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Do-calculus enables causal reasoning with latent variable models [article]

Sara Mohammad-Taheri and Robert Ness and Jeremy Zucker and Olga Vitek
2021 arXiv   pre-print
Despite this intuitive causal interpretation, a directed acyclic latent variable model trained on data is generally insufficient for causal reasoning, as the required model parameters may not be uniquely  ...  These include a machine learning model with multiple causes where there exists a set of latent confounders and a mediator between the causes and the outcome variable, a study where the identifiable causal  ...  Support for Jeremy Zucker was provided by the PNNL Laboratorydirected R&D Data-Model Convergence Initiative and the Mathematics for Artificial Reasoning Systems Initiative.  ... 
arXiv:2102.06626v1 fatcat:k23q4j3rungmxg35eru4e2odue

Replacing the do-calculus with Bayes rule [article]

Finnian Lattimore, David Rohde
2021 arXiv   pre-print
The invariance assumptions underlying causal graphical models can be encoded in ordinary Probabilistic graphical models, allowing causal estimation with Bayesian statistics, equivalent to the do calculus  ...  This has lead to a dichotomy between advocates of causal graphical modeling and the do calculus, and researchers applying Bayesian methods.  ...  Causal Graphical Models And The Do-Calculus A causal graphical model (CGM) is a Probabilistic graphical model, with the additional assumption that a link X → Y means X causes Y .  ... 
arXiv:1906.07125v3 fatcat:kegohngqnzafjie335kgmpm2ai

Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias [article]

Patrick Forré, Joris M. Mooij
2019 arXiv   pre-print
We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal models  ...  Together, our results thus enable causal reasoning in the presence of cycles, latent confounders and selection bias.  ...  All the causal reasoning rules derived so far can thus also be applied to reason about counterfactuals.  ... 
arXiv:1901.00433v2 fatcat:73vbmdjkabaorj7o7bunptllpq

Identifying Causal Effects via Context-specific Independence Relations [article]

Santtu Tikka, Antti Hyttinen, Juha Karvanen
2020 arXiv   pre-print
The approach is provably sound and it includes standard do-calculus as a special case.  ...  Motivated by this, we design a calculus and an automated search procedure for identifying causal effects in the presence of CSIs.  ...  Acknowledgments ST was supported by Academy of Finland grant 311877 (Decision analytics utilizing causal models and multiobjective optimization). AH was supported by Academy of Finland grant 295673.  ... 
arXiv:2009.09768v1 fatcat:pgbw4d7j5zartglujyyov3etcq

Multi-task Causal Learning with Gaussian Processes [article]

Virginia Aglietti, Theodoros Damoulas, Mauricio Álvarez, Javier González
2020 arXiv   pre-print
We propose the first multi-task causal Gaussian process (GP) model, which we call DAG-GP, that allows for information sharing across continuous interventions and across experiments on different variables  ...  This paper studies the problem of learning the correlation structure of a set of intervention functions defined on the directed acyclic graph (DAG) of a causal model.  ...  Characterization of the latent structure in a DAG Next results provide a theoretical foundation for the multi-task causal GP model introduced later.  ... 
arXiv:2009.12821v1 fatcat:ay7trlahbfa3rlf26iu7oqyqvm

Bayesian network structure learning with causal effects in the presence of latent variables [article]

Kiattikun Chobtham, Anthony C. Constantinou
2020 arXiv   pre-print
Latent variables may lead to spurious relationships that can be misinterpreted as causal relationships. In Bayesian Networks (BNs), this challenge is known as learning under causal insufficiency.  ...  The score-based process incorporates Pearl s do-calculus to measure causal effects and orientate edges that would otherwise remain undirected, under the assumption the BN is a linear Structure Equation  ...  While known latent variables pose less of a problem in knowledge-based BNs, where methods exist that enable users to model latent variables not present in the data under the assumption the statistical  ... 
arXiv:2005.14381v2 fatcat:ttag3mx5krar7lu2tam5umi6sq

A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects [article]

Daniel Malinsky and Ilya Shpitser and Thomas Richardson
2019 arXiv   pre-print
Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator.  ...  in causal inference.  ...  Graphical Models With Hidden Variables We also consider causal models where some variables are unmeasured (a.k.a. "latent" or "hidden" variables).  ... 
arXiv:1903.03662v1 fatcat:wfcd6o36ojahle4u2hmqbgthl4

A Simulation-Based Test of Identifiability for Bayesian Causal Inference [article]

Sam Witty, David Jensen, Vikash Mansinghka
2021 arXiv   pre-print
Although the do-calculus is sound and complete given a causal graph, many practical assumptions cannot be expressed in terms of graph structure alone, such as the assumptions required by instrumental variable  ...  This paper introduces a procedure for testing the identifiability of Bayesian models for causal inference.  ...  In Section 5 we demonstrated that SBI correctly determines identifiability empirically with seven well-studied causal designs, three of which are outof-scope for the do-calculus.  ... 
arXiv:2102.11761v1 fatcat:k5qyprfkerft3k4znd22hcdlfq

Interventions and Counterfactuals in Tractable Probabilistic Models: Limitations of Contemporary Transformations [article]

Ioannis Papantonis, Vaishak Belle
2020 arXiv   pre-print
We show that when transforming SPNs to a causal graph interventional reasoning reduces to computing marginal distributions; in other words, only trivial causal reasoning is possible.  ...  We first provide an algorithm for constructing a causal graph from a PSDD, which introduces augmented variables.  ...  For example, given our last observation about latent factors, are there tractable models that enable causal graphs with lie somewhere on the middle ground wrt causal graphs?  ... 
arXiv:2001.10905v1 fatcat:k5eeedjcffc7pgf65v7jptndzq

Contracts in distributed systems

Massimo Bartoletti, Emilio Tuosto, Roberto Zunino
2011 Electronic Proceedings in Theoretical Computer Science  
With the help of a few examples, we discuss the primitives of our calculus, as well as some possible variants.  ...  We present two instances of our calculus, by modelling contracts as (i) processes in a variant of CCS, and (ii) as formulae in a logic.  ...  A valid agreement has to instantiate with a minimal substitution σ all the variables appearing in the latent contracts in K as well as the session variable x; the latter, together with any other session  ... 
doi:10.4204/eptcs.59.11 fatcat:rsag4emr4bcmlhythycgfvvz2a

Bayesian causal inference via probabilistic program synthesis [article]

Sam Witty, Alexander Lew, David Jensen, Vikash Mansinghka
2019 arXiv   pre-print
Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions.  ...  This approach also enables the use of general-purpose inference machinery for probabilistic programs to infer probable causal structures and parameters from data.  ...  Priors on Causal Models To compute the posterior distribution over the two candidate causal models, we first specify a prior distribution over a set of global latent variables.  ... 
arXiv:1910.14124v1 fatcat:ywbfuyq4cjfzhjrpvqf4tqjhbi

Counterfactual Adversarial Learning with Representation Interpolation [article]

Wei Wang, Boxin Wang, Ning Shi, Jinfeng Li, Bingyu Zhu, Xiangyu Liu, Rong Zhang
2021 arXiv   pre-print
Deep learning models exhibit a preference for statistical fitting over logical reasoning.  ...  (CRM) on each original-counterfactual pair to adjust sample-wise loss weight dynamically, which encourages the model to explore the true causal effect.  ...  CMIX Do-calculus is a statistical tool derived from SCM for causal effect adjustments.  ... 
arXiv:2109.04746v1 fatcat:56b6uyiytrdjrfrdyaujspgmgq

Estimation of Causal Effects in the Presence of Unobserved Confounding in the Alzheimer's Continuum [article]

Sebastian Pölsterl, Christian Wachinger
2021 arXiv   pre-print
To alleviate this requirement, we leverage the dependencies among multiple causes by deriving a substitute confounder via a probabilistic latent factor model.  ...  In our theoretical analysis, we prove that using the substitute confounder enables identifiability of the causal effect of neuroanatomy on cognition.  ...  given by the graph in fig. 1 , the one in (8) due to rule 3 of do calculus, equalities (9) and (10) are due to rule 2 of do calculus, and (11) is due to ADAS ⊥ ⊥ p-Tau | x S , xS , age, z.  ... 
arXiv:2006.13135v3 fatcat:5w36a7iodzczbo5xhzkzrmeq5y

Eight Myths About Causality and Structural Equation Models [chapter]

Kenneth A. Bollen, Judea Pearl
2013 Handbooks of Sociology and Social Research  
This permits us to replace the latent variables with the observed variables and our latent variable model becomes the well-known simultaneous equation model of i i i i i        x y B y  (4) We  ...  A second reason that the models resulting from causal assumption are valuable is that they enable an estimate of the coefficients (as well as variances, and covariances) that are important for guiding  ... 
doi:10.1007/978-94-007-6094-3_15 fatcat:dcfeewocdjcpji3fyxtd4rs3yy

Causal Inference in medicine and in health policy, a summary [article]

Wenhao Zhang, Ramin Ramezani, Arash Naeim
2022 arXiv   pre-print
Moreover, we will demonstrate the applications of causal inference in tackling some common machine learning issues such as missing data and model transportability.  ...  Big data has enabled us to carry out countless prediction tasks in conjunction with machine learning, such as identifying high risk patients suffering from a certain disease and taking preventable measures  ...  with do-calculus In this section, we primarily introduce 3 fundamental components of causal reasoning: structural causal model (SCM), directed acyclic graphs (DAG), and intervention with do-calculus.  ... 
arXiv:2105.04655v4 fatcat:x5ud7t4tdbho7jqbqgwxsu4rme
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