Causal Discovery

This paper presents a number of new algorithms for discovering the Markov Blanket of a target variable T from training data. The Markov Blanket can be used for variable selection for classification, for causal discovery, and for Bayesian Network learning. We ...

Causal questions are central to many areas of science. Does high salt intake increase the
risk of heart attack? Does hormone replacement therapy reduce breast cancer risk? Would
upping the minimum wage increase unemployment? These questions have in common that
they require us to predict the consequences of an action. Traditionally machine learning solves
problems of the form given some data, infer properties of the distribution that generated that
data. These problems ask us to predict properties of the distribution after taking some action.
Without experimentally testing the intervention or making assumptions that constrain how
the action can change the distribution such inference is impossible.
The current approach to causal inference in elds such as economics and social science,
where the variables of interest are subject to human experience, is to use expert knowledge to
describe qualitatively how variables relate to one another and then t the statistical aspects
of the model. However there are problems, particularly in bioinformatics, where the number
of variables is large, and we do not have sucient direct human experience or prior theory
to specify causal models. In these cases, automated causal structure learning provides the
prospect of signicant improvements relative to purely nding the strongest associations.
We present a survey of recent research on causality, focusing on the problems of inferring
causal eects from observational data and causal structure learning. The rst problem occurs
when the structure of the relationship between variables is assumed to be at least partially
given by theory or prior knowledge and has been addressed in some depth in statistics [5],
social science [1], economics [2] and machine learning [3]. We describe how causal structural
equation models unify the diering approaches to this problem and provide a complete frame-
work to determine if and how causal queries can be inferred from observational data without
parametric assumptions about the relationship between variables [6]. Causal structure learning
attempts to infer causal structure from data based on more general assumptions. In particular,
algorithms have been developed based on the assumption of faithfulness; that the distribution
was generated by a directed acyclic graph over its variables and all the dependencies in the
distribution are re
ected by d-separation in that graph [7], and additive noise; eects are
deterministic functions of their causes plus an additive noise term [4]. We summarise the
application of these techniques on a range of practical problems and discuss their potential
and limitations.

The standard approach guiding research on the relationship between categories and causality views categories as reXecting causal relations in the world. We provide evidence that the opposite direction also holds: categories that have been acquired in previous learning contexts may inXuence subsequent causal learning. In three experiments we show that identical causal learning input yields diVerent attributions of causal capacity depending on the pre-existing categories to which the learning exemplars are assigned. There is a strong tendency to continue to use old conceptual schemes rather than switch to new ones even when the old categories are not optimal for predicting the new eVect, and when they were motivated by goals that diVered from the present context of causal discovery. However, we also found that the use of prior categories is dependent on the match between categories and causal eVect. Whenever the category labels suggest natural kinds which can be plausibly related to the causal eVects, transfer was observed. When the categories were arbitrary, or could not be plausibly related to the causal eVect learners abandoned the categories, and used diVerent categories to predict the causal eVect.

We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraint-based approach. Both approaches rely on the Causal Markov assumption, but the two di er signi cantly in theory and practice. An important di erence between the approaches is that the constraint-based approach uses categorical information about conditional-independence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraint-based counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of nite size. Two, using the Bayesian approach, ner distinctions among model structures|both quantitative and qualitative|can be made. Three, information from several models can be combined to make better inferences and to better account for modeling uncertainty. In addition to describing the general Bayesian approach to causal discovery, we review approximation methods for missing data and hidden variables, and illustrate di erences between the Bayesian and constraint-based methods using arti cial and real examples.

Objectives: Bayesian networks (BNs) are rapidly becoming a leading technology in applied Artificial Intelligence, with medicine its most popular application area. Both automated learning of BNs and expert elicitation have been used to build these networks, but the potentially more useful combination of these two methods remains underexplored. In this paper we examine a number of approaches to their combination and present new techniques for assessing their results. Methods and materials: Using public-domain data for heart failure, we run an automated causal discovery system (CaMML), which allows the incorporation of multiple kinds of prior expert knowledge into its search, to test and compare unbiased discovery with discovery biased with different kinds of expert opinion. We use adjacency matrices enhanced with numerical and colour labels to assist with the interpretation of the results. These techniques are presented within a wider context of knowledge engineering with Bayesian networks (KEBN). Results: The adjacency matrices make it clear that for our particular application problem, the heart failure data, the simplest kind of prior information (partially sorting variables into tiers) was more effective in aiding model discovery than either using no prior information or using more sophisticated and detailed expert priors. Conclusion: Hybrid causal learning of BNs is an important emerging technology. We present methods for incorporating it into the knowledge engineering process, including visualisation and analysis of the learned networks.

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data modeling. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilistic semantics, it is an ideal representation for combining prior knowledge (which often comes in causal form) and data. Four, Bayesian statistical methods in conjunction with Bayesian networks offer an efficient and principled approach for avoiding the overfitting of data. In this paper, we discuss methods for constructing Bayesian networks from prior knowledge and summarize Bayesian statistical methods for using data to improve these models. With regard to the latter task, we describe methods for learning both the parameters and structure of a Bayesian network, including techniques for learning with incomplete data. In addition, we relate Bayesian-network methods for learning to techniques for supervised and unsupervised learning. We illustrate the graphical-modeling approach using a real-world case study.

We briefly describe recent research on the automatic identification of quasi-experimental designs, a family of methods used in the medical, social, and economic sciences to discover causal knowledge from observational data. These methods are widely used for manual discovery, but recent advances in knowledge representation and databases have made it possible to automate aspects of their use. We report on a prototype system for automatically identifying quasiexperimental designs and suggest future work.

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or extreme sparsity constraints. We relax these assumptions and focus on an important but more specialized problem, namely recovering a directed acyclic subgraph of variables known to be causally descended from some (possibly large) set of confounding covariates, i.e. a confounder blanket. This is useful in many settings, for example when studying a dynamic biomolecular subsystem with genetic data providing causally relevant background information. Under a structural assumption that, we argue, must be satisfied in practice if informative answers are to be found, our method accommodates graphs of low or high sparsity while maintaining polynomial time complexity. We derive a sound and complete algorithm for identifying causal relationships under these conditions and implement testing procedures with provable error control for linear and nonlinear systems. We demonstrate our approach on a range of simulation settings.

La plupart des algorithmes pour découvrir des relations de causalité à partir de données font l'hypothèse que ces données reflètent parfaitement les (in)dépendances entre les variables étudiées. Cette hypothèse permet de retrouver le squelette théorique et le représentant de la classe d'équivalence de Markov du modèle dont sont réellement issues les données. Ce représentant est un graphe généralement partiellement orienté et sans circuit dont les arcs représentent des relations de causalité directe entre un ensemble de parents et le noeud enfant. Nous relachons cette première hypothèse en permettant d'obtenir initialement un graphe pouvant contenir des arêtes "incertaines". Ces arêtes seront ensuite validées (et orientées) ou supprimées lors de l'obtention de nouvelles données expérimentales. Nous présentons alors l'algorithme UnCaDo (UNsure CAusal DiscOvery) qui propose le plain d'expériences nécessaire pour obtenir suffisamment d'informations pour obtenir une structure complétement causale.

We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. It is both sound and complete, in the sense that all invariant features of the corresponding partial ancestral graph (PAG) are identified, even in the presence of latent variables and selection bias. The approach shows that every identifiable causal relation corresponds to one of just two fundamental forms. More importantly, as the basic building blocks of the method do not rely on the detailed (graphical) structure of the corresponding PAG, it opens up a range of new opportunities, including more robust inference, detailed accountability, and application to large models.

In part I of this work we introduced and evaluated the Generalized Local Learning (GLL) framework for producing local causal and Markov blanket induction algorithms. In the present second part we analyze the behavior of GLL algorithms and provide extensions to the core methods. Specifically, we investigate the empirical convergence of GLL to the true local neighborhood as a function of sample size. Moreover, we study how predictivity improves with increasing sample size. Then we investigate how sensitive are the algorithms to multiple statistical testing, especially in the presence of many irrelevant features. Next we discuss the role of the algorithm parameters and also show that Markov blanket and causal graph concepts can be used to understand deviations from optimality of state-of-the-art non-causal algorithms. The present paper also introduces the following extensions to the core GLL framework: parallel and distributed versions of GLL algorithms, versions with false discovery rate control, strategies for constructing novel heuristics for specific domains, and divide-and-conquer local-to-global learning (LGL) strategies. We test the generality of the LGL approach by deriving a novel LGL-based algorithm that compares favorably c 2010 Constantin F. Aliferis, Alexander Statnikov, Ioannis Tsamardinos, Subramani Mani and Xenofon D. Koutsoukos. ALIFERIS, STATNIKOV, TSAMARDINOS, MANI AND KOUTSOUKOS to the state-of-the-art global learning algorithms. In addition, we investigate the use of non-causal feature selection methods to facilitate global learning. Open problems and future research paths related to local and local-to-global causal learning are discussed.

Causal Probabilistic Networks (CPNs), (a.k.a. Bayesian Networks, or Belief Networks) are well-established representations in biomedical applications such as decision support systems and predictive modeling or mining of causal hypotheses. CPNs (a) have well-developed theory for induction of causal relationships, and (b) are suitable for creating sound and practical decision support systems. While several public domain and commercial tools exist for modeling and inference with CPNs, very few software tools and libraries exist currently that give access to algorithms for CPN induction. To that end, we have developed a software library, called Causal Explorer, that implements a suit of global, local and partial CPN induction algorithms. The toolkit emphasizes causal discovery algorithms. Approximately half of the algorithms are enhanced implementations of well-established algorithms, and the remaining ones are novel local and partial algorithms that scale to thousands of variables and thus are particularly suitable for modeling in massive datasets.

In this paper I argue that constitutive relevance relations in mechanisms behave like a special kind of causal relation in at least one important respect: Under suitable circumstances constitutive relevance relations produce the Markov factorization. Based on this observation one may wonder whether standard methods for causal discovery could be fruitfully applied to uncover constitutive relevance relations. This paper is intended as a first step into this new area of philosophical research. I investigate to what extent the PC algorithm, originally developed for causal search, can be used for constitutive relevance discovery. I also discuss possible objections and certain limitations of a constitutive relevance discovery procedure based on PC.

Citation information: Gebharter, A. (2017). Uncovering constitutive relevance relations in mechanisms. Philosophical Studies, 174(11), 2645–2666. doi:10.1007/s11098-016-0803-3

In two experiments, we studied the strategies that people use to discover causal relationships. According to inferential approaches to causal discovery, if people attempt to discover the power of a cause, then they should naturally select the most informative and unambiguous context. For generative causes this would be a context with a low base rate of effects generated by other causes and for preventive causes a context with a high base rate. In the following experiments, we used probabilistic and/or deterministic target causes and contexts. In each experiment, participants observed several contexts in which the effect occurred with different probabilities. After this training, the participants were presented with different target causes whose causal status was unknown. In order to discover the influence of each cause, participants were allowed, on each trial, to choose the context in which the cause would be tested. As expected by inferential theories, the participants preferred t...

A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables. We adopt a Bayesian point of view in order to capture a causal structure via interaction and learning with a causal environment. We test our method over two different scenarios, and the experiments mainly confirm that our technique can learn a causal structure. Furthermore, the experiments and results presented for the first test scenario demonstrate the usefulness of our method to learn a causal structure as well as the optimal action. On the other hand the second experiment, shows that our proposal manages to learn the underlying causal structure of several tasks with different sizes and different causal structures.

Causal discovery from observational data in the presence of unobserved variables is challenging. Identification of so-called Y substructures is a sufficient condition for ascertaining some causal relations in the large sample limit, without the assumption of no hidden common causes. An example of a Y substructure is A → C, B → C, C → D. This paper describes the first asymptotically reliable and computationally feasible scorebased search for discrete Y structures that does not assume that there are no unobserved common causes. For any parameterization of a directed acyclic graph (DAG) that has scores with the property that any DAG that can represent the distribution beats any DAG that can't, and for two DAGs that represent the distribution, if one has fewer parameters than the other, the one with the fewest parameter wins. In this framework there is no need to assign scores to causal structures with unobserved common causes. The paper also describes how the existence of a Y structure shows the presence of an unconfounded causal relation, without assuming that there are no hidden common causes.

Using gridded daily rainfall observations, and monthly satellite land surface data sets, the connection between land use change and monsoonal rainfall climatology is analyzed. A combination of statistical analysis involving genetic algorithm (GA), empirical orthogonal function (EOF), and causal discovery algorithms (CDA) are used. Study objectives are (1) to identify regional trends in the observed precipitation data over the Indian summer monsoon region, (2) to investigate the relation between land use change/agriculture intensification and changes in rainfall, and (3) to explore whether land use change and agricultural intensification have caused change in the rainfall climatology. The satellite-based vegetation data set shows significant agricultural intensification over northern India. For the period just before start of the summer monsoon season (April and May), the normalized differential vegetation index (NDVI) shows an increase only over Peninsular India. The EOF-and GA-based analysis identified the strongest climatic signal for monsoon rainfall with an increasing trend over the east central regions of India and a decreasing trend in monsoon seasonal precipitation over north/northwest India. The areas of decreasing rainfall coincided with regions of agricultural intensive land use and are analyzed further. The correlation and the causal data analysis suggest that premonsoon (March-April) vegetation affects July month precipitation over peninsular India. In particular, a negative relationship exists between them. The results are more robust over peninsular and northern India indicating that an increase in NDVI has possibly weakened the early monsoon rainfall in this region. The results of this study suggest that land use change associated with agricultural intensification could be reducing the summer monsoon rainfall over certain regions of India.

Objective—This study aims at developing and introducing a new algorithm, called direct causal learner (DCL), for learning the direct causal influences of a single target. We applied it to both simulated and real clinical and genome wide association study (GWAS) datasets and compared its performance to classic causal learning algorithms. Method—The DCL algorithm learns the causes of a single target from passive data using Bayesian-scoring, instead of using independence checks, and a novel deletion algorithm. We generate 14400 simulated datasets and measure the number of datasets for which DCL correctly and partially predicts the direct causes. We then compare its performance with the constraint-based path consistency (PC) and conservative PC (CPC) algorithms, the Bayesian-score based fast greedy search (FGS) algorithm, and the partial ancestral graphs algorithm fast causal inference (FCI). In addition, we extend our comparison of all five algorithms to both a real GWAS dataset and real breast cancer datasets over various time-points in order to observe how effective they are at predicting the causal influences of Alzheimer's disease and breast cancer survival. Results—DCL consistently outperforms FGS, PC, CPC, and FCI in discovering the parents of the target for the datasets simulated using a simple network. Overall, DCL predicts significantly more datasets correctly (McNemar's test significance: p ≪ 0.0001) than any of the other algorithms for these network types. For example, when assessing overall performance (simple and complex network results combined), DCL correctly predicts approximately 1400 more datasets than the top FGS method, 1600 more datasets than the top CPC method, 4500 more datasets than the top PC method, and 5600 more datasets than the top FCI method. Although FGS did correctly predict more datasets than DCL for the complex networks, and DCL correctly predicted only a few more datasets than CPC for these networks, there is no significant difference in performance between these three algorithms for this network type. However, when we use a more continuous measure of accuracy, we find that all the DCL methods are able to better partially predict more direct causes than FGS and CPC for the complex networks. In addition, DCL consistently had faster runtimes than the other algorithms. In the application to the real datasets, DCL identified rs6784615, located on the NISCH gene, and rs10824310, located on the PRKG1 gene, as direct causes of late onset Alzheimer's disease (LOAD) development. In addition, DCL identified ER category as a direct predictor of breast cancer mortality within 5 years, and HER2 status as a direct predictor of 10-year breast cancer mortality. These predictors have been identified in previous studies to have a direct causal relationship with their respective phenotypes, supporting the predictive power of DCL. When the other algorithms discovered predictors from the real datasets, these predictors were either also found by DCL or could not be supported by previous studies. Conclusion—Our results show that DCL outperforms FGS, PC, CPC, and FCI in almost every case, demonstrating its potential to advance causal learning. Furthermore, our DCL algorithm effectively identifies direct causes in the LOAD and Metabric GWAS datasets, which indicates its potential for clinical applications.

The standard approach guiding research on the relationship between categories and causality views categories as reXecting causal relations in the world. We provide evidence that the opposite direction also holds: categories that have been acquired in previous learning contexts may inXuence subsequent causal learning. In three experiments we show that identical causal learning input yields diVerent attributions of causal capacity depending on the pre-existing categories to which the learning exemplars are assigned. There is a strong tendency to continue to use old conceptual schemes rather than switch to new ones even when the old categories are not optimal for predicting the new eVect, and when they were motivated by goals that diVered from the present context of causal discovery. However, we also found that the use of prior categories is dependent on the match between categories and causal eVect. Whenever the category labels suggest natural kinds which can be plausibly related to the causal eVects, transfer was observed. When the categories were arbitrary, or could not be plausibly related to the causal eVect learners abandoned the categories, and used diVerent categories to predict the causal eVect.

The Markov blanket of a target variable is the minimum conditioning set of variables that makes the target independent of all other variables. Markov blankets inform feature selection, aid in causal discovery and serve as a basis for scalable methods of constructing Bayesian networks. We apply decision tree induction to the task of Markov blanket identification. Notably, we compare (a) C5.0, a widely used algorithm for decision rule induction, (b) C5C, which post-processes C5.0 's rule set to retain the most frequently referenced variables and (c) PC, a standard method for Bayesian network induction. C5C performs as well as or better than C5.0 and PC across a number of data sets. Our modest variation of an inexpensive, accurate, off-the-shelf induction engine mitigates the need for specialized procedures, and establishes baseline performance against which specialized algorithms can be compared.

In this paper, I want to substantiate three related claims regarding causal discovery from non-experimental data. Firstly, in scientific practice, the problem of ignorance is ubiquitous, persistent, and far-reaching. Intuitively, the problem of ignorance bears upon the following situation. A set of random variables V is studied but only partly tested for (conditional) independencies; i.e. for some variables A and B it is not known whether they are (conditionally) independent. Secondly, Judea Pearl’s most meritorious and influential algorithm for causal discovery (the IC algorithm) cannot be applied in cases of ignorance. It presupposes that a full list of (conditional) independence relations is on hand and it would lead to unsatisfactory results when applied to partial lists. Finally, the problem of ignorance is successfully treated by means of ALIC, the adaptive logic for causal discovery presented in this paper.

At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using statistical dependence testing alone and requires that we make additional assumptions. We propose fast and simple criteria for distinguishing cause and effect in pairs of discrete or continuous random variables. The intuition behind them is that predicting the effect variable using the cause variable should be 'simpler' than the reverse different notions of 'simplicity' giving rise to different criteria. We demonstrate the accuracy of the criteria on synthetic data generated under a broad family of causal mechanisms and types of noise.

At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using statistical dependence testing alone and requires that we make additional assumptions. We propose several fast and simple criteria for distinguishing cause and effect in pairs of discrete or continuous random variables. The intuition behind them is that predicting the effect variable using the cause variable should be `simpler' than the reverse -- different notions of `simplicity' giving rise to different criteria. We demonstrate the accuracy of the criteria on synthetic data generated under a broad family of causal mechanisms and types of noise.

At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using statistical dependence testing alone and requires that we make additional assumptions. We propose several fast and simple criteria for distinguishing cause and effect in pairs of discrete or continuous random variables. The intuition behind them is that predicting the effect variable using the cause variable should be `simpler' than the reverse -- different notions of `simplicity' giving rise to different criteria. We demonstrate the accuracy of the criteria on synthetic data generated under a broad family of causal mechanisms and types of noise.

In part I of this work we introduced and evaluated the Generalized Local Learning (GLL) framework for producing local causal and Markov blanket induction algorithms. In the present second part we analyze the behavior of GLL algorithms and provide extensions to the core methods. Specifically, we investigate the empirical convergence of GLL to the true local neighborhood as a function of sample size. Moreover, we study how predictivity improves with increasing sample size. Then we investigate how sensitive are the algorithms to multiple statistical testing, especially in the presence of many irrelevant features. Next we discuss the role of the algorithm parameters and also show that Markov blanket and causal graph concepts can be used to understand deviations from optimality of state-of-the-art non-causal algorithms. The present paper also introduces the following extensions to the core GLL framework: parallel and distributed versions of GLL algorithms, versions with false discovery rate control, strategies for constructing novel heuristics for specific domains, and divide-and-conquer local-to-global learning (LGL) strategies. We test the generality of the LGL approach by deriving a novel LGL-based algorithm that compares favorably c 2010 Constantin F. Aliferis, Alexander Statnikov, Ioannis Tsamardinos, Subramani Mani and Xenofon D. Koutsoukos. ALIFERIS, STATNIKOV, TSAMARDINOS, MANI AND KOUTSOUKOS to the state-of-the-art global learning algorithms. In addition, we investigate the use of non-causal feature selection methods to facilitate global learning. Open problems and future research paths related to local and local-to-global causal learning are discussed.

At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using statistical dependence testing alone and requires that we make additional assumptions. We propose fast and simple criteria for distinguishing cause and effect in pairs of discrete or continuous random variables. The intuition behind them is that predicting the effect variable using the cause variable should be 'simpler' than the reverse different notions of 'simplicity' giving rise to different criteria. We demonstrate the accuracy of the criteria on synthetic data generated under a broad family of causal mechanisms and types of noise.

Bayesian networks (BNs) are rapidly becoming a leading tool in applied Artificial Intelligence (AI). BNs may be built by eliciting expert knowledge or learned via causal discovery programs. Both approaches have limitations: expert elicitation is expensive, time-consuming and relies on experts having full domain knowledge, while discovery is often ineffective given small or noisy datasets. A hybrid approach is to incorporate prior information elicited from experts into the causal discovery process. We present several ways of using expert information as prior probabilities in the CaMML causal discovery program. We compare CaMML with and without prior information to a variety of other BN learners. Our results show that CaMML achieves comparable results without prior information and superior performance with prior information. We also present results showing that CaMML is well calibrated to variations in the expert's skill and confidence.

The Causality Workbench project provides an environment to test causal discovery algorithms. Via a web portal (http: //clopinet.com/causality), we provide a number of resources, including a repository of datasets, models, and software packages, and a virtual laboratory allowing users to benchmark causal discovery algorithms by performing virtual experiments to study artificial causal systems. We regularly organize competitions. In this paper,

Bayesian Networks (BN) is a knowledge representation formalism that has been proven to be valuable in biomedicine for constructing decision support systems and for generating causal hypotheses from data. Given the emergence of datasets in medicine and biology with thousands of variables and that current algorithms do not scale more than a few hundred variables in practical domains, new efficient and accurate algorithms are needed to learn high quality BNs from data. We present a new algorithm called Max-Min Hill-Climbing (MMHC) that builds upon and improves the Sparse Candidate (SC) algorithm; a state-of-the-art algorithm that scales up to datasets involving hundreds of variables provided the generating networks are sparse. Compared to the SC, on a number of datasets from medicine and biology, (a) MMHC discovers BNs that are structurally closer to the data-generating BN, (b) the discovered networks are more probable given the data, (c) MMHC is computationally more efficient and scal...

Mechanisms play an important role in many sciences when it comes to questions concerning explanation, prediction, and control. Answering such questions in a quantitative way requires a formal represention of mechanisms. Gebharter (2014) suggests to represent mechanisms by an acyclic causal net's arrows. In this paper we show how this approach can be extended in such a way that it can also be fruitfully applied to mechanisms featuring causal feedback.

We briefly describe recent research on the automatic identification of quasi-experimental designs, a family of methods used in the medical, social, and economic sciences to discover causal knowledge from observational data. These methods are widely used for manual discovery, but recent advances in knowledge representation and databases have made it possible to automate aspects of their use. We report on a prototype system for automatically identifying quasiexperimental designs and suggest future work.

Bayesian networks (BN) have been used for prediction or classification tasks in various domains. In the first applications, the BN structure was causally defined by expert knowledge. Then, algorithms were proposed in order to learn the BN structure from observational data. Generally, these algorithms can only find a structure encoding the right conditional independencies but not all the causal relationships. Some new domains appear where the model will only be learnt in order to discover these causal relationships. To this end, we will focus on discovering causal relations in order to get Causal Bayesian Networks (CBN). To learn such models, interventional data (i.e. samples conditioned on the particular values of one or more variables that have been experimentally manipulated) are required. These interventions are usually very expensive to perform, therefore the choice of variables to experiment on can be vital when the number of experimentations is restricted. In many cases, available ontologies provide high level knowledge for the same domain under study. Consequently, using this semantical knowledge can turn out of a big utility to improve causal discovery. This article proposes a new method for learning CBNs from observational data and interventions. We first extend the greedy approach for perfect observational and experimental data proposed in [13], by adding a new step based on the integration of ontological knowledge, which will allow us to choose efficiently the interventions to perform in order to obtain the complete CBN. Then, we propose an enriched visualization for better understanding of the causal graphs.

Learning Causal Bayesian Networks (CBNs) is a new line of research in the machine learning field. Within the existing works in this direction [8, 12, 13], few of them have taken into account the gain that can be expected when integrating additional knowledge during the learning process. In this paper, we present a new serendipitous strategy for learning CBNs using prior knowledge extracted from ontologies. The integration of such domain’s semantic information can be very useful to reveal new causal relations and provide the necessary knowledge to anticipate the optimal choice of experimentations. Our strategy also supports the evolving character of the semantic background by reusing the causal discoveries in order to enrich the domain ontologies.

We organized for WCCI 2008 a challenge to evaluate causal modeling techniques, focusing on predicting the effect of “interventions” performed by an external agent. Examples of that problem are found in the medical domain to predict the effect of a drug prior to administering it, or ...

The standard approach guiding research on the relationship between categories and causality views categories as reflecting causal relations in the world. We provide evidence that the opposite direction also holds: categories that have been acquired in previous learning contexts may influence subsequent causal learning. In three experiments we show that identical causal learning input yields different attributions of causal capacity

A long-standing open research problem is how to use information from different experiments, including background knowledge, to infer causal relations. Recent developments have shown ways to use multiple data sets, provided they originate from identical experiments. We present the MCI-algorithm as the first method that can infer provably valid causal relations in the large sample limit from different experiments. It is fast, reliable and produces very clear and easily interpretable output. It is based on a result that shows that constraint-based causal discovery is decomposable into a candidate pair identification and subsequent elimination step that can be applied separately from different models. We test the algorithm on a variety of synthetic input model sets to assess its behavior and the quality of the output. The method shows promising signs that it can be adapted to suit causal discovery in real-world application areas as well, including large databases.

We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussian-noise case. We also propose a method to learn such models from observational data. In the acyclic case, the method reduces to ordinary regression, but in the more challenging cyclic case, an additional term arises in the loss function, which makes it a special case of nonlinear independent component analysis. We illustrate the proposed method on synthetic data.

In part I of this work we introduced and evaluated the Generalized Local Learning (GLL) framework for producing local causal and Markov blanket induction algorithms. In the present second part we analyze the behavior of GLL algorithms and provide extensions to the core methods. Specifically, we investigate the empirical convergence of GLL to the true local neighborhood as a function of sample size. Moreover, we study how predictivity improves with increasing sample size. Then we investigate how sensitive are the algorithms to multiple statistical testing, especially in the presence of many irrelevant features. Next we discuss the role of the algorithm parameters and also show that Markov blanket and causal graph concepts can be used to understand deviations from optimality of state-of-the-art non-causal algorithms. The present paper also introduces the following extensions to the core GLL framework: parallel and distributed versions of GLL algorithms, versions with false discovery rate control, strategies for constructing novel heuristics for specific domains, and divide-and-conquer local-to-global learning (LGL) strategies. We test the generality of the LGL approach by deriving a novel LGL-based algorithm that compares favorably c 2010 Constantin F. Aliferis, Alexander Statnikov, Ioannis Tsamardinos, Subramani Mani and Xenofon D. Koutsoukos. ALIFERIS, STATNIKOV, TSAMARDINOS, MANI AND KOUTSOUKOS to the state-of-the-art global learning algorithms. In addition, we investigate the use of non-causal feature selection methods to facilitate global learning. Open problems and future research paths related to local and local-to-global causal learning are discussed.