Dongmei Chen

Jiachen Li, Shihao Li, Jiamin Xu et al.

Data-Enabled Predictive Control (DeePC) has emerged as a powerful framework for controlling unknown systems directly from input-output data. For nonlinear systems, recent work has proposed selecting relevant subsets of data columns based on geometric proximity to the current operating point. However, such proximity-based selection ignores the control objective: different reference trajectories may benefit from different data even at the same operating point. In this paper, we propose a datamodel-based approach that learns a context-dependent influence function mapping the current initial trajectory and reference trajectory to column importance scores. Adapting the linear datamodel framework from machine learning, we model closed-loop cost as a linear function of column inclusion indicators, with coefficients that depend on the control context. Training on closed-loop simulations, our method captures which data columns actually improve tracking performance for specific control tasks. Experimental results demonstrate that task-aware selection substantially outperforms geometry-based heuristics, particularly when using small data subsets.

Shihao Li, Jiachen Li, Dongmei Chen

Data attribution methods identify which training examples are responsible for a model's predictions, but their sensitivity to distributional perturbations undermines practical reliability. We present a unified framework for certified robust attribution that extends from convex models to deep networks. For convex settings, we derive Wasserstein-Robust Influence Functions (W-RIF) with provable coverage guarantees. For deep networks, we demonstrate that Euclidean certification is rendered vacuous by spectral amplification -- a mechanism where the inherent ill-conditioning of deep representations inflates Lipschitz bounds by over $10{,}000\times$. This explains why standard TRAK scores, while accurate point estimates, are geometrically fragile: naive Euclidean robustness analysis yields 0\% certification. Our key contribution is the Natural Wasserstein metric, which measures perturbations in the geometry induced by the model's own feature covariance. This eliminates spectral amplification, reducing worst-case sensitivity by $76\times$ and stabilizing attribution estimates. On CIFAR-10 with ResNet-18, Natural W-TRAK certifies 68.7\% of ranking pairs compared to 0\% for Euclidean baselines -- to our knowledge, the first non-vacuous certified bounds for neural network attribution. Furthermore, we prove that the Self-Influence term arising from our analysis equals the Lipschitz constant governing attribution stability, providing theoretical grounding for leverage-based anomaly detection. Empirically, Self-Influence achieves 0.970 AUROC for label noise detection, identifying 94.1\% of corrupted labels by examining just the top 20\% of training data.