approximate_press — PRESS by leave-one-out refitting

Group: Diagnostic · Registry tolerance: 1e-10

Description

Approximate-PRESS component selection (§29)

Registry note — R pls::plsr(validation='LOO', method='simpls', scale=FALSE)$validation$PRESS. Default pls4all path runs true LOO PRESS over the same SIMPLS kernel and matches R bit-for-bit; cfg.approximate_press_legacy = 1 falls back to the pre-0.97.4 Eastment-Krzanowski training-residual approximation.

Parameters

Name	Type	Default	Notes
max_components	int	6	registry benchmark cell value

Explanations

Bibliographic source

Allen, D. M. (1974). The relationship between variable selection and data augmentation and a method for prediction. Technometrics 16(1), 125–127. Verified primary link: https://doi.org/10.1080/00401706.1974.10489157.

Mathematical principle

The default path computes prediction residual error sums of squares by leaving out each observation, refitting PLS, and predicting the held-out row for every requested component count. This is direct LOO PRESS rather than a hat-matrix shortcut.

Appropriate uses

Selecting PLS component count from leave-one-out prediction error on small data sets.

Limits and validation

The default performs n refits for every component count and is expensive; legacy mode uses a constant k/n inflation, not individual hat diagonals.

Implementation

Cost scales with n refits per component count. The compatibility-only legacy branch avoids those refits with a constant k/n residual inflation; it does not calculate observation-specific leverage h_ii.

Sources and provenance

Current implementation: cpp/src/core/extra_pls.cpp.

API and bindings

C ABI (ABI 2): n4m_metrics_approximate_press_compute. Use the linked public header for the exact signature, configuration, and result handles.

Python: no current AST-verified public n4m re-export was found for this method. The linked C ABI above is the documented surface in this checkout.

R (source-verified): approximate_press(X, Y, max_components).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): approximate_press(X, Y, max_components).

The source signature has additional required inputs, so no example call is fabricated.

Registry parity references 📐

• 📐 ref.r_pls (R · r) — pls 2.8.5 · strict (rmse_rel ≤ 1e-10) — R pls::plsr(validation='LOO', method='simpls', scale=FALSE)$validation$PRESS. Default pls4all path runs true LOO PRESS over the same SIMPLS kernel and matches R bit-for-bit; cfg.approximate_press_legacy = 1 falls back to the pre-0.97.4 Eastment-Krzanowski training-residual approximation.

Benchmarks

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

Adaptive wall-clock per cell measured against full_matrix.csv. Only backends that implement this method are listed; libraries without the method are omitted.

Verdict  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = archived binding-harness result agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

Reference gate: strict — numeric equivalence (rmse_rel_tol ≤ 1e-10).

Rows tagged with 📐 are the canonical parity references for this method (declared in parity_timing.registry). C++ and external rows show reference parity; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.

1 thread

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	28.4 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	28.1 ms
pls4all.sklearn	✓ bind	28.1 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	24.7 ms🏆
pls4all.R.formula	✓ bind	25.5 ms
pls4all.R.mdatools	✓ bind	25.3 ms
pls4all.R.pls	✓ bind	25.7 ms
R · external
📐ref.r_pls	source	69.5 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	28.9 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	28.8 ms
pls4all.sklearn	✓ bind	28.8 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	24.9 ms🏆
pls4all.R.formula	✓ bind	25.2 ms
pls4all.R.mdatools	✓ bind	25.5 ms
pls4all.R.pls	✓ bind	25.4 ms
R · external
📐ref.r_pls	source	69.2 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-15	29.4 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	28.6 ms
pls4all.sklearn	✓ bind	28.9 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	24.5 ms🏆
pls4all.R.formula	✓ bind	25.0 ms
pls4all.R.mdatools	✓ bind	24.9 ms
pls4all.R.pls	✓ bind	25.2 ms
R · external
📐ref.r_pls	source	67.7 ms

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