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2 stories in the last 24h

Probabilistic Linear Explanations

Researchers introduce a unified probabilistic explainability framework using sparse anchored linear models that outperforms LIME and MAPLE on relevance error.

The paper proposes probabilistic explanations based on sparse, anchored linear models applicable to both binary classification and continuous regression. It proves that minimizing relevance error for neural-network models is NP-hard and relates it to a tractable fidelity-error surrogate. Solutions are computed via a mixed integer programming formulation with provably optimal empirical solutions and a polynomial-time iterative hard thresholding algorithm with approximation guarantees. Empirical evaluations show lower relevance error than LIME and MAPLE while satisfying anchoring and sparsity constraints by construction.

arXiv cs.AI / cs.LG / cs.CL · 19h agoAI research

Fast Learning Rates for Physics-Informed Kernel Methods

Theoretical analysis proves finite-sample learning rates for physics-informed kernel estimators, showing differential observations can improve rates from n^-1/4 to n^-1/2.

The paper analyzes a physics-informed kernel estimator combining n value observations and m differential observations for a linear differential operator D, asking how much differential information improves prediction. The authors prove finite-sample bounds, supported by simulations, revealing a two-regime structure: when m is limited the rate depends jointly on n and m, and when m exceeds a problem-dependent threshold the rate saturates to the oracle rate. Examples in Sobolev spaces, including partial Laplacian constraints on the torus and gradient observations on bounded domains, illustrate improvements from the nonparametric n^-1/4 rate to the parametric n^-1/2 rate, plus physically consistent rates in a stronger norm.

arXiv cs.AI / cs.LG / cs.CL · 20h agoAI research