The d-separation criterion in Categorical Probability

• URL: http://arxiv.org/abs/2207.05740v1
• Date: Tue, 12 Jul 2022 17:58:31 GMT
• Title: The d-separation criterion in Categorical Probability
• Authors: Tobias Fritz, Andreas Klingler
• Abstract summary: The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. This work introduces a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability theory by introducing a categorical definition of causal models, a categorical notion of d-separation, and proving an abstract version of the d-separation criterion. This approach has two main benefits. First, categorical d-separation is a very intuitive criterion based on topological connectedness. Second, our results apply in measure-theoretic probability (with standard Borel spaces), and therefore provide a clean proof of the equivalence of local and global Markov properties with causal compatibility for continuous and mixed variables.

Related papers

• A General Causal Inference Framework for Cross-Sectional Observational Data [0.4972323953932129]
  General Causal Inference (GCI) framework specifically designed for cross-sectional observational data. This paper proposes a GCI framework specifically designed for cross-sectional observational data.
  arXiv  Detail & Related papers  (2024-04-28T14:26:27Z)
• Generalized Criterion for Identifiability of Additive Noise Models Using Majorization [7.448620208767376]
  We introduce a novel identifiability criterion for directed acyclic graph (DAG) models. We demonstrate that this criterion extends and generalizes existing identifiability criteria. We present a new algorithm for learning a topological ordering of variables.
  arXiv  Detail & Related papers  (2024-04-08T02:18:57Z)
• Identifiable Latent Neural Causal Models [82.14087963690561]
  Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. We determine the types of distribution shifts that do contribute to the identifiability of causal representations. We translate our findings into a practical algorithm, allowing for the acquisition of reliable latent causal representations.
  arXiv  Detail & Related papers  (2024-03-23T04:13:55Z)
• Synergistic eigenanalysis of covariance and Hessian matrices for enhanced binary classification [72.77513633290056]
  We present a novel approach that combines the eigenanalysis of a covariance matrix evaluated on a training set with a Hessian matrix evaluated on a deep learning model. Our method captures intricate patterns and relationships, enhancing classification performance.
  arXiv  Detail & Related papers  (2024-02-14T16:10:42Z)
• String Diagrams with Factorized Densities [0.0]
  Both probabilistic programs and causal models define a joint probability density over a set of random variables. This work builds on work on Markov categories of probabilistic mappings to define a category whose morphisms combine a joint density, factorized over each sample space, with a deterministic mapping from samples to return values.
  arXiv  Detail & Related papers  (2023-05-04T02:30:44Z)
• Identifying Weight-Variant Latent Causal Models [82.14087963690561]
  We find that transitivity acts as a key role in impeding the identifiability of latent causal representations. Under some mild assumptions, we can show that the latent causal representations can be identified up to trivial permutation and scaling. We propose a novel method, termed Structural caUsAl Variational autoEncoder, which directly learns latent causal representations and causal relationships among them.
  arXiv  Detail & Related papers  (2022-08-30T11:12:59Z)
• Bounding Counterfactuals under Selection Bias [60.55840896782637]
  We propose a first algorithm to address both identifiable and unidentifiable queries. We prove that, in spite of the missingness induced by the selection bias, the likelihood of the available data is unimodal.
  arXiv  Detail & Related papers  (2022-07-26T10:33:10Z)
• Typing assumptions improve identification in causal discovery [123.06886784834471]
  Causal discovery from observational data is a challenging task to which an exact solution cannot always be identified. We propose a new set of assumptions that constrain possible causal relationships based on the nature of the variables.
  arXiv  Detail & Related papers  (2021-07-22T14:23:08Z)
• A Unified Joint Maximum Mean Discrepancy for Domain Adaptation [73.44809425486767]
  This paper theoretically derives a unified form of JMMD that is easy to optimize. From the revealed unified JMMD, we illustrate that JMMD degrades the feature-label dependence that benefits to classification. We propose a novel MMD matrix to promote the dependence, and devise a novel label kernel that is robust to label distribution shift.
  arXiv  Detail & Related papers  (2021-01-25T09:46:14Z)
• Conditional canonical correlation estimation based on covariates with random forests [0.0]
  We propose a new method called Random Forest with Canonical Correlation Analysis (RFCCA) to estimate the conditional canonical correlations between two sets of variables. The proposed method and the global significance test is evaluated through simulation studies that show it provides accurate canonical correlation estimations and well-controlled Type-1 error.
  arXiv  Detail & Related papers  (2020-11-23T17:09:46Z)
• Predictive Value Generalization Bounds [27.434419027831044]
  We study a bi-criterion framework for assessing scoring functions in the context of binary classification. We study properties of scoring functions with respect to predictive values by deriving new distribution-free large deviation and uniform convergence bounds.
  arXiv  Detail & Related papers  (2020-07-09T21:23:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.