Monte Carlo simulations to optimize a linear classifier by testing all possible coefficient configurations.
Monte Carlo simulations are a method to randomly test all options for a given situation, in this case all possible configurations of coefficients for the formula y = a * Polarity + b * Hydrophobicity + c with an upper and lower limit for coefficients. More on .
The data consists of a classification of proteins as either membrane proteins (0) or non-membrane proteins (1) with the attributes polarity and hydrophobicity.
The goal is to generate a formula for linear classification that can accurately separate the two protein classes, as shown below:
There are many formulas that will accomplish this, however running all possible configurations within limits should result in the formula with the lowest error.
- Generate a training and test set (by default 50/50).
- Run Monte Carlo simulation with n iterations, create a new model with random coefficients and test its prediction error. Store models with lower prediction errors than all previous models.
- Select and store the best model (lowest prediction error).
- Print (formula, error, confusion matrix) and plot (linear classification and reduction of error per iteration).
It's recommended to run the script in a contained Conda environment to ensure the installation of all dependencies, the required steps are listed below:
$ wget https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh
$ bash Miniconda3-latest-Linux-x86_64.sh
$ conda env create --name {environment-name} --file environment.yml
$ source activate {environment-name}
$ python monte_carlo_linear_classifier.py
$ source deactivate
Alternatively, to run the script as a stand-alone, make sure the following dependencies are included:
- Python version 3
- Pip
- Matplotlib
- Numpy
- Pandas
- Seaborn
There are a couple of configurations that can be edited:
| Variable | Effect |
|---|---|
| n_iterations (int) | Changes the number of iterates, can significantly slow down your system! |
| random_min_range (int) | Changes the lower limit for coefficients |
| random_max_range (int) | Changes the upper limit for coefficients |
| save_image (boolean) | Enables saving output plots |
| training_set_size (float) | Changes the percentage of data used as training set, between 0.0 and 1.0 |
Originally coded as an assignment for a class on data mining. Data was provided in class as-is, original source unknown.