incremental M-mode Block SVD, that employs the lower-level abstractions, the part representations, to represent the higher level of abstractions, the parent wholes. This incremental computational approach may also be employed to update the causal model parameters when data becomes available incrementally. The resulting object representation is an interpretable combinatorial choice of intrinsic causal factor representations related to an object's recursive hierarchy of wholes and parts that renders object recognition robust to occlusion and reduces training data requirements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
