Input validation at the public API boundary

[jc-macdonald]

Summary

Add check_array / validate_data input validation at the public API boundary so errors surface early with clear messages.

Details

Much of the validation already exists deeper in the stack (validate_mask_compatibility in _sparsity.py, _validate_shapes in _rms.py, shape checks in _full_update.py). This issue surfaces those checks to the estimator boundary so users get clear errors instead of cryptic BLAS crashes.

VBPCA

• Add validate_data() or check_array() in fit(): enforce 2-D, numeric dtype, apply NaN policy via tags
• Validate n_components >= 1 and n_components <= min(n_features, n_samples) in fit()
• Guard against all-NaN or empty (0-row / 0-column) input — currently crashes deep in matrix ops
• Add n_features_in_ consistency check in transform() / inverse_transform()

Preprocessing classes

• Add 2-D enforcement in all fit() / transform() methods
• Add dtype checks (numeric for scalers, any for OHE)
• Add n_features_in_ consistency check in MissingAwareOneHotEncoder.transform()

What already exists (leverage, don't duplicate)

• _sparsity.validate_mask_compatibility() — mask/data shape and sparsity checking
• _rms._validate_shapes() — loadings/scores 2-D and dimension compatibility
• _full_update._safe_cholesky() — numerical safety
• _pca_full._validate_dense_mask_budget() — memory budget guard
• _remove_empty.remove_empty_entries() — strips empty rows/cols (but no guard for all-empty)

Depends on

• Issue: Inherit from sklearn BaseEstimator + TransformerMixin

Acceptance criteria

• VBPCA(n_components=5).fit(np.array([1,2,3])) raises clear ValueError (not 2-D)
• VBPCA(n_components=5).fit(np.array([["a","b"],["c","d"]])) raises clear TypeError (not numeric)
• VBPCA(n_components=0).fit(X) raises ValueError
• All-NaN input raises ValueError with message mentioning NaN
• Empty array raises ValueError

[jc-macdonald]

Additional scope: pre-centering warning for bias oscillation

When bias=1 (default) and the input data is not centered, the bias update can create a 2-cycle oscillation in RMS and noise variance. This is because:

1. The bias update uses err_mx from the previous iteration
2. Noise variance V oscillates (e.g. 0.091 ↔ 0.093), feeding back through the shrinkage formula: shrink = 1 / (1 + V / (N_obs * Vmu))
3. The oscillation prevents RMS plateau-based convergence from ever triggering

Pre-centering the data eliminates the oscillation entirely — even with bias=1, because the residual that the bias update corrects is near-zero.

Proposed validation

Add a warning at the VBPCA.fit() boundary when:

• bias=1 (or default)
• Input data has column means significantly different from zero (e.g. abs(mean) > 0.1 * std)

The warning should suggest pre-centering with MissingAwareStandardScaler or setting bias=0.

This fits naturally into the input validation work planned for this issue, alongside the dtype, shape, and NaN checks.

Evidence

See scripts/_rms_oscillation_trace.py for the full characterisation of the oscillation and its elimination by pre-centering.