Decision making under uncertain conditions has been well studied when uncertainty can only be considered at the associative level of information. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rationally making choices using associative information. We provide here a previous result from Pearl and show that it can be considered as a causal version of the von Neumann-Morgenstern Theorem; furthermore, we consider the case when the true causal mechanism that controls the environment is unknown to the decision maker and propose a causal version of the Savage Theorem. As applications, we argue how previous optimal action learning methods for causal environments fit within the Causal Savage Theorem we present thus showing the utility of our result in the justification and design of learning algorithms; furthermore, we define a Causal Nash Equilibria for a strategic game in a causal environment in terms of the preferences induced by our Causal Decision Making Theorem.
@cite_43 provides a framework for defining the notions of cause and effect in terms of decision theoretical concepts, such as states and outcomes and gives a theoretical basis for graphical description of causes and effects, such as causal influence diagrams ( @cite_54 ). Heckerman gave an elegant definition of causality, but did not addressed how to actually make choices using causal information.
@cite_43 @cite_54
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We present a definition of cause and effect in terms of decision-theoretic primitives and thereby provide a principled foundation for causal reasoning. Our definition departs from the traditional view of causation in that causal assertions may vary with the set of decisions available. We argue that this approach provides added clarity to the notion of cause. Also in this paper, we examine the encoding of causal relationships in directed acyclic graphs. We describe a special class of influence diagrams, those in canonical form, and show its relationship to Pearl's representation of cause and effect. Finally, we show how canonical form facilitates counterfactual reasoning. The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X,Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: methods based on Additive Noise Models (ANMs) and Information Geometric Causal Inference (IGCI). We present the benchmark CAUSEEFFECTPAIRS that consists of data for 100 different causee ffect pairs selected from 37 data sets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the method based on Additive Noise Models that has originally been proposed by (2009), which obtains an accuracy of 63 ± 10 and an AUC of 0.74 ± 0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method. One of the key uses of causes is to explain why things happen. Explanations of specific events, like an individual's heart attack on Monday afternoon or a particular car accident, help assign responsibility and inform our future decisions. Computational methods for causal inference make use of the vast amounts of data collected by individuals to better understand their behavior and improve their health. However, most methods for explanation of specific events have provided theoretical approaches with limited applicability. In contrast we make two main contributions: an algorithm for explanation that calculates the strength of token causes, and an evaluation based on simulated data that enables objective comparison against prior methods and ground truth. We show that the approach finds the correct relationships in classic test cases (causal chains, common cause, and backup causation) and in a realistic scenario (explaining hyperglycemic episodes in a simulation of type 1 diabetes). 1. Introduction to probabilities, graphs, and causal models 2. A theory of inferred causation 3. Causal diagrams and the identification of causal effects 4. Actions, plans, and direct effects 5. Causality and structural models in the social sciences 6. Simpson's paradox, confounding, and collapsibility 7. Structural and counterfactual models 8. Imperfect experiments: bounds and counterfactuals 9. Probability of causation: interpretation and identification Epilogue: the art and science of cause and effect.