identifiability op• Data kinds: matrix → table
• Call: import fullseye as fs; fs.ledger.mv_residual_pca(R=None, noise_sigma=None, n_perm=100, seed=0) -> 'dict' (implementation को सीधे call करना हो तो import sensitivity; sensitivity.mv_residual_pca(R=None, noise_sigma=None, n_perm=100, seed=0) -> 'dict', registry से लेना हो तो opsmultivar.get("mv_residual_pca"))
क्या fitted model के residuals में अब भी संरचना है? residual matrix का PCA बनाम noise।
> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।
R is (observations x variables) — e.g. one row per image, one column per pixel or feature, holding measured minus simulated. It is not centred: a bias common to every observation is itself a structure the model lacks.
A component counts as structural when its singular value exceeds the noise edge:
• with noise_sigma (e.g. the temporal noise from an EMVA 1288 characterisation): the largest singular value of an n x p matrix of i.i.d. noise is about sigma (sqrt(n) + sqrt(p)) (Marchenko-Pastur edge), used as the threshold;
• without it: permutation parallel analysis (Buja & Eyuboglu 1992) — each column is shuffled independently n_perm times, which keeps every column's distribution but destroys structure shared across columns, and component i must beat the 95th percentile of the shuffled i-th singular values. (It cannot see a structure that lives inside single columns, e.g. a constant bias column — use noise_sigma for that.)
Returns the singular values, the threshold(s), n_structural, the share of the residual energy in the structural components, and their loadings (reshape a loading to the image shape to see *where* the model is wrong) and scores.
• design_of_experiments family guide
• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।
• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।
• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।
• sensitivity_tour — py -3.11 examples/sensitivity_tour.py
table को input के रूप में लेते हैं)—
identifiability)*Provenance: sensitivity.py — MULTIVAR operator registry. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.