This paper proposes a causal independence principle for value -- the value Causal Markov Condition (v-CMC) -- and develops the conceptual and mathematical foundations of a"causal value theory"linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability-value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.
This work proposes bipartite graphical causal models (BGCMs), in which the structure of a system of equations is encoded by a bipartite graph with variable and equation nodes, and forms a Markov property in terms of a new graphical separation criterion (B-separation) that exploits the functional determinism inherent in...
We study causal discovery where each node is a random function. Previous studies on this topic rely on structural assumptions, e.g., linearity or non-linearity, and distributional assumptions, e.g., Gaussianity or non-Gaussianity. In contrast, we make use of covariance operators to avoid these assumptions. Under functi...
Probabilistic Causal Impact (PCI) builds on actual causality and on Pearl's notions of probability of necessity and sufficiency, but recasts the question of explainability as an estimation problem on a probabilistic causal model that is easily approximated via Monte Carlo.
R. Urbaniak, Sam Witty, Daniel Waxman et al.· 1 citation
The R package CausalQueries can be used to make, update, and query causal models defined on binary nodes. Users provide a causal statement of the form X -> M <- Y; M <-> Y which is interpreted as a structural causal model over a collection of binary nodes. Then CausalQueries allows users to (1) identify the set of prin...
Till Tietz, Lily Medina, G. Syunyaev et al.· Journal of Statistical Softw...· 1 citation
Recursive application of the law of total variance decomposes the marginal variance of an outcome into components attributed to explanatory variables and a residual component. The resulting decomposition depends on the chosen conditioning order, and its components do not in general have causal interpretations. We devel...
The coupling that keeps the direct effect estimable once contexts diverge is derived, with a closed form for its degradation, and it is shown that the mediated share on which a natural ranking is built is not a share under suppression.
Ajay Pravin Mahale· 0 citations
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