scholarly journals Analysing causal structures with entropy

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170483 ◽  
Author(s):  
Mirjam Weilenmann ◽  
Roger Colbeck
Keyword(s):  
Causal Inference ◽  
Quantum Cryptography ◽  
Decision Problem ◽  
Causal Structure ◽  
Central Question ◽  
Open Problems ◽  
Classical Quantum ◽  
The Difference ◽  
Key Aspects ◽  
Causal Structures

A central question for causal inference is to decide whether a set of correlations fits a given causal structure. In general, this decision problem is computationally infeasible and hence several approaches have emerged that look for certificates of compatibility. Here, we review several such approaches based on entropy. We bring together the key aspects of these entropic techniques with unified terminology, filling several gaps and establishing new connections, all illustrated with examples. We consider cases where unobserved causes are classical, quantum and post-quantum, and discuss what entropic analyses tell us about the difference. This difference has applications to quantum cryptography, where it can be crucial to eliminate the possibility of classical causes. We discuss the achievements and limitations of the entropic approach in comparison to other techniques and point out the main open problems.

scholarly journals Quantum violations in the Instrumental scenario and their relations to the Bell scenario

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 186 ◽  
Author(s):  
Thomas Van Himbeeck ◽  
Jonatan Bohr Brask ◽  
Stefano Pironio ◽  
Ravishankar Ramanathan ◽  
Ana Belén Sainz ◽  
...  
Keyword(s):  
Opposite Direction ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Causal Models ◽  
Classical Quantum ◽  
Bell Nonlocality ◽  
Causal Structures

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

scholarly journals Complex Causal Structures of Neighbourhood Change: Evidence From a Functionalist Model and Yelp Data

2021 ◽  
Author(s):  
Daniel Silver ◽  
Thiago H Silva
Keyword(s):  
Large Scale ◽  
Causal Structure ◽  
Functional Model ◽  
Large Scale Data ◽  
Proposed Model ◽  
Neighbourhood Change ◽  
Key Aspects ◽  
Open Question ◽  
Causal Structures ◽  
Scale Data

Why some neighbourhoods change over time but others retain their identity remains an open question. Several attempts have been made to answer this question, with a family of models emerging as a result. However, empirically evaluating neighbourhood evolution models is a challenging task, because most require information that is difficult to obtain in traditional sources. For this reason, researchers have turned to new datasets, such as census microdata, Twitter, and Yelp. In this study, we articulate a functional model of neighbourhood change and continuity, adapted from a classical functionalist model proposed by Stinchcombe in 1968. We argue this model provides a relatively simple way to capture key aspects of the complex causal structure of neighbourhood change that are implicit in much neighbourhood change research but rarely formulated explicitly. We demonstrate how to assess the proposed model empirically using large-scale data from Yelp.com. Our results indicate that our approach can potentially help to understand the nature of neighbourhood change and be useful in different applications.

scholarly journals Analysing causal structures in generalised probabilistic theories

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 236 ◽  
Author(s):  
Mirjam Weilenmann ◽  
Roger Colbeck
Keyword(s):  
Classical Theory ◽  
Convex Cone ◽  
Causal Explanation ◽  
Causal Structure ◽  
Quantum Mechanical ◽  
Probabilistic Theory ◽  
Special Cases ◽  
Classical Quantum ◽  
Causal Structures ◽  
Probabilistic Theories

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad range of theories, which include both quantum and classical theory as special cases. We propose a method for analysing differences between such theories based on the so-called measurement entropy. We apply this method to several causal structures, deriving new relations that separate classical, quantum and more general theories within these causal structures. The constraints we derive for the most general theories are in a sense minimal requirements of any causal explanation in these scenarios. In addition, we make several technical contributions that give insight for the entropic analysis of quantum causal structures. In particular, we prove that for any causal structure and for any generalised probabilistic theory, the set of achievable entropy vectors form a convex cone.

scholarly journals Bridging Causality and Learning: How Do They Benefit from Each Other?

2020 ◽  
Author(s):  
Mingming Gong
Keyword(s):  
Machine Learning ◽  
Causal Inference ◽  
Causal Structure ◽  
Machine Learning Algorithms ◽  
Machine Learning Techniques ◽  
Randomized Controlled ◽  
Learning Techniques ◽  
The One ◽  
Causal Structures ◽  
Modern Machine

Modern machine learning techniques can discover complicated statistical dependencies between ran- dom variables, usually in the form a statistical model, and make use of these dependencies to per- form predictions on future observations. How- ever, many real problems involve causal inference, which aims to infer how the data generating sys- tem should behave under changing conditions. To perform causal inference, we need not only statisti- cal dependencies but also causal structures to deter- mine the system’s behavior under external interven- tions. In this paper, I will be focusing on two essen- tial problems that bridge causality and learning and investigate how they can benefit from each other. On the one hand, since conducting randomized controlled experiments for causal structure discov- ery is often expensive or infeasible, it would be valuable to investigate how we can explore modern machine learning algorithms to search for causal structures from observational data. On the other hand, since causal structure provides information about the distribution changing properties, it can be used as a fundamental tool to tackle a major chal- lenge for machine learning: the capability of gener- alization to new distributions and prediction in non- stationary environment.

scholarly journals Epistemic values of quantity and variety of evidence in biological mechanism research

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Yin Chung Au
Keyword(s):  
Experimental Data ◽  
Causal Inference ◽  
Case Studies ◽  
Biological Mechanism ◽  
Data Generation ◽  
Extended Version ◽  
Epistemic Values ◽  
Difference Making ◽  
Mechanism Research ◽  
The Difference

AbstractThis paper proposes an extended version of the interventionist account for causal inference in the practical context of biological mechanism research. This paper studies the details of biological mechanism researchers’ practices of assessing the evidential legitimacy of experimental data, arguing why quantity and variety are two important criteria for this assessment. Because of the nature of biological mechanism research, the epistemic values of these two criteria result from the independence both between the causation of data generation and the causation in question and between different interventions, not techniques. The former independence ensures that the interventions in the causation in question are not affected by the causation that is responsible for data generation. The latter independence ensures the reliability of the final mechanisms not only in the empirical but also the formal aspects. This paper first explores how the researchers use quantity to check the effectiveness of interventions, where they at the same time determine the validity of the difference-making revealed by the results of interventions. Then, this paper draws a distinction between experimental interventions and experimental techniques, so that the reliability of mechanisms, as supported by the variety of evidence, can be safely ensured in the probabilistic sense. The latter process is where the researchers establish evidence of the mechanisms connecting the events of interest. By using case studies, this paper proposes to use ‘intervention’ as the fruitful connecting point of literature between evidence and mechanisms.

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 Anticoagulant effects of different calcium supplementation pathways in calcium-free RCA-CVVH: a study protocol for a prospective randomized cross-over trial

2019 ◽  
Author(s):  
Biantong JIANG ◽  
Zhigang ZHANG ◽  
Xiu JIN ◽  
Haiye WANG ◽  
Yuchen WU ◽  
...  
Keyword(s):  
Renal Replacement Therapy ◽  
Calcium Ions ◽  
Calcium Supplementation ◽  
Incidence Rates ◽  
Regional Citrate Anticoagulation ◽  
Citrate Anticoagulation ◽  
Catheter Dysfunction ◽  
Calcium Effect ◽  
The Difference ◽  
Key Aspects

Abstract Background When regional citrate anticoagulation used in continuous renal replacement therapy, one of the key aspects to achieve safe and effective extracorporeal circulation is the management of calcium ions. For calcium-free RCA-CVVH, the anticoagulant effects of different calcium supplementation pathways have not yet been explored. In this trial, we would test our hypothesis that compared with the SCV, when calcium was infused through the VL-FV, the arterial iCa2+ was lower. Methods This is a prospective randomized cross-over trial involving 24 patients undergoing RCA-CVVH. The patients were randomly divided into two groups: VL-FV—SCV group and SCV—VL-FV group. The difference of iCa2+ between arterial iCa2+ and post-filtration iCa2+ was compared. Secondary indicators included the incidence rates of catheter dysfunction and hypocalcemia. Discussion This is the first trial on the anticoagulant effects of calcium-free RCA-CVVH through different calcium supplement routes. We will confirm that the arterial iCa2 + level is slightly lower when calcium is infused in the VL-FV than in the SCV, and the incidence rates of catheter dysfunction and hypocalcemia will help us to determine which site is safer. Trial Registration CHiCTR registry: ChiCTR1800020046. Registered on 12 December 2018. (http://www.chictr.org.cn/listbycreater.aspx). Keywords: Continuous venous-venous hemofiltration, regional citrate anticoagulation, calcium, effect, safety, cross-over trial

scholarly journals Is coding a relevant metaphor for the brain?

2018 ◽  
Vol 42 ◽  
Author(s):  
Romain Brette
Keyword(s):  
Brain Function ◽  
Neural Coding ◽  
Causal Structure ◽  
Linear Chain ◽  
Neural Codes ◽  
Experimental Parameters ◽  
Representational Power ◽  
Causal Structures ◽  
Perceptual Systems ◽  
The Brain

Abstract “Neural coding” is a popular metaphor in neuroscience, where objective properties of the world are communicated to the brain in the form of spikes. Here I argue that this metaphor is often inappropriate and misleading. First, when neurons are said to encode experimental parameters, the neural code depends on experimental details that are not carried by the coding variable (e.g., the spike count). Thus, the representational power of neural codes is much more limited than generally implied. Second, neural codes carry information only by reference to things with known meaning. In contrast, perceptual systems must build information from relations between sensory signals and actions, forming an internal model. Neural codes are inadequate for this purpose because they are unstructured and therefore unable to represent relations. Third, coding variables are observables tied to the temporality of experiments, whereas spikes are timed actions that mediate coupling in a distributed dynamical system. The coding metaphor tries to fit the dynamic, circular, and distributed causal structure of the brain into a linear chain of transformations between observables, but the two causal structures are incongruent. I conclude that the neural coding metaphor cannot provide a valid basis for theories of brain function, because it is incompatible with both the causal structure of the brain and the representational requirements of cognition.

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