Causal Discovery

What assumptions and methods allow us to turn observations into causal knowledge, and how can even incomplete causal knowledge be used in planning and prediction to influence and control our environment? In this book Peter Spirtes, Clark Glymour, and Richard Scheines address these questions using the formalism of Bayes networks, with results that have been applied in diverse areas of research in the social, behavioral, and physical sciences. The authors show that although experimental and observational study designs ...

Data sets with many discrete variables and relatively few cases arise in many domains. Several studies have sought to identify the Markov Blanket (MB) of a target variable by filtering variables using statistical decisions for conditional independence and ...

We introduce a new abstract approach to the study of conditional independence, founded on a concept analogous to the factorization properties of probabilistic independence, rather than the separation properties of a graph. The basic ingredient is the \conditional product", which provides a way of combining the objects under consideration while preserving as much independence as possible. We introduce an appropriate axiom system for conditional product, and show how, when these axioms are obeyed, it induces a derived concept of conditional independence which obeys the usual semigraphoid axioms. The general structure is used to throw light on three speci c areas: the familiar probabilistic framework (both the discrete and the general case); a set-theoretic framework related to \variation independence"; and a variety of graphical frameworks.

This paper proposes an AI-assisted approach aimed at accelerating chemical process design through causal incremental reinforcement learning (CIRL) where an intelligent agent is interacting iteratively with a process simulation environment (e.g., Aspen HYSYS, DWSIM, etc.). The proposed approach is based on an incremental learnable optimizer capable of guiding multi-objective optimization towards optimal design variable configurations, depending on several factors including the problem complexity, selected RL algorithm and hyperparameters tuning. One advantage of this approach is that the agent-simulator interaction significantly reduces the vast search space of design variables, leading to an accelerated and optimized design process. This is a generic causal approach that enables the exploration of new process configurations and provides actionable insights to designers to improve not only the process design but also the design process across various applications. The approach was validated on industrial processes including an absorption-based carbon capture, considering the economic and technological uncertainties of different capture processes, such as energy price, production cost, and storage capacity. It achieved a cost reduction of up to 5.5% for the designed capture process, after a few iterations, while also providing the designer with actionable insights. From a broader perspective, the proposed approach paves the way for accelerating the adoption of decarbonization technologies (CCUS value chains, clean fuel production, etc.) at a larger scale, thus catalyzing climate change mitigation.

One fundamental problem in the empirical sciences is of reconstructing the causal structure that underlies a phenomenon of interest through observation and experimentation. While there exists a plethora of methods capable of learning the equivalence class of causal structures that are compatible with observations, it is less well-understood how to systematically combine observations and experiments to reconstruct the underlying structure. In this paper, we investigate the task of structural learning in non-Markovian systems (i.e., when latent variables affect more than one observable) from a combination of observational and soft experimental data when the interventional targets are unknown. Using causal invariances found across the collection of observational and interventional distributions (not only conditional independences), we define a property called Ψ-Markov that connects these distributions to a pair consisting of (1) a causal graphD and (2) a set of interventional targets I...

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‐bas...

We propose a method for learning causal relations within high-dimensional tensor data as they are typically recorded in non-experimental databases. The method allows the simultaneous inclusion of numerous dimensions within the data analysis such as samples, time and domain variables construed as tensors. In such tensor data we exploit and integrate non-Gaussian models and tensor analytic algorithms in a novel way. We prove that we can determine simple causal relations independently of how complex the dimensionality of the data is. We rely on a statistical decomposition that flattens higher-dimensional data tensors into matrices. This decomposition preserves the causal information and is therefore suitable for structure learning of causal graphical models, where a causal relation can be generalised beyond dimension, for example, over all time points. Related methods either focus on a set of samples for instantaneous effects or look at one sample for effects at certain time points. We evaluate the resulting algorithm and discuss its performance both with synthetic and real-world data.

Two experiments investigated the roles of contingency and temporal contiguity in causal reasoning, and the trade-off between them. Participants observed an ongoing, continuous stream of events, which was not segmented into discrete learning trials. Four potential candidate ...

Abstract. Ontologies are in the heart of the knowledge management process. Different semantic measures have been proposed in the literature to evaluate the strength of the semantic link between two concepts or two groups of concepts from either two different ...

Reinforcement learning and Causal Inference are indispensable part of machine learning. However, they are usually treated separately, although that both are directly relevant to problem solving methods. One of the challenges that emerge in Reinforcement Learning, is the trade-off between exploration and exploitation. In this work we propose to use causal models to attend the learning process of an agent. The causal models helps to restrict the search space by reducing the actions that an agent can take through interventional queries like: Would I have achieved my goal if I had drop the passenger off here?. This simulates common sense that lightens the time it takes the trial and error approach. We attack the classic taxi problem and we show that using causal models in the Q-learning action selection step leads to higher and faster jump-start reward and convergence, respectively.

Causal Reinforcement Learning (CRL) is an emerging field where two essential areas for the development of artificial intelligence are integrated. Existing works in the area have shown how causality can contribute to mitigate some of the limitations of reinforcement learning (RL), ranging from data-inefficiency, lack of interpretability, and long learning times, among others. However, how to use reinforcement learning to
support causal discovery (CD) has so far been less explored. In this article, we introduce CARL, a CausalityAware Reinforcement Learning framework for simultaneously learning and using causal models to speed-up the policy learning in online Markov decision process (MDP) settings. In a synergistic way, our method alternates between: (i) (RL for CD), where it promotes the selection of actions to obtain better causal models in fewer episodes than traditional methods of obtaining data in RL, (ii) (CD), where a score-based algorithm is used to learn causal models and (iii) (RL using CD), where the learned models are used to select actions that speed up the learning of the optimal policy by reducing the number of interactions with the environment. Experiments in simulated environments show that our method achieves better results in policy learning than traditional model-free and model-based algorithms while it is also able to learn the underlying causal models. We also demonstrate how the learned causal models can be directly transferred to a similar task of greater complexity, significantly reducing the number of episodes required to learn an optimal policy Finally, the method’s scalability to high-dimensional states, where the action-value function needs to be represented with deep neural networks, was verified.

Learning causal models hidden in the background of observational data has been a difficult issue. Dealing with latent common causes and selection bias for constructing causal models in real data is often necessary because observing all relevant variables is difficult. Ancestral graph models are effective and useful for representing causal models with some information of such latent variables. The causal faithfulness condition, which is usually assumed for determining the models, is known to often be weakly violated in statistical view points for finite data. One of the authors developed a constraint-based causal learning algorithm that is robust against the weak violations while assuming no latent variables. In this study, we applied and extended the thoughts of the algorithm to the inference of ancestral graph models. The practical validity and effectiveness of the algorithm are also confirmed by using some standard datasets in comparison with FCI and RFCI algorithms.

In this paper, we focus on the reliability, or data efficiency, problem of the existing Markov blanket learning algorithms. We first define as well as demonstrate the seriousness of this problem. Secondly, we review eleven published algorithms ranging from 1996 to 2010, including their design and the reliability problem. Then, we discuss the challenge to improve this performance for different strategy as taken in existing works. Finally, we point out IPC-MB [1, 2] is the one with best data efficiency among published works, but it is still only sub-optimal. This work can be a reference for future effort aiming at a more reliable solution, though we conclude here that the best solution may not exist if an optimal output is expected.

There are domains, such as in biology, medicine, and neuroscience, where the causal relations vary across members of a population, and where it may be difficult to collect data for some specific members. For these domains, it is convenient to develop algorithms that, from small sample sizes, can discover the specific causal relations of a subject. Learning these subject-specific models with the existing causal discovery algorithms could be difficult. Most of them were designed to find the common causal relations of a population in the large sample limit. Although transfer learning techniques have shown to be useful for improving predictive associative models learned with limited data sets, their application in the field of causal discovery has not been sufficiently explored. In this paper, we propose a knowledge transfer algorithm for discovering Markov equivalence classes for subject-specific causal models. We explore transferring weighted instances of auxiliary data sets, accordin...

Causal structure learning algorithms construct Bayesian networks from observational data. Using noninterventional data, existing constraint-based algorithms may return I-equivalent partially directed acyclic graphs. However, these algorithms do not fully exploit the graphical properties of Bayesian networks, and require many redundant tests that reduce both speed and accuracy. In this paper, we introduce ideas to exploit such properties to increase the speed and accuracy of causal structure learning for multivariate normal data. In numerical experiments on five benchmarking networks our proposed algorithm was faster and more accurate than recently-developed algorithms.

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...

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.

Unobserved confounding is the main obstacle to causal effect estimation from observational data. Instrumental variables (IVs) are widely used for causal effect estimation when there exist latent confounders. With the standard IV method, when a given IV is valid, unbiased estimation can be obtained, but the validity requirement of standard IV is strict and untestable. Conditional IV has been proposed to relax the requirement of standard IV by conditioning on a set of observed variables (known as a conditioning set for a conditional IV). However, the criterion for finding a conditioning set for a conditional IV needs complete causal structure knowledge or a directed acyclic graph (DAG) representing the causal relationships of both observed and unobserved variables. This makes it impossible to discover a conditioning set directly from data. In this paper, by leveraging maximal ancestral graphs (MAGs) in causal inference with latent variables, we propose a new type of IV, ancestral IV i...

Recent approaches to causal modeling rely upon the Causal Markov Condition, which specifies which probability distributions are compatible with a Directed Acyclic Graph (DAG). Further principles are required in order to choose among the large number of DAGs compatible with a given probability distribution. Here we present a principle that we call frugality. This principle tells one to choose the DAG with the fewest causal arrows. We argue that frugality has several desirable properties compared to the other principles that have been suggested, including the well-known Causal Faithfulness Condition.

This paper describes the adaptive logic of compatibility and its dynamic proof theory. The results derive from insights in inconsistency-adaptive logic, but are themselves very simple and philosophically unobjectionable. In the absence of a positive test, dynamic proof theories lead, in the long run, to correct results and, in the short run, sometimes to final decisions but always to sensible estimates. The paper contains a new and natural kind of semantics for S5from which it follows that a specific subset of the standard worlds-models is characteristic for S5.

The development of the civil aviation industry has continuously increased the requirements for the efficiency of airport ground support services. In the existing ground support research, there has not yet been a process model that directly obtains support from the ground support log to study the causal relationship between service nodes and flight delays. Most ground support studies mainly use machine learning methods to predict flight delays, and the flight support model they are based on is an ideal model. The study did not conduct an in-depth study of the causal mechanism behind the ground support link and did not reveal the true cause of flight delays. Therefore, there is a certain deviation in the prediction of flight delays by machine learning, and there is a certain deviation between the ideal model based on the research and the actual service process. Therefore, it is of practical significance to obtain the process model from the guarantee log and analyze its causality. Howe...

Editor: Isabelle Guyon et al. In this paper we propose an energy-based model (EBM) for selecting subsets of features that are both causally and predictively relevant for classification tasks. The proposed method is tested in the causality challenge, a competition that promotes research on strengthen feature selection by taking into account causal information of features. Under the proposed approach, an energy value is assigned to every configuration of features and the problem is reduced to that of finding the configuration that minimizes an energy function. We propose an energy function that takes into account causal, predictive, and relevance/correlation information of features. Particularly, we introduce potentials that combine the rankings of individual feature selection methods, Markov blanket information and predictive performance estimations. The configuration with lower energy will be that offering the best tradeoff between these sources of information. Experimental results ...

In this paper we propose an energy-based model (EBM) for selecting subsets of features that are both causally and predictively relevant for classification tasks. The proposed method is tested in the causality challenge, a competition that promotes research on strengthen feature selection by taking into account causal information of features. Under the proposed approach, an energy value is assigned to every configuration of features and the problem is reduced to that of finding the configuration that minimizes an energy ...

We use an analogy between non-isomorphic mathematical structures defined over the same set and the algebras induced by associative and causal levels of information in order to argue that Reinforcement Learning, in its current formulation, is not a causal problem, independently if the motivation behind it has to do with an agent taking actions.

I present a formalism that combines two methodologies: objective Bayesianism and Bayesian nets. According to objective Bayesianism, an agent's degrees of belief (i) ought to satisfy the axioms of probability, (ii) ought to satisfy constraints imposed by background knowledge, and (iii) should otherwise be as non-committal as possible (i.e. have maximum entropy). Bayesian nets offer an efficient way of representing and updating probability functions. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function. I show how objective Bayesian nets can be constructed, updated and combined, and how they can deal with cases in which the agent's background knowledge includes knowledge of qualitative influence relationships, e.g. causal influences. I then sketch a number of applications of the resulting formalism, showing how it can shed light on probability logic, causal modelling, logical reasoning, semantic reasoning, argumentation and recursive modelling.

Causal discovery is the task of finding plausible causal relationships from statistical data [1, 2]. Such methods rely on various assumptions about the data generating process to identify it from uncontrolled observations. We have recently proposed a causal discovery method based on independent component analysis (ICA) called LiNGAM [3], showing how to completely identify the data generating process under the assumptions of linearity, non-gaussianity, and no hidden variables. In this paper, after briefly recapitulating this approach, we focus on the algorithmic problems encountered when the number of variables considered is large. Thus we extend the applicability of the method to data sets with tens of variables or more. Experiments confirm the performance of the proposed algorithms, implemented as part of the latest version of our freely available Matlab/Octave LiNGAM package.

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.

Several paradigms exist for modeling causal graphical models for discrete variables that can handle latent variables without explicitly modeling them quantitatively. Applying them to a problem domain consists of different steps: structure learning, parameter learning and using them for probabilistic or causal inference. We discuss two well-known formalisms, namely semi-Markovian causal models and maximal ancestral graphs and indicate their strengths and limitations. Previously an algorithm has been constructed that by combining elements from both techniques allows to learn a semi-Markovian causal models from a mixture of observational and experimental data. The goal of this paper is to recapitulate the integral learning process from observational and experimental data and to demonstrate how different types of inference can be performed efficiently in the learned models. We will do this by proposing an alternative representation for semi-Markovian causal models.

We discuss a decision theoretic approach to learn causal Bayesian networks from observational data and experiments. We use the information of observational data to learn a completed partially directed acyclic graph using a structure learning technique and try to discover the directions of the remaining edges by means of experiment. We will show that our approach allows to learn a causal Bayesian network optimally with relation to a number of decision criteria. Our method allows the possibility to assign costs to each experiment and each measurement. We introduce an algorithm that allows to actively add results of experiments so that arcs can be directed during learning. A numerical example is given as demonstration of the techniques.

In this paper we propose a distributed structure learning algorithm for the recently introduced Multi-Agent Causal Models (MACMs). MACMs are an extension of Causal Bayesian Networks (CBN) to a distributed domain. In this setting it is assumed that there is no single database containing all the information of the domain. Instead, there are several sites holding non-disjoint subsets of the domain variables. At each site there is an agent capable of learning a local causal model. We study the possibility of combining the information of the local models into one globally consistent model. We propose an algorithm that yields the possibility to learn new local structures that can be combined to perform globally consistent causal inference.

ABSTRACT. Most algorithms to learn causal relationships from data assume that the provided data perfectly mirrors the (in) dependencies in the system under study. This allows us to recover the correct dependence skeleton and the representative of the Markov equivalence class of Bayesian networks that models the data. This complete partially directed acyclic graph contains some directed links that represent a direct causal influence from parent to child. In this paper we relax the mentioned requirement by allowing unsure ...

Causal models could increase interpretability, robustness to distributional shift and sample efficiency of RL agents. In this vein, we address the question of learning a causal model of an RL environment. This problem is known to be difficult due to spurious correlations. We overcome this difficulty by rewarding an RL agent for designing and executing interventions to discover the true model. We compare rewarding the agent for disproving uncertain edges in the causal graph, rewarding the agent for activating a certain node, or rewarding the agent for increasing the causal graph loss. We show that our methods result in a better causal graph than one generated by following the random policy, or a policy trained on the environment's reward. We find that rewarding for the causal graph loss works the best.

Service level is considered to be the most important criterion in evaluating application services. In our study we empirically investigated how perceived service level (PSL) influenced healthcare workers' willingness to use application service oriented medical records. In particular, we extended the technology acceptance model (TAM) by embedding PSL as a causal antecedent. We found that PSL explained 61% of the variation in ease of use, which is twice as much as our current understanding. We also found that TAM was validated when tested in isolation but failed within the larger nomological network. We provided an explanation based on the notion of conditional independence. We further applied TETRAD III to explore the phenomenon and discovered two spurious associations in TAM, successfully confirming the explanation.

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.

Many real-world decision-making tasks require learning casual relationships between a set of variables. Typical causal discovery methods, however, require that all variables are observed, which might not be realistic in practice. Unfortunately, in the presence of latent confounding, recovering casual relationships from observational data without making additional assumptions is an ill-posed problem. Fortunately, in practice, additional structure among the confounders can be expected, one such example being pervasive confounding, which has been exploited for consistent causal estimation in the special case of linear causal models. In this paper, we provide a proof and method to estimate causal relationships in the non-linear, pervasive confounding setting. The heart of our procedure relies on the ability to estimate the pervasive confounding variation through a simple spectral decomposition of the observed data matrix. We derive a DAG score function based on this insight, and empiric...

Social media systems have become increasingly attractive to both users and companies providing those systems. Efficient management of these systems is essential and requires knowledge of cause-and-effect relationships within the system. Online experimentation can be used to discover causal knowledge; however, this ignores the observational data that is already being collected for operational purposes. Quasiexperimental designs (QEDs) are commonly used in social sciences to discover causal knowledge from observational data, and QEDs can be exploited to discover causal knowledge about social media systems. In this paper, we apply three different QEDs to demonstrate how one can gain a causal understanding of a social media system. The conclusions drawn from using a QED can have threats to their validity, but we show how one can carefully construct sophisticated designs to overcome some of those threats.

Probabilistic Graphical Models (PGMs) offer a popular framework including a variety of statistical formalisms, such as Bayesian networks (BNs). These latter are able to depict real-world situations with high degree of uncertainty. Due to their power and flexibility, several extensions were proposed, ensuring thereby the suitability of their use. Probabilistic Relational Models (PRMs) extend BNs to work with relational databases rather than propositional data. Their construction represents an active area since it remains the most complicated issue. Only few works have been proposed in this direction, and most of them don’t guarantee an optimal identification of their dependency structure. In this paper we intend to propose an approach that ensures returning an optimal PRM structure. It is inspired from a BN method whose performance was already proven.

With the rising need to reuse the existing domain knowledge when learning causal Bayesian networks, the ontologies can supply valuable semantic information to dene explicit cause-to-eect relationships and make further interesting discoveries with the minimum expected cost and eort. This thesis studies the crossing-over between causal Bayesian networks and ontologies, establishes the main correspondences between their elements and develops a cyclic approach in which we make use of the two formalisms in an interchangeable way. The rst direction involves the integration of semantic knowledge contained in the domain ontologies to anticipate the optimal choice of experimentations via a serendipitous causal discovery strategy. The semantic knowledge may contain some causal relations in addition to the strict hierarchical structure. So instead of repeating the eorts that have already been spent by the ontology developers and curators, we can reuse these causal relations by integrating them as prior knowledge when applying existing structure learning algorithms to induce partially directed causal graphs from pure observational data. To complete the full orientation of the causal network, we need to perform active interventions on the system under study. We therefore present a serendipitous decision-making strategy based on semantic distance calculus to guide the causal discovery process to investigate unexplored areas and conduct more informative experiments. The idea mainly arises from the fact that the semantically related concepts are generally the most extensively studied ones. For this purpose, we propose to supply issues for insight by favoring the experimentation on the more distant concepts according to the ontology subsumption hierarchy. The second complementary direction concerns an enrichment process by which it will be possible to reuse these causal discoveries, support the evolving character of the semantic background and make an ontology evolution. Extensive experimentations are conducted using the well-known Saccharomyces cerevisiae cell cycle microarray data and the Gene Ontology to show the merits of the SemcaDo approach in the biological eld where microarray gene expression experiments are usually very expensive to perform, complex and time consuming.

We describe a mechanism which receives as input a segmented argument composed of NL sentences, and generates an interpretation. Our mechanism relies on the Minimum Message Length Principle for the selection of an interpretation among candidate options. This enables our mechanism to cope with noisy input in terms of wording, beliefs and argument structure; and reduces its reliance on a particular knowledge representation. The performance of our system was evaluated by distorting automatically generated arguments, and passing them to the system for interpretation. In 75% of the cases, the interpretations produced by the system matched precisely or almost-precisely the representation of the original arguments.

We present a logic, ELI r , for the discovery of deterministic causal regularities starting from empirical data. Our approach is inspired by Mackie's theory of causes as INUS-conditions, and implements a more recent adjustment to Mackie's theory according to which the left-hand side of causal regularities is required to be a minimal disjunction of minimal conjunctions. To derive such regularities from a given set of data, we make use of the adaptive logics framework. Our knowledge of deterministic causal regularities is, as Mackie noted, most often gappy or elliptical. The adaptive logics framework is well-suited to explicate both the internal and the external dynamics of the discovery of such gappy regularities. After presenting ELI r , we first discuss these forms of dynamics in more detail. Next, we consider some criticisms of the INUS-account and show how our approach avoids them, and we compare ELI r with the CNA algorithm that was recently proposed by Michael Baumgartner.

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...

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.

This work introduces the Bayesian local causal discovery framework, a method for discovering unconfounded causal relationships from observational data. It addresses the hypothesis that causal discovery using local search methods will outperform causal discovery algorithms that employ global search in the context of large datasets and limited computational resources. Several Bayesian local causal discovery (BLCD) algorithms are described and results presented comparing them with two well-known global causal discovery algorithms PC and FCI, and a global Bayesian network learning algorithm, the optimal reinsertion (OR) algorithm which was post-processed to identify relationships that under assumptions are causal. Methodologically, this research formalizes the task of causal discovery from observational data using a Bayesian approach and local search. It specifically investigates the so called Y structure in causal discovery and classifies the various types of Y structures present in the data generating networks. It identifies the Y structures in the Alarm, Hailfinder, Barley, Pathfinder and Munin networks and categorizes them. A proof of the convergence of the BLCD algorithm based on the identification of Y structures, is also provided. Principled methods of combining global and local causal discovery algorithms to improve upon the performance of the individual algorithms are discussed. In particular, a post-processing method for identifying plausible causal relationships from the output of global Bayesian network learning algorithms is described, thereby extending them to be causal discovery algorithms. In an experimental evaluation, simulated data from synthetic causal Bayesian networks representing five different domains, as well as a real-world medical dataset, were used. Causal iv discovery performance was measured using precision and recall. Sometimes the local methods performed better than the global methods, and sometimes they did not (both in terms of precision/recall and in terms of computation time). When all the datasets were considered in aggregate, the local methods (BLCD and BLCDpk) had higher precision. The general performance of the BLCD class of algorithms was comparable to the global search algorithms, implying that the local search algorithms will have good performance on very large datasets when the global methods fail to scale up. The limitations of this research and directions for future research are also discussed.

In part I of this work we introduced and evaluated the Generalized Local Learning (GLL) frame- work for producing local causal and Markov blanket induction algorithms. In the present sec- ond part we analyze the behavior of GLL algorithms and provide extensions to the core methods. Specifically, we investigate the empirical convergence of G LL to the true local neighborhood

Gebharter ([2017b]) has proposed to use one of the best known Bayesian network (BN) causal discovery algorithms, PC, to identify the constitutive dependencies underwriting mechanistic explanations. His proposal assumes that mechanistic constitution behaves like deterministic direct causation, such that PC is directly applicable to mixed variable sets featuring both causal and constitutive dependencies. Gebharter claims that such mixed sets, under certain restrictions, comply with PC's background assumptions. The aim of this paper is to show that Gebharter's proposal incurs severe problems, ultimately rooted in the widespread non-compliance of mechanistic systems with PC's assumptions. This casts severe doubts on the attempt to implicitly define constitution as a form of deterministic direct causation complying with PC's assumptions.

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. This paper applies 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.

The gold standard for discovering causal relations is by means of experimentation. Over the last decades, alternative methods have been proposed that can infer causal relations between variables from certain statistical patterns in purely observational data. We introduce Joint Causal Inference (JCI), a novel approach to causal discovery from multiple data sets from different contexts that elegantly unifies both approaches. JCI is a causal modeling framework rather than a specific algorithm, and it can be implemented using any causal discovery algorithm that can take into account certain background knowledge. JCI can deal with different types of interventions (e.g., perfect, imperfect, stochastic, etc.) in a unified fashion, and does not require knowledge of intervention targets or types in case of interventional data. We explain how several well-known causal discovery algorithms can be seen as addressing special cases of the JCI framework, and we also propose novel implementations that extend existing causal discovery methods for purely observational data to the JCI setting. We evaluate different JCI implementations on synthetic data and on flow cytometry protein expression data and conclude that JCI implementations can considerably outperform state-of-the-art causal discovery algorithms.

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.