supervised_pca – Supervised PCA (Giglio-Xiu-Zhang 2025) – screen-then-PCA on a target panel.#

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

Function signature#

mf.functions.supervised_pca_transform(
    panel: pd.DataFrame,
    target: pd.Series,
    n_components: 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 supervised principal components (P). Clamped internally to the number of columns kept after correlation screening.

Returns#

pd.DataFrame — scalar result.

Behavior#

Two-stage supervised reduction:

  1. For each target column g, rank panel columns by univariate correlation with g and keep the top ⌊q · M⌋ (q ∈ (0, 1] hyperparameter; default 0.5);

  2. Run PCA on the screened sub-panel, returning P supervised components.

Refinement of Giglio-Xiu (2021) three-pass: screening makes the construction robust to weak factors and omitted-variable bias. Used as the asset-side stage of Rapach & Zhou (2025) Sparse Macro-Finance Factors for risk-premium estimation. Distinct from partial_least_squares (PLS uses covariance-maximising NIPALS over all columns; SPCA uses correlation-screened PCA on a sub-panel) and from scaled_pca (Huang-Jiang-Tu-Zhou 2022 weights every column; SPCA hard-screens).

Operational v0.9.1 dev-stage v0.9.0C-4. Hyperparams: n_components (= P; default 4), q (screening rate; default 0.5).

When to use

Cross-sectional asset-pricing factor extraction; weak-factor-robust supervised reduction; Rapach-Zhou (2025) replication.

When NOT to use

When the supervisory signal is dense (every panel column matters) – prefer scaled_pca or partial_least_squares.

In recipe context#

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

# Layer L3 recipe fragment
params:
  op: supervised_pca

References#

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

  • Giglio, Xiu & Zhang (2025) ‘Test Assets and Weak Factors’, Journal of Finance, forthcoming.

  • Giglio & Xiu (2021) ‘Asset Pricing with Omitted Factors’, Journal of Political Economy 129(7): 1947-1990.

  • Rapach & Zhou (2025) ‘Sparse Macro-Finance Factors’ working paper – §2.2 eqs. (5)-(8).