aiqbench analysis
This paper establishes a rigorous mathematical framework linking causality and utility through the value Causal Markov Condition (v-CMC), effectively generalizing Bellman recursion from linear chains to complex causal DAGs. By proving soundness for conditional value independence, it provides new theoretical tools for modularly transferring utility information across different contexts in advanced AI systems.
A Causal Markov Condition for Value
arXiv:2607.16717v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
arXiv:2607.16717 [stat.ML]
(or arXiv:2607.16717v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.16717 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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