# `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_estimators_rosa_fit`. Reference: CRAN `multiblock 0.8.10`. R roxygen note (`methods_extra.R::rosa_fit`): > ROSA — Response-Oriented Sequential Alternation. > @param n_components Integer. Number of latent components. > @param block_sizes Integer vector. Per-block feature counts for multi-block PLS. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export MATLAB header (`bindings/matlab/+pls4all/rosa.m`): ```text 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** ::::{tab-set} :class: pls4all-bindings :::{tab-item} C ABI · libn4m :sync: c :class-label: lang-c ```c /* C ABI — libn4m */ n4m_context_t* ctx = n4m_context_create(); n4m_config_t* cfg = n4m_config_create(); n4m_method_result_t* res = NULL; n4m_estimators_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); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python 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"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import ROSARegression mdl = ROSARegression(n_components=2, block_sizes=None) mdl.fit(X, y) y_hat = mdl.predict(X_test) ``` ::: :::{tab-item} R · pls4all_method() :sync: r-dispatcher :class-label: lang-r ```r 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. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- rosa_fit(X, Y, n_components, block_sizes) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab 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); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("rosa", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_numpy`** (python · python) — `numpy` 2.2.6 · 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`](../benchmarks/overview.md). 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`](../benchmarks/methodology.md)). 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. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
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
::: :::{tab-item} 3 threads :sync: threads-3
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
::: :::{tab-item} 10 threads :sync: threads-10
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](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)