sliced_inverse_regression – sSUFF / Sliced inverse regression (scaled) – supervised dimension reduction (Huang-Jiang-Li-Tong-Zhou 2022).#

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Operational op under axis op, sub-layer L3_A_step_op, layer l3. Standalone callable: mf.functions.sliced_inverse_regression_transform.

Function signature#

mf.functions.sliced_inverse_regression_transform(
    panel: pd.DataFrame,
    target: pd.Series,
    n_components: int,
    n_slices: int,
) -> pd.DataFrame

Parameters#

name

type

default

constraint

description

panel

pd.DataFrame

—

—

Input panel. Each column is a variable; rows are time periods. Series is promoted to a single-column DataFrame internally.

target

pd.Series

—

—

Supervisory signal aligned to the panel index. Must share at least one index value with panel; raises ValueError if the intersection is empty.

n_components

int

3

>= 1

Number of SIR directions (effective rank of the between-slice covariance matrix).

n_slices

int

10

>= 2

Number of contiguous slices of the target distribution. Clamped internally to the number of aligned clean rows.

Returns#

pd.DataFrame — scalar result.

Behavior#

Supervised dimension reduction extending scaled_pca to non-linear y → X dependence. Pipeline: (1) standardise X; (2) optional column-wise predictive scaling (scaling_method = scaled_pca reuses the Huang-Zhou OLS-slope; marginal_R2 uses sign(β_j)·√R²_j; none skips); (3) sort rows by y and partition into n_slices H contiguous slices; (4) compute weighted between-slice covariance Σ_S = Σ_h (n_h/n) · m̄_h · m̄_h^⊤; (5) take the top-n_components eigenvectors as factor loadings; (6) project the full panel onto these directions. The sSUFF augmentation (Huang-Zhou-Tong 2022) recovers latent factors with higher correlation than plain SIR in the macro-panel regime where signals are sparse over predictors.

Defaults: n_components = 2, n_slices = 10, scaling_method = 'scaled_pca'. Requires a target_signal input port; temporal_rule is required and rejects full_sample_once.

When to use

Supervised factor extraction from macro panels with non-linear y → X structure; alternative to scaled_pca when the predictive direction is non-monotone.

When NOT to use

Very small T (need ≥ 5·n_slices observations after dropping NaN); strictly linear y → X relationship (scaled_pca is sufficient).

In recipe context#

Set params.op = "sliced_inverse_regression" in the relevant layer to activate this op within a recipe:

# Layer L3 recipe fragment
params:
  op: sliced_inverse_regression

References#

  • macroforecast design Part 2, L3: ‘feature engineering is a DAG of typed transforms; cascade-depth bounds the longest chain at cascade_max_depth.’

  • Huang, Jiang, Li, Tong & Zhou (2022) ‘Scaled PCA: A New Approach to Dimension Reduction’, Management Science 68(3): 1678-1695.

  • Fan, Xue & Yao (2017) ‘Sufficient forecasting using factor models’, Journal of Econometrics 201(2): 292-306.

  • Li (1991) ‘Sliced Inverse Regression for Dimension Reduction’, JASA 86(414): 316-327.