tlars-python

A Python port of the tlars R package for Terminating-LARS (T-LARS) algorithm.

Overview

The Terminating-LARS (T-LARS) algorithm is a modification of the Least Angle Regression (LARS) algorithm that allows for early termination of the forward selection process. This is particularly useful for high-dimensional data where the number of predictors is much larger than the number of observations.

This Python package provides a port of the original R implementation by Jasin Machkour, maintaining the same functionality while providing a more Pythonic interface. The Python port was created by Arnau Vilella (avp@connect.ust.hk).

Installation

The package is available on PyPI for Windows, macOS, and Linux:

pip install tlars

This is the recommended installation method as it will automatically install pre-built wheels for your platform with all required dependencies.

Usage

import numpy as np
from tlars import TLARS, generate_gaussian_data

# Generate some example data using the built-in function
n, p = 100, 20
X, y, beta = generate_gaussian_data(n=n, p=p, seed=42)

# Alternatively, create your own data
X = np.random.randn(n, p)
beta = np.zeros(p)
beta[:5] = np.array([1.5, 0.8, 2.0, -1.0, 1.2])
y = X @ beta + 0.5 * np.random.randn(n)

# Create dummy variables
num_dummies = p
dummies = np.random.randn(n, num_dummies)
XD = np.hstack([X, dummies])

# Create and fit the model
model = TLARS(XD, y, num_dummies=num_dummies)
model.fit(T_stop=3, early_stop=True)

# Get the coefficients
print(model.coef_)

# Get other properties
print(f"Number of active predictors: {model.n_active_}")
print(f"Number of active dummies: {model.n_active_dummies_}")
print(f"R² values: {model.r2_}")

# Plot the solution path
model.plot(include_dummies=True, show_actions=True)

Library Reference

TLARS Class

Constructor

TLARS(X=None, y=None, verbose=False, intercept=True, standardize=True, 
      num_dummies=0, type='lar', lars_state=None, info=True)

• X: numpy.ndarray - Real valued predictor matrix.
• y: numpy.ndarray - Response vector.
• verbose: bool - If True, progress in computations is shown.
• intercept: bool - If True, an intercept is included.
• standardize: bool - If True, the predictors are standardized and the response is centered.
• num_dummies: int - Number of dummies that are appended to the predictor matrix.
• type: str - Type of used algorithm (currently possible choices: 'lar' or 'lasso').
• lars_state: object - Previously saved TLARS state to resume from.
• info: bool - If True, information about the initialization is printed.

Methods

• fit(T_stop=None, early_stop=True, info=True): Fit the TLARS model.

  • T_stop: int - Number of included dummies after which the random experiments are stopped.
  • early_stop: bool - If True, then the forward selection process is stopped after T_stop dummies have been included.
  • info: bool - If True, informational messages are displayed during fitting.

• plot(xlabel="# Included dummies", ylabel="Coefficients", include_dummies=True, show_actions=True, col_selected="black", col_dummies="red", ls_selected="-", ls_dummies="--", legend_pos="best", figsize=(10, 6)): Plot the T-LARS solution path.

  • xlabel: str - Label for the x-axis.
  • ylabel: str - Label for the y-axis.
  • include_dummies: bool - If True, solution paths of dummies are added to the plot.
  • show_actions: bool - If True, marks for added variables are shown above the plot.
  • col_selected: str - Color of lines corresponding to selected variables.
  • col_dummies: str - Color of lines corresponding to dummy variables.
  • ls_selected: str - Line style for selected variables.
  • ls_dummies: str - Line style for dummy variables.
  • legend_pos: str - Position of the legend.
  • figsize: tuple - Figure size.

• get_all(): Returns a dictionary with all the results and properties.

Properties

• coef_: numpy.ndarray - The coefficients of the model.
• coef_path_: list - A list of coefficient vectors at each step.
• n_active_: int - The number of active predictors.
• n_active_dummies_: int - The number of active dummy variables.
• n_dummies_: int - The total number of dummy variables.
• actions_: list - The indices of added/removed variables along the solution path.
• df_: list - The degrees of freedom at each step.
• r2_: list - The R² statistic at each step.
• rss_: list - The residual sum of squares at each step.
• cp_: numpy.ndarray - The Cp-statistic at each step.
• lambda_: numpy.ndarray - The lambda-values (penalty parameters) at each step.
• entry_: list - The first entry/selection steps of the predictors.

Helper Functions

• generate_gaussian_data(n=50, p=100, seed=789): Generate synthetic Gaussian data for testing.
  • n: int - Number of observations.
  • p: int - Number of variables.
  • seed: int - Random seed for reproducibility.
  • Returns: tuple - (X, y, beta) where X is the design matrix, y is the response, and beta is the true coefficient vector.

License

This project is licensed under the GNU General Public License v3.0 (GPL-3.0).

Acknowledgments

The original R package tlars was created by Jasin Machkour. This Python port was developed by Arnau Vilella (avp@connect.ust.hk).