rosa — ROSA (Response-Oriented Sequential Alternation)

Group: Multi-block / cross-modal · Registry tolerance: 1e-06

Description

ROSA — Response-Oriented Sequential Alternation (§19)

From the pls4all.sklearn.ROSARegression docstring:

Response-Oriented Sequential Alternation (Liland & Næs 2016).

Registry note — Canonical multiblock ROSA (Liland, Næs & Indahl 2016). Both references implement the canonical formulation; pls4all matches them bit-for-bit (max_abs < 1e-6) for single-target Y. The R reference centers multi-target Y incorrectly (recycles colMeans(y) rather than broadcasting), so multi-target parity is intentionally evaluated against the NumPy reference.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

block_sizes

—

None

Sequence of contiguous block widths defining the X-block partition (columns of X).

n_targets

int

1

registry benchmark cell value

n_blocks

int

3

registry benchmark cell value

Explanations

Bibliographic source

Liland, K. H. & Næs, T. (2016). Response-oriented sequential alternation: a fast multiblock regression algorithm. Journal of Chemometrics 30(11), 651–662.

Mathematical principle

ROSA is a forward-greedy multi-block PLS: at each component extraction step, it tries one new component from every block and keeps the block whose new component most reduces residual variance in \(\mathbf{y}\). The component sequence is therefore data-driven rather than pre-specified by the user.

This auto-attribution makes ROSA a strong default when the analyst has no prior on which block matters most: the block budget is allocated dynamically. ROSA is also much faster than SO-PLS for large block counts because it adds one component per iteration rather than refitting an inner PLS per block.

Output includes the block-attribution vector — the sequence of block indices selected — which is the main interpretive artefact: it tells you which block contributed which component, in order.

Implementation

n4m_rosa_fit. Reference: CRAN multiblock 0.8.10.

MATLAB header (bindings/matlab/+pls4all/rosa.m):

pls4all.rosa  Response-Oriented Sequential Alternation (Liland & Næs 2016).

Usage

Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in benchmarks.parity_timing.registry. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN pls package (plsr, pcr, mvr) and for the mdatools::pls(x, y, ...) matrix idiom — those tabs appear only on the methods that have a meaningful equivalence.

pls4all bindings

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_rosa_fit(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res);
/* … read coefficients / mask / scores via */
/* n4m_method_result_get_double_matrix / vector / scalar … */
n4m_method_result_destroy(res);
n4m_config_destroy(cfg);
n4m_context_destroy(ctx);

import pls4all
from pls4all._methods import rosa_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = rosa_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import ROSARegression
mdl = ROSARegression(n_components=2, block_sizes=None)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("rosa", X, y,
                      n_components = 4L, params = list(n_targets = 1L, n_blocks = 3L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.rosa(X, y, 4);
% see header of bindings/matlab/+pls4all/rosa.m for full
% parameter surface:
%   res = rosa(X, Y, n_components, block_sizes)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("rosa", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 ref.python_numpy (python · python) — numpy 2.3.5 · strict (rmse_rel ≤ 1e-06) — Canonical multiblock ROSA in NumPy (Liland, Næs & Indahl 2016). Reproduces R multiblock::rosa(canonical=TRUE) exactly for single-target Y; for q >= 2 it uses proper column-mean centering and diverges from R multiblock because that package recycles colMeans(y) incorrectly. pls4all matches this NumPy reference for q == 1 at IEEE round-off.

  • 📐 ref.r_multiblock (R · r) — multiblock 0.8.10 · strict (rmse_rel ≤ 1e-06) — R multiblock::rosa 0.8.10 (Liland, Næs & Indahl 2016). ROSA’s greedy block-selection-per-component may diverge from pls4all’s ordering — tolerance widened.

Benchmarks

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 = pls4all binding 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-06).

Rows tagged with 📐 are the canonical parity references for this method (declared in parity_timing.registry). C++ and external rows show reference parity; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band.

BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 2e-167.07 ms
Python · pls4all
pls4all.python✓ bind2.41 ms
pls4all.sklearn✓ bind2.56 ms
R · pls4all
pls4all.R✓ bind5.46 ms
pls4all.R.formula✓ bind6.38 ms
pls4all.R.mdatools✓ bind6.80 ms
pls4all.R.pls✓ bind6.68 ms
Python · external
📐ref.python_numpysource1.43 ms🏆
R · external
📐ref.r_multiblock⇄ +1e-152.9 s
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 2e-161.24 ms🏆
Python · pls4all
pls4all.python✓ bind1.36 ms
pls4all.sklearn✓ bind1.42 ms
R · pls4all
pls4all.R✓ bind3.82 ms
pls4all.R.formula✓ bind4.80 ms
pls4all.R.mdatools✓ bind5.17 ms
pls4all.R.pls✓ bind4.86 ms
Python · external
📐ref.python_numpysource6.48 ms
R · external
📐ref.r_multiblock⇄ +1e-151.8 s
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 2e-161.33 ms🏆
Python · pls4all
pls4all.python✓ bind1.99 ms
pls4all.sklearn✓ bind1.42 ms
R · pls4all
pls4all.R✓ bind4.13 ms
pls4all.R.formula✓ bind4.17 ms
pls4all.R.mdatools✓ bind23.1 ms
pls4all.R.pls✓ bind15.6 ms
Python · external
📐ref.python_numpysource6.60 ms
R · external
📐ref.r_multiblock⇄ +1e-152.2 s

See also: benchmark overview · methods index · interactive dashboard