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Feature selection for hard voting classifier and NN sparse weight initialization.

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Feature selection for hard voting classifier and NN sparse weight initialization.


I am naming this software package in memory of my late nephew Max Joshua Hamster (* 2005 to † June 18, 2022).


Forward Selection for Hard Voting Classifier

Load toy data set and convert features to binary.

from sklearn.datasets import load_breast_cancer
from sklearn.preprocessing import scale
X = scale(load_breast_cancer().data, axis=0) > 0  # convert to binary features
y = load_breast_cancer().target

Select binary features. Each row in the results list contains the n_select column indices of X, the notice if the binary features were negated, and the sum of absolute MCC correlation coeffcients between the selected features.

import maxjoshua as mh
idx, neg, rho, results = mh.binsel(
    X, y, preselect=0.8, oob_score=True, subsample=0.5,
    n_select=5, unique=True, n_draws=100, random_state=42)

Algorithm. The task is to select e.g. n_select features from a pool of many features. These features might be the prediction of binary classifiers. The selected features are then combined into one hard-voting classifier.

A voting classifier should have the following properties

  • each voter (a binary feature) should be highly correlated to the target variable

  • the selected features should be uncorrelated.

The algorithm works as follows

  1. Generate multiple correlation matrices by bootstrapping. This includes corr(X_i, X_j) as well as corr(Y, X_i) computation. Also store the oob samples for evaluation.

  2. For each correlation matrix do …

    1. Preselect the i* with the highest abs(corr(Y, X_i)) estimates (e.g. pick the n_pre=? highest absolute correlations)

    2. Slice a correlation matrix corr(X_i*, X_j*) and find the least correlated combination of n_select features. (see `korr.mincorr <>`__)

    3. Compute the out-of-bag (OOB) performance (see step 1) of the hard-voter with the selected n_select=? features

  3. Select the feature combination with the best OOB performance as final model.

Forward Selection for Linear Regression

Load toy dataset.

from sklearn.preprocessing import scale
from sklearn.datasets import fetch_california_housing
housing = fetch_california_housing()
X = scale(housing["data"], axis=0)
y = scale(housing["target"])

Select real-numbered features. Each row in the results list contains the n_select column indices of X, the ridge regression coefficents beta and the RMSE loss. Warning! Please note that the features X and the target y must be scaled because mh.fltsel uses an L2-penalty on beta coefficients, and doesn’t used an intercept term to shift y.

import maxjoshua as mh
from sklearn.preprocessing import scale

idx, beta, loss, results = mh.fltsel(
    scale(X), scale(y), preselect=0.8, oob_score=True, subsample=0.5,
    n_select=5, unique=True, n_draws=100, random_state=42, l2=0.01)

Initialize Sparse NN Layer

The idea is to run mh.fltsel to generate an ensemble of linear models, and combine them in a sparse linear neural network layer, i.e., the number of output neurons is the ensemble size. In case of small datasets, the sparse NN layer is non-trainable because because each submodel was already estimated and selected with two-way data splits in mh.fltsel (see oob_scores and subsample). The sparse NN layers basically produces submodel predictions for meta model in the next layer, i.e., a simple dense linear layer. The inputs of the sparse NN layer must be normalized for which a layer normalization layers is trained.

import maxjoshua as mh
import tensorflow as tf
import sklearn.preprocessing

# create toy dataset
import sklearn.datasets
X, y = sklearn.datasets.make_regression(
    n_samples=1000, n_features=100, n_informative=20, n_targets=3)

# feature selection
# - always scale the inputs and targets -
indices, values, num_in, num_out = mh.pretrain_submodels(
    num_out=64, n_select=3)

# specify the model
model = tf.keras.models.Sequential([
    # sub-models
    # meta model
        units=3, use_bias=False,
        # kernel_constraint=tf.keras.constraints.NonNeg()
    # scale up
        learning_rate=3e-4, beta_1=.9, beta_2=.999, epsilon=1e-7, amsgrad=True),

# train
history =, y, epochs=3)



The maxjoshua git repo is available as PyPi package

pip install maxjoshua

Install a virtual environment

python3.7 -m venv .venv
source .venv/bin/activate
pip install --upgrade pip
pip install -r requirements.txt
pip install -r requirements-dev.txt
pip install -r requirements-demo.txt

(If your git repo is stored in a folder with whitespaces, then don’t use the subfolder .venv. Use an absolute path without whitespaces.)

Python commands

  • Jupyter for the examples: jupyter lab

  • Check syntax: flake8 --ignore=F401 --exclude=$(grep -v '^#' .gitignore | xargs | sed -e 's/ /,/g')

  • Run Unit Tests: pytest


pandoc --from markdown --to rst -s -o README.rst
python sdist
twine upload -r pypi dist/*

Clean up

find . -type f -name "*.pyc" | xargs rm
find . -type d -name "__pycache__" | xargs rm -r
rm -r .venv


Please open an issue for support.


Please contribute using Github Flow. Create a branch, add commits, and open a pull request.

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