mv_residual_pca — MULTIVAR `identifiability` op

• データ種: matrix → table

• 呼び出し: import fullseye as fs; fs.ledger.mv_residual_pca(R=None, noise_sigma=None, n_perm=100, seed=0) -> 'dict' (実装を直接呼ぶなら import sensitivity; sensitivity.mv_residual_pca(R=None, noise_sigma=None, n_perm=100, seed=0) -> 'dict'、台帳から引くなら opsmultivar.get("mv_residual_pca"))

使い方

Do the residuals of a fitted model still carry structure? PCA of a residual matrix vs. noise.

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.

詳しい使い方ガイド

• design_of_experiments ファミリガイド

参考(サンプルデータ・文献)

• サンプルデータカタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• sensitivity_tour — py -3.11 examples/sensitivity_tour.py

型が繋がる次の op(`table` を入力に取れる)

—

同カテゴリ(`identifiability`)

mv_confounding

*Provenance: sensitivity.py — MULTIVAR operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

mv_residual_pca — MULTIVAR identifiability op

使い方