Master Quantile Regression with Adaptive Lasso in Python using asgl

What is Quantile Regression?

Quantile regression models the τ‑th conditional quantile of a response variable Y given predictors X. It solves

\min_{\beta}\;\sum_{i=1}^{n}\rho_{\tau}(y_i - x_i^{\top}\beta)

where ρ_τ(u)=τ·u if u≥0 and (τ‑1)·u otherwise. By varying τ∈(0,1) the method provides estimates for any quantile, allowing analysis of the entire conditional distribution rather than only the mean.

Why use Quantile Regression instead of OLS?

Ordinary least squares (OLS) minimizes squared error and therefore estimates the conditional mean. When data contain outliers, heteroscedasticity, or skewed distributions, the mean can be misleading. Quantile regression fits separate models for lower, median, and upper parts of the distribution (e.g., τ=0.1, 0.5, 0.9), revealing how different quantiles respond to covariates.

High‑dimensional settings

In fields such as genomics or image analysis the number of predictors p often exceeds the number of observations n. Standard quantile‑regression tools lack built‑in penalization (Lasso, Group Lasso, etc.) for p≫n, which is required for variable selection and stable estimation.

The asgl Python package

asgl

provides a unified, scikit‑learn‑compatible API for fitting linear, quantile, and logistic regression models with a wide range of penalties: Lasso, Ridge, Group Lasso, Sparse Group Lasso, Adaptive Lasso, and their adaptive variants. The implementation works efficiently for both low‑ and high‑dimensional data.

Installation

pip install asgl

Example: Median (τ=0.5) quantile regression with Adaptive Lasso

The script below generates synthetic data (n=100, p=200, 10 informative features), splits it, fits a penalized quantile regression model, and evaluates mean absolute error.

# Generate synthetic data
import numpy as np
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_absolute_error
from asgl import Regressor

X, y = make_regression(
    n_samples=100,
    n_features=200,
    n_informative=10,
    noise=0.1,
    random_state=42
)

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

# Define and train the quantile regression model with adaptive Lasso
model = Regressor(
    model='qr',            # quantile regression
    penalization='alasso',# adaptive Lasso penalty
    quantile=0.5           # median
)

model.fit(X_train, y_train)

# Predict and evaluate
pred = model.predict(X_test)
mae = mean_absolute_error(y_test, pred)
print(f'Mean Absolute Error: {mae:.3f}')

Changing the quantile argument to any value in (0, 1) fits the corresponding quantile. The penalization='alasso' option first computes adaptive weights from an initial fit and then applies a weighted L1 penalty, which is effective for variable selection when p≫n.

Key capabilities of asgl

Scalability: Efficient algorithms (coordinate descent and proximal gradient) handle datasets with thousands of predictors.

Flexibility: Supports linear, quantile, and logistic models; multiple penalty families (Lasso, Ridge, Group Lasso, Sparse Group Lasso, Adaptive variants) via a single Regressor class.

Integration with scikit‑learn: The estimator follows the scikit‑learn interface, enabling use in pipelines, cross‑validation, and hyper‑parameter search.

Source code and documentation are available at:

https://github.com/alvaromc317/asgl