factorlasso 0.1.0

Sparse factor model estimation with sign-constrained LASSO, prior-centered regularisation, and hierarchical group LASSO (HCGL)

factorlasso

Sparse factor model estimation with sign-constrained LASSO, prior-centered regularisation, and hierarchical group LASSO (HCGL)

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Overview

factorlasso solves the sparse multi-output regression problem

$$Y_t = \alpha + \beta X_t + \varepsilon_t$$

where $\beta$ is $(N \times M)$, $\alpha$ is $(N \times 1)$ intercept, $Y_t$ is $(N \times 1)$, and $X_t$ is $(M \times 1)$, under:

• Sign constraints on individual coefficients (non-negative, non-positive, zero, or free)
• Prior-centered regularisation — penalise $|\beta - \beta_0|$ instead of $|\beta|$, shrinking toward domain-specific priors
• Group structure — Group LASSO with user-defined groups or automatic hierarchical clustering (HCGL)
• EWMA-weighted observations — exponential decay for non-stationary data
• NaN-aware estimation — validity masking handles variables with different observation lengths

After estimation, factorlasso assembles the consistent factor covariance decomposition

$$\Sigma_y = \beta,\Sigma_x,\beta^\top + D$$

where $\Sigma_x$ is the factor covariance and $D$ is diagonal idiosyncratic variance.

No existing Python package combines sign-constrained penalised regression with prior-centered shrinkage and integrated factor covariance assembly.

Installation

pip install factorlasso

Quick Start

import numpy as np, pandas as pd
from factorlasso import LassoModel, LassoModelType

# Simulate: Y = X @ beta_true.T + noise
np.random.seed(42)
T, M, N = 200, 3, 5
X = pd.DataFrame(np.random.randn(T, M), columns=['f0', 'f1', 'f2'])
beta_true = np.array([[1, 0, .5], [0, 1, 0], [.3, 0, 0], [0, .8, .2], [1, .5, 0]])
Y = pd.DataFrame(X.values @ beta_true.T + .1*np.random.randn(T, N),
                  columns=[f'y{i}' for i in range(N)])

model = LassoModel(model_type=LassoModelType.LASSO, reg_lambda=1e-4)
model.fit(x=X, y=Y)
print(model.coef_.round(2))       # β (N × M)
print(model.intercept_.round(4))  # α (N,)

Predict and Score (scikit-learn compatible)

y_hat = model.predict(X)  # Ŷ = α + X β'
r2 = model.score(X, Y)    # mean R² across response variables

Sign Constraints

# 1 = non-negative, -1 = non-positive, 0 = zero, NaN = free
signs = pd.DataFrame([[1, np.nan, 1], [np.nan, 1, 0], [1, 0, np.nan],
                       [np.nan, 1, 1], [1, 1, np.nan]],
                      index=Y.columns, columns=X.columns)

model = LassoModel(reg_lambda=1e-4, factors_beta_loading_signs=signs)
model.fit(x=X, y=Y)

Prior-Centered Regularisation

beta_prior = pd.DataFrame(beta_true, index=Y.columns, columns=X.columns)
model = LassoModel(reg_lambda=1e-2, factors_beta_prior=beta_prior)
model.fit(x=X, y=Y)  # shrinks toward beta_prior instead of zero

Hierarchical Clustering Group LASSO (HCGL)

model = LassoModel(
    model_type=LassoModelType.GROUP_LASSO_CLUSTERS,
    reg_lambda=1e-5, span=52,
)
model.fit(x=X, y=Y)
print(model.clusters)  # auto-discovered groups

Factor Covariance Assembly

from factorlasso import CurrentFactorCovarData, VarianceColumns
from factorlasso.ewm_utils import compute_ewm_covar

# Assemble Sigma_y = beta @ Sigma_x @ beta.T + D
sigma_y = CurrentFactorCovarData(
    x_covar=factor_covariance,
    y_betas=model.coef_,
    y_variances=diagnostics_df,
).get_y_covar()

API Summary

The API follows scikit-learn conventions: fit / predict / score.

Method	Description
model.fit(x, y)	Estimate α, β — returns self
model.predict(x)	Return Ŷ = α + X β'
model.score(x, y)	Return mean R²

Fitted attribute	Shape	Description
coef_	(N, M)	Factor loadings β
intercept_	(N,)	Intercept α
estimated_betas	(N, M)	Alias for coef_ (backward compat)
clusters_	(N,)	HCGL cluster labels

Estimation Methods

Method	LassoModelType	Penalty
LASSO	LASSO	$\lambda|\beta - \beta_0|_1$
Group LASSO	GROUP_LASSO	$\sum_g \lambda\sqrt{
HCGL	GROUP_LASSO_CLUSTERS	Same as Group LASSO with auto-clustering

All methods support sign constraints, prior-centered shrinkage, EWMA weighting, and NaN-aware estimation.

Applications

The methodology is domain-agnostic. Examples are provided for:

• Finance — Multi-asset factor models with sign-constrained betas and consistent covariance estimation (examples/finance_factor_model.py)
• Genomics — Gene expression driven by pathway activity factors with biological sign priors (examples/genomics_factor_model.py)

The same estimation problem (sparse factor loadings with sign priors and consistent covariance) appears in macro-econometrics, signal processing, and multi-task learning.

Dependencies

Only standard scientific Python:

• numpy ≥ 1.22
• pandas ≥ 1.4
• scipy ≥ 1.9
• cvxpy ≥ 1.3

Related Packages

Package	Key Difference
scikit-learn Lasso	No sign constraints, no multi-output Group LASSO
skglm	No sign constraints, no prior-centered shrinkage
abess	Best-subset selection (L0), not L1/Group L2
group-lasso	No sign constraints, no EWMA, no prior-centered

factorlasso is the only package that combines sign-constrained penalised regression, prior-centered shrinkage, HCGL clustering, and integrated factor covariance assembly.

References

Sepp A., Ossa I., Kastenholz M. (2026), "Robust Optimization of Strategic and Tactical Asset Allocation for Multi-Asset Portfolios", The Journal of Portfolio Management, 52(4), 86–120. Paper link

Citation

@software{sepp2026factorlasso,
  author = {Sepp, Artur},
  title = {factorlasso: Sparse Factor Model Estimation with Constrained LASSO in Python},
  year = {2026},
  url = {https://github.com/ArturSepp/factorlasso}
}

License

MIT — see LICENSE.