We develop a category-theoretic criterion for determining the equivalence of causal models having different but homomorphic directed acyclic graphs over discrete variables. Following Jacobs et al. (2019), we define a causal model as a probabilistic interpretation of a causal string diagram, i.e., a functor from the ``syntactic'' category $\textsf{Syn}_G$ of graph $G$ to the category $\textsf{Stoch}$ of finite sets and stochastic matrices. The equivalence of causal models is then defined in terms of a natural transformation or isomorphism between two such functors, which we call a $Φ$-abstraction and $Φ$-equivalence, respectively. It is shown that when one model is a $Φ$-abstraction of another, the intervention calculus of the former can be consistently translated into that of the latter. We also identify the condition under which a model accommodates a $Φ$-abstraction, when transformations are deterministic.
University of Strathclyde（思克莱德大学）；University of Copenhagen（哥本哈根大学）
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and make predictions about the variables upon intervening on the system. Yet, it is difficult to formalise how we may change the underlying variables used to describe the system, say moving from fine-grained to coarse-grained variables. Here, we argue that compositionality is a desideratum for such model transformations and the associated errors: When abstracting…
Adobe Research（奥多比研究院）；University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）
We propose a layered hierarchical architecture called UCLA (Universal Causality Layered Architecture), which combines multiple levels of categorical abstraction for causal inference. At the top-most level, causal interventions are modeled combinatorially using a simplicial category of ordinal numbers. At the second layer, causal models are defined by a graph-type category. The non-random ``surgical" operations on causal structures, such as edge deletion, are captured using degeneracy and face operators from the simplicial layer above. The third categorical abstraction layer corresponds to the …
Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models
School of Management, University of Science and Technology of China（管理学院，中国科学技术大学）；School of Computer Science and Engineering, University of Science and Technology of China（计算机科学与工程学院，中国科学技术大学）
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Shiga University（滋贺大学）
Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than in linear cases. In this study, we focus on causal additive models in the presence of unobserved variables. Causal additive models exhibit structural equations that are additive in the variables and error terms. We take into account the presence of not only unobserved common causes but also unobserved intermediate variables. Our theoretical results show that…
College of Computer Science and Technology, Jilin University, Changchun, China（吉林大学计算机科学与技术学院）；School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu, China（西南财经大学计算机与人工智能学院）
Score-Based Causal Discovery of Latent Variable Causal Models
Carnegie Mellon University（卡内基梅隆大学）；University of California, San Diego（加州大学圣地亚哥分校）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
GfK SE（GfK公司）；AlgoBalance UG (limited liability)（AlgoBalance有限责任公司）
Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it is possible to solve that task. If X is causing Y, then it does not matter if we observe an effect in Y by observing changes in X or by intervening actively on X. This invariance principle creates a link between observational and interventional distributions in a higher dimensional probability space. We embed distributions that originate from samples of X and…
University of Technology Sydney（悉尼科技大学）；Curtin University（科廷大学）
Counterfactual fairness alleviates the discrimination between the model prediction toward an individual in the actual world (observational data) and that in counterfactual world (i.e., what if the individual belongs to other sensitive groups). The existing studies need to pre-define the structural causal model that captures the correlations among variables for counterfactual inference; however, the underlying causal model is usually unknown and difficult to be validated in real-world scenarios. Moreover, the misspecification of the causal model potentially leads to poor performance in model pr…
University College London（伦敦大学学院）；Nanyang Technological University（南洋理工大学）；Noah’s Ark Lab, Huawei（华为诺亚方舟实验室）；Renmin University of China（中国人民大学）
It is evidence that representation learning can improve model's performance over multiple downstream tasks in many real-world scenarios, such as image classification and recommender systems. Existing learning approaches rely on establishing the correlation (or its proxy) between features and the downstream task (labels), which typically results in a representation containing cause, effect and spurious correlated variables of the label. Its generalizability may deteriorate because of the unstability of the non-causal parts. In this paper, we propose to learn causal representation from observati…
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries leveraging the exposed. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a more general view on neural-causal models, revealing…
Seoul National University（首尔大学）；Adobe Research（Adobe研究院）
We propose an information-theoretic bias measurement technique through a causal interpretation of spurious correlation, which is effective to identify the feature-level algorithmic bias by taking advantage of conditional mutual information. Although several bias measurement methods have been proposed and widely investigated to achieve algorithmic fairness in various tasks such as face recognition, their accuracy- or logit-based metrics are susceptible to leading to trivial prediction score adjustment rather than fundamental bias reduction. Hence, we design a novel debiasing framework against t…
Radboud University（拉德堡德大学）；University College London（伦敦大学学院）
Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effec…
