# CausalX: Causal Explanations and Block Multilinear Factor Analysis

arXiv: https://arxiv.org/abs/2102.12853 · HTML: https://mlsanity.com/paper/2102.12853/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 50 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 5 of 5)

- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Compositional Hierarchical Tensor Factorization: Representing Hierarchical Intrinsic and Extrinsic Causal Factors](https://mlsanity.com/paper/1911.04180/) (2019)

## Built on by (most cited first, 3 of 3)

- [Eigenspace Restructuring: a Principle of Space and Frequency in Neural Networks](https://mlsanity.com/paper/2112.05611/) (2021)
- [Causal Deep Learning](https://mlsanity.com/paper/2301.00314/) (2023)
- [Deepfake Representation with Multilinear Regression](https://mlsanity.com/paper/2108.06702/) (2021)

## Abstract (arXiv)

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.