lab04.py

"""
# Probability densities and ML estimates

Try fitting uni-variate Gaussian models to the different features of the
different classes of the project dataset. For each class, for each component of
the feature vector of that class, compute the ML estimate for the parameters of
a 1D Gaussian distribution. Plot the distribution density (remember that you
have to exponentiate the log-density) on top of the normalized histogram (set
density=True when creating the histogram, see Laboratory 2). What do you
observe? Are there features for which the Gaussian densities provide a good fit?
Are there features for which the Gaussian model seems significantly less
accurate?

## Note:
for this part of the project, since we are still performing some preliminary,
qualitative analysis, you can compute the ML estimates and the plots either on
the whole training set. In the following labs we will employ the densities for
classification, and we will need to perform model selection, therefore we will
re-compute ML estimates on the model training portion of the dataset only
(see Laboratory 3).
"""

import numpy as np
from rich.console import Console

from project.figures.plots import densities
from project.figures.rich import table
from project.funcs.base import load_data
from project.funcs.log_pdf import log_pdf_gaussian


def lab04(DATA: str):
    X, y = load_data(DATA)

    classes = np.unique(y)

    means = np.array([np.mean(X[y == c], axis=0) for c in classes])

    # If we want to analyze the data ina uni-variate way Covariance(X, X) = Var(X)
    vars = np.array([np.var(X[y == c], axis=0) for c in classes])

    densities(X, y, means, vars, log_pdf_gaussian)

    table(
        Console(),
        "ML estimates for the parameters",
        {
            "means": f"{means}",
            "vars": f"{vars}",
        },
    )