Physical-Support Confidence Sets for Highly Coherent Dictionaries
2026-08-20 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how to accurately identify physical features from data when using learned dictionaries that can represent signals in multiple, possibly ambiguous ways. They develop a method that considers uncertainty in both the learned dictionary and the new data to find a reliable physical interpretation of the signal. Their approach helps avoid overprecise conclusions that aren't supported by the data by focusing only on plausible explanations. They also introduce a computational strategy called active endpoint bracketing to efficiently narrow down physical interpretations. Tests show their method balances accuracy and computational effort better than simpler approaches.
sparse pursuitdictionary learningcoherent dictionariesphysical-support inferenceminimax resolutionorientation-information scaleactive endpoint bracketingsparse representationsignal calibrationfinite-bank evaluation
Authors
Guan-Ju Peng
Abstract
Sparse pursuit after dictionary learning can yield a precise atom support even when its physical interpretation is not justified by the calibration data, especially for highly coherent dictionaries where alternative calibration-compatible dictionaries may assign different physical meanings to the same selected support. We develop resolution-aware physical-support inference that jointly accounts for uncertainty in the learned dictionary and in the representation of a deployment signal. Our cross-dictionary confidence correspondence retains calibration-compatible dictionaries and deployment-compatible sparse representations, then projects the surviving explanations onto physical-support space. For local coherent-atom classes with separation scale s, once the deployment data resolve the coherent-block explanation and its atom support, the minimax physical resolution from N calibration signals satisfies $δ_{\mathrm{opt}}(N,s)\asymp\min\{s,\frac{1}{\sqrt{N}s^2}\}$, with relative resolution governed by the orientation-information scale $Ns^6$. Deployment replication improves physical localization only when orientation changes cannot be absorbed by adjusting the active coefficients. For computation, we introduce active endpoint bracketing (AEB), an adaptive finite-bank procedure that evaluates only candidates that can still affect the physical report and otherwise safely coarsens or abstains. Finite-bank experiments, including a four-region synthetic application, show that a point-valued plug-in selector can be physically overprecise, whereas AEB avoids unsupported refinement with fewer candidate evaluations.