🤖 AI Summary
This study investigates the fundamental structural limitations governing the predictive performance of machine learning–based decision systems, demonstrating that these constraints arise from intrinsic properties of the data-generating process rather than algorithmic choices. By integrating information-theoretic bounds (Fano’s and Cramér–Rao inequalities), models of interaction dependencies (Markov random fields and potential functions), and feedback-driven stochastic dynamical systems—including those incorporating large language model agents—the work establishes a unified analytical framework. This framework reveals how structural assumptions such as independence and ergodicity critically determine the validity of statistical inference. The analysis proves that the ultimate ceiling on predictive capability is dictated by the underlying data-generation mechanism, thereby providing a theoretical foundation for designing reliable decision systems that respect these inherent structural constraints.
📝 Abstract
Machine learning procedures are commonly evaluated in terms of predictive accuracy and computational efficiency. However, their achievable performance is fundamentally constrained by structural properties of the underlying data-generating process, which are formalized in terms of informational bounds. In this work we examine intrinsic limits of data-driven decision systems from an information-theoretic and interaction-based perspective. We analyze minimal achievable error in classification through Fano-type bounds and precision limits in parametric estimation via the Cramér-Rao inequality, emphasizing that such limits depend on the underlying model rather than on algorithmic sophistication alone. We further discuss how implicit assumptions, such as independence, ergodicity, and distributional stability, affect the validity of inferential procedures. Building on interaction-based modeling principles, we review typical frameworks such as Markov Random Fields and potential based representations for encoding dependence mechanisms. We also describe decision systems, including LLM-integrated agent architectures, as feedback-driven stochastic processes where state-dependent dynamics may induce emergent macroscopic behavior. This perspective highlights the importance of having adequate models for the data as a prerequi- site for expanding predictive capability, and situates algorithmic learning within the informational limits imposed by the models.