SparseRegression

A Python package for sparse linear regression using mixed-integer optimization. Given a feature matrix and a sparsity budget k, it finds the best subset of at most k features that minimises the sum of squared residuals.

Installation

pip install sparseregression

Note: The solver IPOPT must be installed separately and its executable path passed at runtime.

Quick Start

import sklearn.datasets as sd
import sparseregression.linear as sl

# Load example data
data = sd.load_boston()
X, y = data.data, data.target

# Fit sparse regression with at most 10 non-zero coefficients
results, coefficients = sl.sparse_linear_regression(
    X, y, k=10, executable="~/Ipopt/ipopt"
)

print(coefficients)

API Reference

sparseregression.linear.sparse_linear_regression

sparse_linear_regression(X, y, k, engine='ipopt', executable='~', verbose=False)

Solves the sparse linear regression problem via mixed-integer programming:

$$\min_{\beta,, z} \sum_i \left(y_i - X_i \cdot \beta\right)^2 \quad \text{s.t.} \quad \sum_j z_j \leq k,; -Mz_j \leq \beta_j \leq Mz_j,; z_j \in {0,1}$$

Parameter	Type	Description
X	ndarray	Feature matrix of shape (n, p)
y	ndarray	Target vector of length n
k	int	Maximum number of non-zero coefficients
engine	str	Optimisation solver name (default: 'ipopt')
executable	str	Path to solver executable (default: '~')
verbose	bool	Print solver output (default: False)

Returns: (results, coefficients) — solver result object and a list of regression coefficients.

License

Distributed under the MIT License.