detectability bound analysis

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.

This paper investigates the fundamental detectability limits of propagative attacks in static graphs and temporal networks. Methodologically, it establishes a unified information-theoretic framework to characterize the critical signal-to-noise conditions for reliable anomaly detection under random graph and point-process models—specifically, Poisson and Hawkes processes. It is the first work to tightly match information-theoretic upper and lower bounds on detection performance across both model classes, yielding universal thresholds: a $k^2 chi^2$-based edge-signal accumulation metric for static graphs and the Kullback–Leibler information rate $I$ for temporal networks; moreover, it proves that the optimal detection delay is achieved by the CUSUM procedure. The analysis integrates non-backtracking spectral statistics, multivariate point-process modeling, and robust information-theoretic techniques. The theory yields explicit thresholds $c log n$ and $T I geq log n$, constructs near-optimal robust detectors, substantially improves detection power under low signal-to-noise ratios, and provides actionable guidelines for system parameter design.

This study addresses identifiability in linear stochastic state-space models used in ecology, distinguishing fundamental theoretical identifiability (arising from model structure) from practical identifiability (limited by data quality). Methodologically, it introduces a novel joint sufficient statistic—constructed from the spectral density of observed time series—that simultaneously captures both mean and noise variance parameters, thereby extending beyond conventional first-moment–based identifiability analysis. Leveraging dynamical systems theory and rigorous identifiability diagnostics, the work establishes theoretical identifiability for several canonical ecological models under full observation. It further demonstrates that estimation difficulties commonly encountered in practice stem not from structural unidentifiability but from low signal-to-noise ratios, sparse sampling, or unobserved latent variables. The results provide a theoretical benchmark and diagnostic framework for parameter inference in ecological modeling, clarifying when inferential challenges are intrinsic to model specification versus extrinsic to data constraints.

This work investigates the stability of continuous-time Kalman–Bucy filtering under stochastic sensing, where both the measurement matrix and noise covariance are random processes—inducing measurement dropouts and dynamic uncertainty. To address this, we propose a differential-entropy-based “clarity” metric and derive, for the first time, a closed-form upper bound on the expected estimation error covariance and a mesh-independent lower bound on the spatially averaged clarity. Our key innovation is the introduction of a composite sensing parameter that jointly characterizes sensor count, noise intensity, and sampling frequency—thereby revealing their fundamental trade-offs in estimation performance. The theoretical bounds are tight and empirically validated to approximate well even in discrete-time settings. Crucially, they avoid recursive computation, enabling efficient, interpretable pre-deployment design of sensor networks.

This paper addresses the problem of sequential anomaly detection in a multi-process dynamic system: normal processes remain perpetually in a zero (quiescent) state, whereas anomalous processes evolve their latent states over time according to a Markov chain; observations are obtained only by sequentially probing a subset of processes, and each probe’s outcome depends stochastically on the probed process’s current latent state. Departing from conventional i.i.d. observation assumptions, we introduce, for the first time, a hidden Markov model (HMM) into this sequential search framework. We propose ADHM—an adaptive probing algorithm that jointly models latent-state evolution and observation uncertainty via Bayesian belief updating and statistical evidence accumulation. We establish its asymptotic optimality and derive a fundamental oracle lower bound on detection delay. Simulation results demonstrate that, under strict false-alarm probability constraints, ADHM reduces the average detection time by 32% compared to state-of-the-art methods.

This study addresses the feasibility determination problem under subjective probability constraints within a finite set of alternative systems. The authors propose a statistical inference method that operates directly on Bernoulli simulation outputs, uniquely integrating multi-threshold subjective constraints with Bernoulli observations without relying on normal approximations. To handle extreme scenarios—such as when all systems are feasible or none are—the method incorporates two heuristic strategies that dynamically adjust thresholds during execution. The resulting batch-mean-independent testing algorithm maintains rigorous statistical validity while significantly outperforming existing approaches designed for normally distributed data. Empirical experiments demonstrate the method’s computational efficiency and robust adaptability across diverse problem settings.

This study addresses the reconstruction of high-dimensional dynamical system states by replacing a subset of spatial sensors with temporal measurements. The authors develop a theoretical framework grounded in prior whitening information operators, integrating Fisher information analysis, delay-map injectivity, and spectral separation in dynamical modeling to establish a general spatiotemporal information exchange theorem. This theorem precisely characterizes the necessary and sufficient conditions for reducing sensor count while preserving a prescribed fraction of spatial information. For both linear and nonlinear systems, the work provides the first explicit upper bounds on the required length of temporal history and demonstrates the existence of an information ceiling. Exact history-length bounds are derived for contractive systems, spectrally separated unitary systems, and simultaneously diagonalizable dissipative systems. Numerical experiments confirm the discriminative power of delay embeddings and the predictive efficacy of local Fisher information.

This work addresses the remote tracking problem under heterogeneous sensors, where both sampling cost and communication delay coexist. The authors propose a belief-state-based dynamic request scheduling method that models the problem as a continuous-state partially observable Markov decision process (POMDP) by constructing a sufficient statistic combining the joint Markov source state and the age of incorrect information. For the first time, this approach jointly optimizes the average age of incorrect information and sampling cost. Innovatively integrating model predictive control with watermarking-based trust calibration (MPC-WTC) and reinforcement learning (RL-MPC), the method enables efficient decision-making while handling partial observability. Numerical experiments demonstrate that the proposed scheme significantly reduces the weighted total cost, confirming its superiority over existing approaches.