Data-driven Sensor Placement for Predictive Applications: A Correlation-Assisted Attribution Framework (CAAF)

Anomaly detection in multivariate time series is a central challenge in industrial monitoring, as failures frequently arise from complex temporal dynamics and cross-sensor interactions. While recent deep learning models, including graph neural networks and Transformers, have demonstrated strong empirical performance, most approaches remain primarily correlational and offer limited support for causal interpretation and root-cause localization. This study introduces a causally-constrained probabilistic forecasting framework which is a Causally Guided Transformer (CGT) model for multivariate time-series anomaly detection, integrating an explicit time-lagged causal graph prior with deep sequence modeling. For each target variable, a dedicated forecasting block employs a hard parent mask derived from causal discovery to restrict the main prediction pathway to graph-supported causes, while a latent Gaussian head captures predictive uncertainty. To leverage residual correlational information without compromising the causal representation, a shadow auxiliary path with stop-gradient isolation and a safety-gated blending mechanism is incorporated to suppress non-causal contributions when reliability is low. Anomalies are identified using negative log-likelihood scores with adaptive streaming thresholding, and root-cause variables are determined through per-dimension probabilistic attribution and counterfactual clamping. Experiments on the ASD and SMD benchmarks indicate that the proposed method achieves state-of-the-art detection performance, with F1-scores of 96.19% on ASD and 95.32% on SMD, and enhances variable-level attribution quality. These findings suggest that causal structural priors can improve both robustness and interpretability in detecting deep anomalies in multivariate sensor systems.

Cyber-physical system (CPS) forecasting models depend on sensor streams with noisy, biased, missing, or temporally misaligned readings, yet standard forecasting evaluation often selects models by nominal error without showing whether they remain robust under such faults. We introduce SensorFault-Bench, a shared CPS-grounded sensor-fault stress-test protocol for evaluating forecasting architectures and robustness-improvement methods, and an operational taxonomy organizing the method comparison. Across four real-world datasets and eight scored scenarios governed by a standardized severity model, it reports worst-scenario degradation, clean mean squared error (MSE), and worst-scenario fault-time MSE, separating relative robustness from absolute error. A disjoint fault-transfer split lets explicit fault-training methods train on adjacent fault families while evaluation uses separate benchmark scenarios. Empirically, forecasting architectures favored by clean MSE can degrade sharply under faults, and clean-MSE rankings can disagree with worst-scenario fault-time error rankings. Chronos-2, the evaluated zero-shot foundation-model representative, matches or trails the last-value naive forecaster in clean MSE on the two single-target datasets and has the largest worst-scenario degradation on ETTh1 and Traffic, where all channels are forecast targets. For the evaluated robustness-improvement method set, paired deltas show selective degradation reductions: projected gradient descent adversarial training and randomized training lead where value faults dominate observed degradation, while fault augmentation leads where availability faults dominate. SensorFault-Bench provides open-source code, documented data access, and reproduction and extension guides, so new datasets, architectures, and robustness-improvement methods can be evaluated under the same CPS sensor-fault robustness protocol.

State estimation is a critical task in scientific, engineering and control applications. Since the reliability of reconstructions depends on the number and position of sensors, optimal sensor placement (OSP) is essential in scenarios where measurements are sparse and expensive. Classical OSP approaches rely on Gaussian assumptions and are consequently unable to account for the complex distributions encountered in many real-world systems. Generative-model-based reconstruction using sensor guided diffusion posterior sampling (DPS) has emerged as a promising technique for reconstructing states from highly complex distributions. However, existing sensor-selection methods either require unrealistically many sensors or emulate classical OSP, creating a mismatch between modern recovery models with classical OSP tools motivating the need for fundamentally new ideas towards OSP that match the recent advances made in powerful recovery models. We introduce a distribution-free sensor placement framework based on the Christoffel function: a mathematical formulation of optimal sampling and recovery guarantees for posterior sampling with arbitrary sensors and signal distributions, from which we derive a new OSP strategy with non-asymptotic bounds on the number of sensors needed for recovery. We develop Christoffel-DPS, with offline and online variants, instantiating Christoffel sampling for generative models. Christoffel-DPS outperforms Gaussian OSP baselines and existing generative-model placement methods, validating that distribution-free sensing is both theoretically principled and practically superior. The framework is model-agnostic; we demonstrate its application to a range of unconditional DPS and flow-matching models on structurally non-Gaussian benchmarks, showing the efficacy of Christoffel-DPS in low sensor budget regimes.