Probabilistic Theories of Causation

This is the first test in establishing causation. It asks the simple question: "But for the defendant's actions, would the harm have occurred?" If the answer is yes (the harm would have happened anyway), the defendant is not the factual cause. If the answer is no (the harm would not have happened without the defendant's actions), the defendant is the factual cause.. For example A shoots B, and B dies. But for A's action (shooting), B would not have died. Therefore, A is the factual cause of B's death. A commonly used test for factual causation is the "But For" Test, as seen in R v White (1910). In this case, the defendant put poison in his mother's drink, but she died of a heart attack before the poison took effect. The court held that the defendant was not the factual cause of death because the harm (death) would have happened regardless of his actions.

This text is an unpublished Introduction into the process theory of causation – not causation in general. However, not much knowledge of causation theories is a prerequisite. Instead of a rough overview as one would get in a “handbook” of causation theories, I go into more detail of the main aspects so that you know the actual theory. In this spirit, it is dense and a bit technical – intended for philosophy (of the sciences) students. Comments and criticism always appreciated, drop me an e-mail.
I hope you enjoy the text!

The process theory of causation represents one major account amongst all relevant causal theories today. Its main idea is to give up on the “traditional view” of causation, spelled out roughly by “event C causes event E” where the causal relation is then analyzed in terms of concepts involving for example necessity, counterfactual dependence, or constant conjunction. Rather, “processes” transmit causal influence even over long distances, sometimes interacting with other processes. The main proponent of this idea was Wesley C. Salmon, and his version of it can be deemed the core of the concept.

The sciences frequently endorse generalizations that hold only ceteris paribus—“all else
being equal” or “excluding all interfering factors”—raising the challenge of explicating such
clauses. On the one hand, they risk reducing generalizations to empty tautologies, asserting
that F is G when F is G. On the other hand, removing the clause renders the generalizations
false. This challenge, known as Lange’s dilemma, is addressed in this paper through an
evidentialist theory of epistemic justification. The solution argues that the proper scope and
content of generalizations are determined by the evidence from which they arise. This
evidentialist account not only resolves the dilemma but also unifies and explains alternative
solutions proposed in the literature. In addition, by prioritizing the evidential basis (matter) of
generalizations over their linguistic formulation (form), this framework aligns with broader
trends in the philosophy of science, advocating for a research program that explicitly and
self-consciously embraces a non-formal approach for understanding scientific reasoning.

Address of institutions at which work was carried out: Division of Physiotherapy Education and Department of Philosophy, University of Nottingham, Nottingham, United Kingdom; Department of Economics and Resource Management, Norwegian University of Life Sciences, Ås, Norway; University Hospital of North Norway, the Department of Work and Environmental Medicine, Tromsø, Norway; Department of Philosophy, University of Tromsø, Norway.

The pervasive adoption of Artificial Intelligence (AI) models in the modern information society, requires counterbalancing the growing decision power demanded to AI models with risk assessment methodologies. In this paper, we consider the risk of discriminatory decisions and review approaches for discovering discrimination and for designing fair AI models. We highlight the tight relations between discrimination discovery and explainable AI, with the latter being a more general approach for understanding the behavior of black boxes. SUMMARY: 1. AI risks. – 2. Discrimination discovery and fairness in AI. – 3. Explainable AI. – 4. Closing the gap. – 5. Conclusion.

How can we teach machine learning to identify causal patterns in data?  This book explores the very notion of “causality”, identifying from a naturalistic and evolutionary perspective how living systems deal with causal relationships. At the same time, using this knowledge to identify the best ways to apply such biological models in machine learning scenarios.

One of the more fundamental challenges for AI experts is to design machines that can understand the world, identifying the basic rules that govern reality.  Statistics are powerful and fundamental for this process, but they are only one of the necessary tools. Counterfactual thinking is the other part of the necessary process that will help machines to become intelligent. This book explains the paths that can lead to algorithmic causality.

It is essential reading for those who are not afraid of thinking at the interface of various academic disciplines or fields (AI, machine learning, philosophy,  neuroscience, anthropology, psychology, computer sciences), and who are interested in the analysis of causal thinking and the ways in which cognitive systems (natural or artificial) can act in order to understand their environment.

Professor Vallverdú is currently working on biomimetic cognitive architectures and multicognitive systems. His research has explored two main areas: epistemology and cognition. Since his early Ph.D. research on epistemic controversies, he has analyzed several aspects of computational epistemology.

His latest research has focused on the causal challenges of machine learning techniques, particularly deep learning. One of his most promising advances is statistics meets causal graph reasoning (via Directed Acyclic Graphs), which still has several conceptual paths that need to be explored and identified. Counterfactual reasoning is a fundamental part of these open debates, which are under the analysis of Prof. Vallverdú.

His current research is supported as part of the following projects: GEHUCT and ICREA Acadèmia.

We study the problem of tracing actual causes, i.e. given an event e, we seek to fully explain why that event happened. This problem was articulated by David Lewis in his work on causal explanations [Lewis, 1986a]. We address the problem by defining the causal history of the explanandum event. Informally, the causal history traces the immediate causes of the explanandum event, the causes of those causes, and so on to produce a full explanation. While related, this problem differs from the problem of determining actual causes where the focus is on identifying individual events that contributed to causing the explanandum event. The central technical contributions of this paper are (a) a formal definition of causal history in the structural equations model; and (b) a theorem that establishes the complexity of the decision problem for causal histories. In addition, we show that our definition cleanly explains a battery of problematic examples from the actual cause literature.

This Article amends an important theory by Mark Grady on nondurable precaution (Grady, 1988). We present a formal model on (non)durable precautions which focuses on memory costs, and add three insights to the literature. First, we argue that, under current tort doctrine, the interaction between nondurable precautions and mental costs create a self-sustaining expansion of tort law. Because the risk of liability creates additional interference effects, tort law perpetuates the expansion of awards. Second, we demonstrate that socially excessive suits are more likely to be filed in the event of nondurable technology. This is because a plaintiff does not consider the increase of interference costs as a private cost, when initiating a lawsuit. Third, while new harm-reducing technology likely increases accident rates, it also raises the ratio of trial costs to harm, thus leaving undetermined the overall effect of new technology on the rate of litigation.

Atypical chronic myeloid leukemia (aCML) is a rare BCR-ABL1 negative clonal disorder, which belongs to the myelodysplastic/myeloproliferative group. This disease is characterized by recurrent somatic mutations in several genes including SETBP1, ASXL1 and ETNK1, as well as high genetic heterogeneity, thus posing a great therapeutic challenge. The clinical prognosis for aCML is poor, with a median overall survival of 18 months after diagnosis, and no established standards of care exist for its treatment. The dissection of the molecular processes underlying aCML leukemogenesis could therefore result decisive in ameliorating the prognosis for aCML. With the aim to provide a comprehensive genomic characterization of aCML and to link the detected alterations with the clinical course of the disease, we applied a high-throughput sequencing strategy to 43 aCML samples, including whole-exome sequencing and RNA sequencing. Our study confirms ASXL1 and SETBP1 as the most frequently mutated gene...

The aim of this note is to analyze to the extent to which causation requirement is consistent with the provision of efficient incentives to potential tortfeasors. Specifically, we study focus on the role of the well-known “but for” or “sine qua non” test. According to the “but for” test, an action is a “sine qua non” condition of an accident if, given the state of the world, the accident would not have occurred had another action been taken. Thus, the ”but for” test seems to isolate something we care a lot about in explaining events and in assessing responsability: the idea that the defendant’s act makes a difference. Reaching beyond the sole ”metaphysical” interest of this causation concept, the theoretical analysis developed in this paper investigates to what extent the “but for” causation requirement has a deterrence effect on the behavior of potential tortfeasors, particularly in situations where the tort system may provide sub-optimal incentives. Already Pigou (1920) emphasized...

A theory of necessary and sufficient conditions is presented, as well as a theory of necessary and sufficient causes and effects, viewed as a particular case of the former. Ambiguities of the terms 'condition' and 'necessary condition' are explored, and a neutral meaning for 'condition' is favoured. The relation between necessary and sufficient conditions and implicative conditionals (including counterfactuals) is also discussed. Two problems of counterfactual theories of causal explanation are indicated, concerning (i) how to account for causes that are not necessary and (ii) how to interpret the counterfactual from the negation of the effect to the negation of the cause. Application of the theory of necessary and sufficient conditions to Euler's explanation of the Königsberg bridge problem is discussed. The theory of necessary and sufficient causes and effects is then applied to the flagpole shadow explanation and to two biological explanations, one involving a sufficient but not necessary cause and the other a necessary but not sufficient cause. Causes that are neither sufficient nor necessary are also recognized. Finally, a probabilistic approach to causes that are either not sufficient or not necessary is explored, including its application to examples of such cases.

Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is further complicated by many theoretical issues, such as the I-equivalence among different structures. In this work, we focus on a specific subclass of BNs, named Suppes-Bayes Causal Networks (SBCNs), which include specific structural constraints based on Suppes' probabilistic causation to efficiently model cumulative phenomena. Here we compare the performance, via extensive simulations, of various state-of-the-art search strategies, such as local search techniques and Genetic Algorithms, as well as of distinct regularization methods. The assessment is performed on a large number of simulated datasets from topologies with distinct levels of complexity, various sample size and different rates of errors in the data. Among the main results, we show that the introduction of Suppes' constraints dramatically improve the inference accuracy, by reducing the solution space and providing a temporal ordering on the variables. We also report on trade-offs among different search techniques that can be efficiently employed in distinct experimental settings.

Data mining is an important technology for extracting useful patterns from large amount of data. Two major prevalent issues in data mining are privacy violation and discrimination. Discrimination arises when people are given unfair treatment on the basis of their sensitive features like gender, race, religion etc. Types of discrimination are direct and indirect discrimination. Direct discrimination consists of rules based on sensitive attributes like religion, race, community etc. Indirect discrimination occurs when decisions are based on non sensitive attributes which are closely related to sensitive attributes. Automated data collection and data mining techniques such as classification rule mining are used for making automated decisions by decision support systems. These systems are used for personnel selection, loan granting etc. If the training data sets are biased with respect to the sensitive features, discriminatory decisions may occur. Antidiscrimination techniques including...

Conventional wisdom in tort law holds that an injurer's negligence, a product design defect, and a victim's contributory negligence should all be decided by weighing the costs and benefits of the relevant activity. In multiple-victim accidents, the current paradigm maintains that liability should be determined by comparing aggregate costs with aggregate benefits. However, this aggregate liability paradigm-adopted by courts, scholars and the Restatement (Third) of Torts-fails to account for the natural differences that exist between tort victims. When victims are heterogeneous with regard to their expected harm or costs of precaution-as they typically are in real lifebasing liability on aggregate amounts may be incorrect, and generate overdeterrence in some cases and under-deterrence and dilution of liability in other. A new paradigm for liability in multiple-victim torts is, therefore, needed. This Article suggests a novel and superior liability regime for multiple-victim accidents, which forsakes the traditional economic distinction between precaution costs and expected harm. The new liability regime combines disaggregated liability analyses with indemnification for efficient investment in precautions and a small "bonus," given as an incentive to exercise efficient care.

In this paper I put forward a probabilistic analysis of the notion of cause. I argue that for an event A to be a cause of an event C is for A to have some positive causal impact on C. I provide a probabilistic analysis of the notion of some positive causal impact, mainly in terms of the concept of a strict increaser, and argue that, roughly, for A to have some positive causal impact on C is for there to be a strict increaser for A and C. I relate the notion of some positive causal impact to my account of counterfactuals. Finally, I contrast my account with the theories of D. Lewis and W. Salmon. 1. Lewis-Exposition Lewis's theory of cause is a counterfactual theory. 1 Lewis's conception of counterfactuals (Lewis, 1973) was originally developed for a deterministic world. 2 On this account, one orders possible worlds by the relation of intuitive overall similarity, and the counterfactual is (non-vacuously) true iff the consequent is true in all the antecedent-worlds in some sphere (centered around the world in which the counterfactual is assessed, and which includes some antecedentworlds). This theory faced robust counterexamples, in particular counterfactuals which have generally been taken to come out true on Lewis's theory, though they shouldn't. One, for instance, is the false counterfactual 'Had I been at least an inch taller than I am, I would have been exactly an inch taller.'The most notorious counterexample involves the counterfactual 'Had Nixon pushed the nuclear button, there would have been no nuclear blast'. 3 These counterfactuals are patently false, but come out true on Lewis's theory, one should think, since there are antecedent-worlds in which the consequent is true which are more intuitively similar to the actual world than the antecedent-worlds in which the consequent is false. Lewis consequently modified his original theory by abandoning the reliance on intuitive overall similarity, and moved to a conception of weights and priorities for similarity (Lewis, 1979) 4 on which the overall similarity relation is not

Mainstream economic analysis of Tort Law assumes that efficiency cannot be formally assured by allocating liability according to causal apportioning. In this paper we will present some ways to escape from the full scope of this claim. We start by reviewing the standard conception of causality in the economic analysis of Tort Law, to show how some underlying assumptions influence the currently held view on the relation between causal apportioning and efficiency. Then, we revisit those assumptions to see how plausible they actually are. In the light of this discussion we introduce an alternative framework of causal reasoning in Tort Law. We will show how our model yields a way of allocating liability in terms of a causal apportioning rule. The outcomes obtained through this procedure are closer to efficiency than those prescribed by the mainstream.

Atypical chronic myeloid leukemia (aCML) is a BCR-ABL1-negative clonal disorder, which belongs to the myelodysplastic/ myeloproliferative group. This disease is characterized by recurrent somatic mutations in SETBP1, ASXL1 and ETNK1 genes, as well as high genetic heterogeneity, thus posing a great therapeutic challenge. To provide a comprehensive genomic characterization of aCML we applied a high-throughput sequencing strategy to 43 aCML samples, including both whole-exome and RNA-sequencing data. Our dataset identifies ASXL1, SETBP1, and ETNK1 as the most frequently mutated genes with a total of 43.2%, 29.7 and 16.2%, respectively. We characterized the clonal architecture of 7 aCML patients by means of colony assays and targeted resequencing. The results indicate that ETNK1 variants occur early in the clonal evolution history of aCML, while SETBP1 mutations often represent a late event. The presence of actionable mutations conferred both ex vivo and in vivo sensitivity to specific inhibitors with evidence of strong in vitro synergism in case of multiple targeting. In one patient, a clinical response was obtained. Stratification based on RNA-sequencing identified two different populations in terms of overall survival, and differential gene expression analysis identified 38 significantly overexpressed genes in the worse outcome group. Three genes correctly classified patients for overall survival.

Atypical chronic myeloid leukemia (aCML) is a BCR-ABL1-negative clonal disorder, which belongs to the myelodysplastic/ myeloproliferative group. This disease is characterized by recurrent somatic mutations in SETBP1, ASXL1 and ETNK1 genes, as well as high genetic heterogeneity, thus posing a great therapeutic challenge. To provide a comprehensive genomic characterization of aCML we applied a high-throughput sequencing strategy to 43 aCML samples, including both whole-exome and RNA-sequencing data. Our dataset identifies ASXL1, SETBP1, and ETNK1 as the most frequently mutated genes with a total of 43.2%, 29.7 and 16.2%, respectively. We characterized the clonal architecture of 7 aCML patients by means of colony assays and targeted resequencing. The results indicate that ETNK1 variants occur early in the clonal evolution history of aCML, while SETBP1 mutations often represent a late event. The presence of actionable mutations conferred both ex vivo and in vivo sensitivity to specific inhibitors with evidence of strong in vitro synergism in case of multiple targeting. In one patient, a clinical response was obtained. Stratification based on RNA-sequencing identified two different populations in terms of overall survival, and differential gene expression analysis identified 38 significantly overexpressed genes in the worse outcome group. Three genes correctly classified patients for overall survival.

Atypical chronic myeloid leukemia (aCML) is a BCR-ABL1-negative clonal disorder, which belongs to the myelodysplastic/ myeloproliferative group. This disease is characterized by recurrent somatic mutations in SETBP1, ASXL1 and ETNK1 genes, as well as high genetic heterogeneity, thus posing a great therapeutic challenge. To provide a comprehensive genomic characterization of aCML we applied a high-throughput sequencing strategy to 43 aCML samples, including both whole-exome and RNA-sequencing data. Our dataset identifies ASXL1, SETBP1, and ETNK1 as the most frequently mutated genes with a total of 43.2%, 29.7 and 16.2%, respectively. We characterized the clonal architecture of 7 aCML patients by means of colony assays and targeted resequencing. The results indicate that ETNK1 variants occur early in the clonal evolution history of aCML, while SETBP1 mutations often represent a late event. The presence of actionable mutations conferred both ex vivo and in vivo sensitivity to specific inhibitors with evidence of strong in vitro synergism in case of multiple targeting. In one patient, a clinical response was obtained. Stratification based on RNA-sequencing identified two different populations in terms of overall survival, and differential gene expression analysis identified 38 significantly overexpressed genes in the worse outcome group. Three genes correctly classified patients for overall survival.

Atypical chronic myeloid leukemia (aCML) is a rare BCR-ABL1 negative clonal disorder, which belongs to the myelodysplastic/myeloproliferative group. This disease is characterized by recurrent somatic mutations in several genes including SETBP1, ASXL1 and ETNK1, as well as high genetic heterogeneity, thus posing a great therapeutic challenge. The clinical prognosis for aCML is poor, with a median overall survival of 18 months after diagnosis, and no established standards of care exist for its treatment. The dissection of the molecular processes underlying aCML leukemogenesis could therefore result decisive in ameliorating the prognosis for aCML. With the aim to provide a comprehensive genomic characterization of aCML and to link the detected alterations with the clinical course of the disease, we applied a high-throughput sequencing strategy to 43 aCML samples, including whole-exome sequencing and RNA sequencing. Our study confirms ASXL1 and SETBP1 as the most frequently mutated gene...

As decision-making increasingly relies on Machine Learning (ML) and (big) data, the issue of fairness in datadriven Artificial Intelligence (AI) systems is receiving increasing attention from both research and industry. A large variety of fairness-aware machine learning solutions have been proposed which involve fairness-related interventions in the data, learning algorithms and/or model outputs. However, a vital part of proposing new approaches is evaluating them empirically on benchmark datasets that represent realistic and diverse settings. Therefore, in this paper, we overview real-world datasets used for fairness-aware machine learning. We focus on tabular data as the most common data representation for fairness-aware machine learning. We start our analysis by identifying relationships between the different attributes, particularly w.r.t. protected attributes and class attribute, using a Bayesian network. For a deeper understanding of bias in the datasets, we investigate the interesting relationships using exploratory analysis.

According to Antoine Augustine Cournot, chance events are the result of the intersection between independent causal chains. This coincidental notion of chance is not a new one, but-as Cournot remarks-it comes from Saint Thomas Aquinas, Boethius, and more probably from Jean de La Placette. Such a conception of chance phenomena seems to be very important, not only because it is closely related to the Principle of Causality, but also since it grounds Cournot's theory of objective probability. Starting from Martin's work (Probabilités et Critique Philosophique selon Cournot. Vrin, Paris, 1996), the main attempt of this survey is to endorse the idea that Cournot's coincidental notion of hasard is objective, that is it is ontic (i.e. it comes from some real feature of the world) and it does not dependin some sense-on our degree of knowledge. In order to do that, a central role in the discussion will be given to the meaning of the independence between the intersecting causal chains and to Cournot's conception of causation.

Mainstream economic analysis of tort law takes for granted that efficiency cannot be reached by allocating liability according to causal apportioning. In this paper we will present some ways to escape from the full scope of this claim. We start by reviewing the standard conception of causality in the economic analysis of tort law, to show how some underlying assumptions influence the currently held view on the relation between causal apportioning and efficiency. Then, we revisit those assumptions to see how plausible they actually are. ...

In Le Hasard et La Nécessité, one of the most influential books in the story of Biology, Jacques Monod presents his non-teleological evolutionary biological theory. Starting from the idea – which someone ascribes to Democritus – that everything existing in the Universe is the fruit of chance and necessity, Monod maintains that each alteration in the DNA happens by chance. Hence, chance – according to Monod – is the origin of every novelty happening in the biosphere, and then the driving force of the evolution. But which conception of chance is at the core of Monod's non-teleological theory? According to Monod, chance events are the result of the intersection between different processes that belong to independent causal chains. These accidental events are called “absolute coincidences”. Despite its importance, this coincidental notion of chance is quite neglected in contemporary literature and it seems to eschew a precise definition. This study takes into proper consideration thi...

proposed a new counterfactual analysis of causation. We argue that this – the PCA-analysis – is incorrect. In section 1, we explain David Lewis’s first counterfactual analysis of causation, and a problem that led him to propose a second. In section 2 we explain the PCA-analysis, advertised as an improvement on Lewis’s later account. We then give counterexamples to the necessity (section 3) and sufficiency (section 4) of the PCA-analysis. 1. Lewis’s two analyses and the problem of late preemption Following Lewis, say that event e counterfactually depends on event c iff, if c had not occurred, e would not have occurred. In his 1973, Lewis proposed that c causes e iff e is related to c by the ancestral of the relation of counterfactual dependence. (Following Ganeri et al., say that e is a descendant of c, and c is an ancestor of e, iff Lewis’s analysans holds.) However, this analysis does not give a necessary condition for c to cause e, as figure 1 shows: c

I would like to thank Louis Kaplow, Steven Shavell, and an anonymous referee for their comments and to acknowledge the financial support from the John M. Olin Foundation. In the words of Prosser, "A failure to fence a hole in the ice plays no part in causing the death of runaway horses which could not have been halted if the fence had been there, though of course making the hole did play a part. A failure to have a lifeboat ready is not a cause of the death of a person who sinks without trace immediately upon falling into the ocean, though taking the person out to sea was a cause. The failure to install a proper fire escape on a hotel is no cause of the death of a man suffocated in bed by smoke. The omission of crossing signals by an approaching train is of no significance when an automobile driver runs into the sixty-eighth car. The presence of a railroad embankment may be no cause of the inundation of the plaintiff's land by a cloudburst which would have flooded it in any case." (footnotes omitted). W. Page Keeton et al., Prosser and Keeton on Torts, § 41 (5th ed. 1984). 2 Injurers will also have incentives to take care inasmuch as additional care reduces the amount of damages for which they are liable. For simplicity, this analysis will assume that care affects only the likelihood of, but not the magnitude of, damages in accidents. Thus, negligence will have caused either all or none of the damages in a particular accident. The results of this analysis depend, however, in no way on this assumption. See also Restatement (Second) of Torts, § 454 (1964).

Social discrimination is considered illegal and unethical in the modern world. Such discrimination is often implicit in observed decisions' datasets, and anti-discrimination organizations seek to discover cases of discrimination and to understand the reasons behind them. Previous work in this direction adopted simple observational data analysis; however, this can produce biased results due to the effect of confounding variables. In this paper, we propose a causal discrimination discovery and understanding approach based on propensity score analysis. The propensity score is an effective statistical tool for filtering out the effect of confounding variables. We employ propensity score weighting to balance the distribution of individuals from protected and unprotected groups w.r.t. the confounding variables. For each individual in the dataset, we quantify its causal discrimination or favoritism with a neighborhood-based measure calculated on the balanced distributions. Subsequently...

The discovery of discriminatory bias in human or automated decision making is a task of increasing importance and difficulty, exacerbated by the pervasive use of machine learning and data mining. Currently, discrimination discovery largely relies upon correlation analysis of decisions records, disregarding the impact of confounding biases. We present a method for causal discrimination discovery based on propensity score analysis, a statistical tool for filtering out the effect of confounding variables. We introduce causal measures of discrimination which quantify the effect of group membership on the decisions, and highlight causal discrimination/favoritism patterns by learning regression trees over the novel measures. We validate our approach on two real world datasets. Our proposed framework for causal discrimination has the potential to enhance the transparency of machine learning with tools for detecting discriminatory bias both in the training data and in the learning algorithms.

Mainstream economic analysis of tort law takes for granted that efficiency cannot be reached by allocating liability according to causal apportioning. In this paper we will present some ways to escape from the full scope of this claim. We start by reviewing the standard conception of causality in the economic analysis of tort law, to show how some underlying assumptions influence the currently held view on the relation between causal apportioning and efficiency. Then, we revisit those assumptions to see how plausible they actually are. ...

In The Chances of Explanation, Paul Humphreys presents a metaphysical analysis of causation. In this paper, I argue that this analysis is flawed. Humphreys' model of Causality incorporates three completeness requirements, I show that these completeness requirements, when applied to the world, force us to take causally irrelevant factors to be causally relevant. On this basis, I argue that Humphreys' analysis should be rejected.

In some recent works, negligence-based liability has been severely criticized. It has been argued that negligence-based liability does not form a convincing basis for liability assignment. Causation-based liability has been proposed as an alternative basis of liability determination. Parisi and Fon (2004) have studied the efficiency properties of the causal apportionment of liability. The authors have shown that when care levels as well as activity levels of the parties affect the causation of an accident, causation based liability does not provide efficient incentives for the parties. In this paper, we assume the activity levels to be constant. Under this assumption, we have demonstrated the existence of liability rules that are efficient and at the same time 'consistent' with the requirement of causation liability. In addition, it is shown that under these rules the equilibrium outcome is unique. The analysis has been undertaken in a very general framework.

Discrimination discovery from data consists in the extraction of discriminatory situations and practices hidden in a large amount of historical decision records. We discuss the challenging problems in discrimination discovery, and present, in a unified form, a framework based on classification rules extraction and filtering on the basis of legally-grounded interestingness measures. The framework is implemented in the publicly available DCUBE tool. As a running example, we use a public dataset on credit scoring.

Address of institutions at which work was carried out: Division of Physiotherapy Education and Department of Philosophy, University of Nottingham, Nottingham, United Kingdom; Department of Economics and Resource Management, Norwegian University of Life Sciences, Ås, Norway; University Hospital of North Norway, the Department of Work and Environmental Medicine, Tromsø, Norway; Department of Philosophy, University of Tromsø, Norway.

Social discrimination is considered illegal and unethical in the modern world. Such discrimination is often implicit in observed decisions' datasets, and anti-discrimination organizations seek to discover cases of discrimination and to understand the reasons behind them. Previous work in this direction adopted simple observational data analysis; however, this can produce biased results due to the effect of confounding variables. In this paper, we propose a causal discrimination discovery and understanding approach based on propensity score analysis. The propensity score is an effective statistical tool for filtering out the effect of confounding variables. We employ propensity score weighting to balance the distribution of individuals from protected and unprotected groups w.r.t. the confounding variables. For each individual in the dataset, we quantify its causal discrimination or favoritism with a neighborhood-based measure calculated on the balanced distributions. Subsequently...

The discovery of discriminatory bias in human or automated decision making is a task of increasing importance and difficulty, exacerbated by the pervasive use of machine learning and data mining. Currently, discrimination discovery largely relies upon correlation analysis of decisions records, disregarding the impact of confounding biases. We present a method for causal discrimination discovery based on propensity score analysis, a statistical tool for filtering out the effect of confounding variables. We introduce causal measures of discrimination which quantify the effect of group membership on the decisions, and highlight causal discrimination/favoritism patterns by learning regression trees over the novel measures. We validate our approach on two real world datasets. Our proposed framework for causal discrimination has the potential to enhance the transparency of machine learning with tools for detecting discriminatory bias both in the training data and in the learning algorithms.

This paper integrates Pearl's seminal work on probability and causality with that of Shafer. Using the language of CP-logic, it transposes Pearl's analysis of interventions and counterfactuals to the semantic context of Shafer's probability trees. This gives us definitions that work not on the level of random variables, but on the level of Humean events. There are some tangible benefits to our approach: we can elegantly handle counterfactuals in the context of cyclic causal relations, and are able to consider interventions that are both more fine-grained and more elaborate than Pearl's.

Abstract: Data mining is most necessary technology for extracting useful knowledge and valuable data in large collection of information. There having some negative social aspects about data processing such as invasion, potential privacy, and potential discrimination. The latter consist of affair or unequally treating people on the basis of their cast, religion or specific community. Automatic knowledge collection and data processing techniques such as classification rule mining have paved the way to making automated decision, like loan granting or denial, insurance or premium computation etc. If the given data sets having with discriminatory (sensitive) attributes like gender, race, religion, community, etc .For this reason, antidiscrimination techniques including discrimination discovery and prevention are introduce in data processing .Discrimination either direct or indirect .Here ,we tried for solution to prevent discrimination in data processing and will try to bring new techniq...

On David Lewis's original analysis of causation, c causes e only if c is linked to e by a chain of distinct events such that each event in the chain (counterfactually) depends on the former one. But, this requirement precludes the possibility of late pre-emptive causation, of causation by fragile events, and of indeterministic causation. Lewis proposes three different strategies for accommodating these three kinds of cases, but none of these turn out to be satisfactory. I offer a single analysis of causation that resolves these problems in one go but which respects Lewis's initial insights. One distinctive feature of my account is that it accommodates indeterministic causation without resorting to probabilities.

Social discrimination is considered illegal and unethical in the modern world. Such discrimination is often implicit in observed decisions' datasets, and anti-discrimination organizations seek to discover cases of discrimination and to understand the reasons behind them. Previous work in this direction adopted simple observational data analysis; however, this can produce biased results due to the effect of confounding variables. In this paper, we propose a causal discrimination discovery and understanding approach based on propensity score analysis. The propensity score is an effective statistical tool for filtering out the effect of confounding variables. We employ propensity score weighting to balance the distribution of individuals from protected and unprotected groups w.r.t. the confounding variables. For each individual in the dataset, we quantify its causal discrimination or favoritism with a neighborhood-based measure calculated on the balanced distributions. Subsequently...

Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel theoretical framework called CAPRESE (CAncer PRogression Extraction with Single Edges) to reconstruct such models based on the notion of probabilistic causation defined by Suppes. We consider a general reconstruction setting complicated by the presence of noise in the data due to biological variation, as well as experimental or measurement errors. To improve tolerance to noise we define and use a shrinkage-like estimator. We prove the correctness of our algorithm by showing asymptotic convergence to the correct tree under mild constraints on the level of noise. Moreover, on synthetic data, we show that our approach outperforms the state-of-the-art, that it is efficient even with a relatively small number of samples and that its performance quickly converges to its asymptote as the number of samples increases. For real cancer datasets obtained with different technologies, we highlight biologically significant differences in the progressions inferred with respect to other competing techniques and we also show how to validate conjectured biological relations with progression models.

It is a common opinion that chance events cannot be understood in causal terms. Conversely, according to a causal view of chance, intersections between independent causal chains originate accidental events, called “coincidences.” The present paper takes into proper consideration this causal conception of chance and tries to shed new light on it. More precisely, starting from Hart and Honoré’s view of coincidental events (Hart and Honoré in  Causation in the Law. Clarendon Press, Oxford, 1959), this paper furnishes a more detailed account on the nature of coincidences, according to which coincidental events are hybrids constituted by ontic (physical) components, that is the intersections between independent causal chains, plus epistemic aspects; where by “epistemic” we mean what is related, in some sense, to knowledge: for example, access to information, but also expectations, relevance, significance, that is psychological aspects. In particular, this paper investigates the role of t...

Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is further complicated by many theoretical issues, such as the I-equivalence among different structures. In this work, we focus on a specific subclass of BNs, named Suppes-Bayes Causal Networks (SBCNs), which include specific structural constraints based on Suppes' probabilistic causation to efficiently model cumulative phenomena. Here we compare the performance, via extensive simulations, of various state-of-the-art search strategies, such as local search techniques and Genetic Algorithms, as well as of distinct regularization methods. The assessment is performed on a large number of simulated datasets from topologies with distinct levels of complexity, various sample size and different rates of errors in the data. Among the main results, we show that the introduction of Suppes' constraints dramatically improve the inference accuracy, by reducing the solution space and providing a temporal ordering on the variables. We also report on trade-offs among different search techniques that can be efficiently employed in distinct experimental settings.

The emergence and development of cancer is a consequence of the accumulation over time of genomic mutations involving a specific set of genes, which provides the cancer clones with a functional selective advantage. In this work, we model the order of accumulation of such mutations during the progression, which eventually leads to the disease, by means of probabilistic graphic models, i.e., Bayesian Networks (BNs). We investigate how to perform the task of learning the structure of such BNs, according to experimental evidence, adopting a global optimization meta-heuristics. In particular, in this work we rely on Genetic Algorithms, and to strongly reduce the execution time of the inference-which can also involve multiple repetitions to collect statistically significant assessments of the data-we distribute the calculations using both multi-threading and a multi-node architecture. The results show that our approach is characterized by good accuracy and specificity; we also demonstrate its feasibility, thanks to a 84× reduction of the overall execution time with respect to a traditional sequential implementation.

Several diseases related to cell proliferation are characterized by the accumulation of somatic DNA changes, with respect to wildtype conditions. Cancer and HIV are two common examples of such diseases, where the mutational load in the cancerous/viral population increases over time. In these cases, selective pres sures are often observed along with competition, co-operation and parasitism among distinct cellular clones. Recently, we presented a mathematical framework to model these phenomena, based on a combination of Bayesian inference and Suppes’ theory of probabilistic causation, depicted in graphical structures dubbed Suppes-Bayes Causal Networks (SBCNs). SBCNs are generative probabilistic graphical models that recapitulate the potential ordering of accumulation of such DNA changes during the progression of the disease. Such models can be inferred from data by exploiting likelihood-based model-selection strategies with regularization. In this paper we discuss the theoretical fou...

Motivation: We introduce TRONCO (TRanslational ONCOlogy), an open-source R package that implements the state-of-the-art algorithms for the inference of cancer progression models from (epi)genomic mutational profiles. TRONCO can be used to extract population-level models describing the trends of accumulation of alterations in a cohort of cross-sectional samples, e.g., retrieved from publicly available databases, and individual-level models that reveal the clonal evolutionary history in single cancer patients, when multiple samples, e.g., multiple biopsies or single-cell sequencing data, are available. The resulting models can provide key hints in uncovering the evolutionary trajectories of cancer, especially for precision medicine or personalized therapy. Availability: TRONCO is released under the GPL license, it is hosted in the Software section at http://bimib.disco.unimib.it/ and archived also at bioconductor.org. Contact: tronco@disco.unimib.it

Models of cancer progression provide insights on the order of accumulation of genetic alterations during cancer development. Algorithms to infer such models from the currently available mutational profiles collected from different cancer patiens (cross-sectional data) have been defined in the literature since late 90s. These algorithms differ in the way they extract a graphical model of the events modelling the progression, e.g., somatic mutations or copy-number alterations. TRONCO is an R package for TRanslational ONcology which provides a serie of functions to assist the user in the analysis of cross sectional genomic data and, in particular, it implements algorithms that aim to model cancer progression by means of the notion of selective advantage. These algorithms are proved to outperform the current state-of-the-art in the inference of cancer progression models. TRONCO also provides functionalities to load input cross-sectional data, set up the execution of the algorithms, asse...