AcceleratedCVonMLR_Python

AcceleratedCVonMLR_Python is a Python module for approximate cross-validation for multinomial logistic regression with L1-penalty.

This is a free software, you can redistribute it and/or modify it under the terms of the GNU General Public License, version 3 or above. See LICENSE.txt for details.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

INSTALL

• Compile from sourse

git clone https://github.com/T-Obuchi/AcceleratedCVonMLR_python.git
cd AcceleratedCVonMLR_python
python setup.py install

• currentry, pip installation is not supported yet.

DESCRIPTION

Using estimated weight vectors wV given the feature data X and the class Ycode for multinomial logistic regression penalized by L1 norm, this program computes and returns an approximate leave-one-out estimator (LOOE) and its standard error of predictive likelihood. All required modules are in the "accelerated_cv_on_mlr" package. Note that this program itself does not contain any solver to obtain wV. Please use other distributed programs for the purpose.

Requirement

• NumPy

  • the modules use NumPy arrays
  • URL: https://github.com/numpy/numpy

• glmnet_py

  • sample notebook uses glmnet_python module for logistic regression to get weight vector wV
  • URL: https://github.com/bbalasub1/glmnet_python

• Matplotlib

  • sample notebook uses Matplotlib module for the result visualization
  • URL: https://github.com/matplotlib/matplotlib

USAGE

multinomial case

For multinomial logistic regression with Np (>2) classes,

import accelerated_cv_on_mlr as acv
[LOOE,ERR] = acv.acv_mlr(wV, X, Ycode, Np)

• Arguments and Returns

  • Arguments:

    • wV: weight vectors (p, N)-shape np.float64 array
    • X: input feature matrix (M, N)-shape np.float64 array
    • Ycode: class representative binary matrix (M, p)-shape np.int64 array
    • Np: number of classes

  • Returns:

    • LOOE: Approximate value of the leave-one-out estimator
    • ERR: Approximate standard error of the leave-one-out estimator

binomial case

For binomial logistic regression (logit model),

import accelerated_cv_on_mlr as acv
[LOOE,ERR] = acv.acv_logit(w, X, Ycode)

• Arguments and Returns

  • Arguments:
    • w: weight vector ((1,N)-shape np.float64 array)
    • X: input feature matrix ((M, N)-shape np.float64 array)
    • Ycode: binary matrix representing the class to which the corresponding feature vector belongs ((M, 2)-shape np.int64 array)
  • Returns:
    • LOOE: Approximate value of the leave-one-out estimator
    • ERR: Approximate standard error of the leave-one-out estimator

• For more details, see docstrings.

acv.acv_mlr?
acv.acv_logit?

• or see the api-documentation:
  • (PATH_TO_AcceleratedCVonMLR_python)/docs/_build/_html/index.html

DEMONSTRATION

In the "sample" folder, demonstration Jupyter notebooks for the multinomial and binomial logistic regressions, sample_logit.ipynb and sample_mlr.ipynb, respectively, are available.

• multinomial sample notebook
• binomial sample notebook

REFERENCE

Tomoyuki Obuchi and Yoshiyuki Kabashima: "Accelerating Cross-Validation in Multinomial Logistic Regression with $ell_1$-Regularization", arXiv: 1711.05420