scholarly journals The Inflation Technique for Causal Inference with Latent Variables

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Elie Wolfe ◽  
Robert W. Spekkens ◽  
Tobias Fritz
Keyword(s):  
Probability Distribution ◽  
Causal Inference ◽  
Latent Variables ◽  
Causal Model ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Difficult Case ◽  
Common Causes ◽  
Multiple Copies ◽  
New Inequalities

AbstractThe problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce the inflation technique for tackling this problem. An inflation of a causal structure is a new causal structure that can contain multiple copies of each of the original variables, but where the ancestry of each copy mirrors that of the original. To every distribution of the observed variables that is compatible with the original causal structure, we assign a family of marginal distributions on certain subsets of the copies that are compatible with the inflated causal structure. It follows that compatibility constraints for the inflation can be translated into compatibility constraints for the original causal structure. Even if the constraints at the level of inflation are weak, such as observable statistical independences implied by disjoint causal ancestry, the translated constraints can be strong. We apply this method to derive new inequalities whose violation by a distribution witnesses that distribution’s incompatibility with the causal structure (of which Bell inequalities and Pearl’s instrumental inequality are prominent examples). We describe an algorithm for deriving all such inequalities for the original causal structure that follow from ancestral independences in the inflation. For three observed binary variables with pairwise common causes, it yields inequalities that are stronger in at least some aspects than those obtainable by existing methods. We also describe an algorithm that derives a weaker set of inequalities but is more efficient. Finally, we discuss which inflations are such that the inequalities one obtains from them remain valid even for quantum (and post-quantum) generalizations of the notion of a causal model.

scholarly journals Experimental Connection between the Instrumental and Bell Inequalities

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 27
Author(s):  
Iris Agresti ◽  
Gonzalo Carvacho ◽  
Davide Poderini ◽  
Leandro Aolita ◽  
Rafael Chaves ◽  
...  
Keyword(s):  
Causal Model ◽  
Probability Distributions ◽  
Causal Structure ◽  
Joint Probability ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Causal Processes ◽  
Chsh Inequality ◽  
Joint Probability Distributions ◽  
Selection Of

An investigated process can be studied in terms of the causal relations among the involved variables, representing it as a causal model. Some causal models are particularly relevant, since they can be tested through mathematical constraints between the joint probability distributions of the observables. This is a valuable tool because, if some data violates the constraints of a causal model, the implication is that the observed statistics is not compatible with that causal structure. Strikingly, when non-classical correlations come to play, a discrepancy between classical and quantum causal predictions can arise, producing a quantum violation of the classical causal constraints. The simplestscenario admitting such quantum violation is given by the instrumental causal processes. Here, we experimentally violate an instrumental test on a photonic platform and show how the quantum correlations violating the CHSH inequality can be mapped into correlations violating an instrumental test, despite the different forms of non-locality they display. Indeed, starting from a Bell-like scenario, we recover the violation of the instrumental scenario through a map between the two behaviours, which includes a post-selection of data and then we test an alternative way to violate the CHSH inequality, adopting the instrumental process platform.

scholarly journals The Role of Instrumental Variables in Causal Inference Based on Independence of Cause and Mechanism

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 928
Author(s):  
Nataliya Sokolovska ◽  
Pierre-Henri Wuillemin
Keyword(s):  
Causal Inference ◽  
Instrumental Variables ◽  
Latent Variables ◽  
Conditional Independence ◽  
State Of The Art ◽  
Simulated Data ◽  
Research Directions ◽  
Common Causes ◽  
Inference Methods

Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.

scholarly journals Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 280 ◽  
Author(s):  
Elie Wolfe ◽  
David Schmid ◽  
Ana Belén Sainz ◽  
Ravi Kunjwal ◽  
Robert W. Spekkens
Keyword(s):  
Lower Bound ◽  
Causal Model ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Resource Theory ◽  
Theoretic Approach ◽  
Binary Outcome ◽  
Common Cause ◽  
Complete Set ◽  
Probabilistic Processes

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them "common-cause boxes". We define the distinction between classical and nonclassical resources in terms of whether or not a classical causal model can explain the correlations. One can then quantify the relative nonclassicality of resources by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. We moreover define two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and use these to reveal various properties of the pre-order of resources, including a lower bound on the cardinality of any complete set of monotones. In particular, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. Finally, we show that the continuous set of convexly extremal quantumly realizable correlations are all at the top of the pre-order of quantumly realizable correlations. In addition to providing new insights on Bell nonclassicality, our work also sets the stage for quantifying nonclassicality in more general causal networks.

scholarly journals Cyclic quantum causal models

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jonathan Barrett ◽  
Robin Lorenz ◽  
Ognyan Oreshkov
Keyword(s):  
Causal Reasoning ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Causal Models ◽  
Causal Order ◽  
Quantum Processes ◽  
Causal Explanations ◽  
Causal Structures

AbstractCausal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

scholarly journals The Inflation Technique Completely Solves the Causal Compatibility Problem

2020 ◽  
Vol 8 (1) ◽  
pp. 70-91 ◽  
Author(s):  
Miguel Navascués ◽  
Elie Wolfe
Keyword(s):  
Linear Programming ◽  
Latent Variables ◽  
Causal Explanation ◽  
Causal Structure ◽  
Categorical Variables ◽  
False Negatives ◽  
The Given ◽  
Causal Structures ◽  
Compatibility Question ◽  
Structure Graph

AbstractThe causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020, one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the nth-order inflation test must be $\begin{array}{} \displaystyle {O}{\left(n^{{{-}{1}}/{2}}\right)} \end{array}$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test.

scholarly journals Attention controls multisensory perception via 2 distinct mechanisms at different levels of the cortical hierarchy

PLoS Biology ◽  
2021 ◽  
Vol 19 (11) ◽  
pp. e3001465
Author(s):  
Ambra Ferrari ◽  
Uta Noppeney
Keyword(s):  
Causal Inference ◽  
Causal Structure ◽  
Multisensory Perception ◽  
Spatial Representations ◽  
Perceptual Inference ◽  
Sensory Signals ◽  
Cortical Hierarchy ◽  
Parietal Cortices ◽  
The Brain ◽  
Different Levels

To form a percept of the multisensory world, the brain needs to integrate signals from common sources weighted by their reliabilities and segregate those from independent sources. Previously, we have shown that anterior parietal cortices combine sensory signals into representations that take into account the signals’ causal structure (i.e., common versus independent sources) and their sensory reliabilities as predicted by Bayesian causal inference. The current study asks to what extent and how attentional mechanisms can actively control how sensory signals are combined for perceptual inference. In a pre- and postcueing paradigm, we presented observers with audiovisual signals at variable spatial disparities. Observers were precued to attend to auditory or visual modalities prior to stimulus presentation and postcued to report their perceived auditory or visual location. Combining psychophysics, functional magnetic resonance imaging (fMRI), and Bayesian modelling, we demonstrate that the brain moulds multisensory inference via 2 distinct mechanisms. Prestimulus attention to vision enhances the reliability and influence of visual inputs on spatial representations in visual and posterior parietal cortices. Poststimulus report determines how parietal cortices flexibly combine sensory estimates into spatial representations consistent with Bayesian causal inference. Our results show that distinct neural mechanisms control how signals are combined for perceptual inference at different levels of the cortical hierarchy.

scholarly journals Invariant Causal Prediction for Nonlinear Models

2018 ◽  
Vol 6 (2) ◽  
Author(s):  
Christina Heinze-Deml ◽  
Jonas Peters ◽  
Nicolai Meinshausen
Keyword(s):  
Linear Models ◽  
Causal Model ◽  
Nonlinear Models ◽  
Causal Structure ◽  
Nonparametric Tests ◽  
Population Projections ◽  
World Population ◽  
Residual Distribution ◽  
Using Data

AbstractAn important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system’s underlying causal structure. To this end, Invariant Causal Prediction (ICP) [1] has been proposed which learns a causal model exploiting the invariance of causal relations using data from different environments. When considering linear models, the implementation of ICP is relatively straightforward. However, the nonlinear case is more challenging due to the difficulty of performing nonparametric tests for conditional independence.In this work, we present and evaluate an array of methods for nonlinear and nonparametric versions of ICP for learning the causal parents of given target variables. We find that an approach which first fits a nonlinear model with data pooled over all environments and then tests for differences between the residual distributions across environments is quite robust across a large variety of simulation settings. We call this procedure “invariant residual distribution test”. In general, we observe that the performance of all approaches is critically dependent on the true (unknown) causal structure and it becomes challenging to achieve high power if the parental set includes more than two variables.As a real-world example, we consider fertility rate modeling which is central to world population projections. We explore predicting the effect of hypothetical interventions using the accepted models from nonlinear ICP. The results reaffirm the previously observed central causal role of child mortality rates.

scholarly journals Interrelations among SMED Stages: A Causal Model

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
José Roberto Díaz-Reza ◽  
Jorge Luis García-Alcaraz ◽  
José Roberto Mendoza-Fong ◽  
Valeria Martínez-Loya ◽  
Emilio Jiménez Macías ◽  
...  
Keyword(s):  
Latent Variables ◽  
Causal Model ◽  
Structural Equations ◽  
Direct And Indirect Effects ◽  
Know How ◽  
Wide Range ◽  
Implementation Stages ◽  
Identification Stage ◽  
Stage 1 ◽  
Structural Equations Model

Mexico has received a lot of foreign investment that has brought in a wide range of novel production philosophies, such as Single Minute Exchange of Dies (SMED). Despite its popularity and reported effectiveness, Mexican companies often quit SMED implementation as they consider it challenging. This usually happens when organizations are not familiarized enough with each one of the SMED stages or do not know how they are interrelated. In this article the interrelations among the different SMED implementation stages by means of a structural equations model are analyzed. Data for constructing the model were gathered from a survey administered to 250 employees from the Mexican maquiladora industry. The survey assessed the importance of 14 activities belonging to the four SMED stages. The descriptive analyses of these stages were conducted and integrated into a structural equations model as latent variables, to find their level of dependency. The model was constructed using WarpPLS 5 software, and direct, indirect, and total effects among variables are analyzed and validated. Results from the model revealed that Stage 1 of SMED implementation, known as the Identification Stage, has both direct and indirect effects on all the other SMED stages, being the most important stage.

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