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"""

imbalance_coefficient.py



Provides a function `imb_coef` to quantify imbalance in regression targets

for both continuous and discrete settings. It estimates the deviation of the

empirical distribution from the uniform distribution using KDE or frequency analysis.



Author: Samuel Stocksieker

License: MIT or CC-BY-4.0

Date: 2025-08-06

"""

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.stats import gaussian_kde, uniform
from scipy.integrate import quad


def imb_coef(

    y,

    bdw='scott',

    n_map=100_000,

    distfunc='pdf',

    disttype='cont',  # 'cont' for continuous, 'dis' for discrete

    plot=False,

    p=1,

    k=1,

    w=None,

    scale=True,

    save=False,

    rep='',

):
    """

    Computes an imbalance coefficient for a target variable in regression tasks.



    Parameters:

    ----------

    y : array-like

        Target variable (continuous or discrete).

    bdw : str or float

        Bandwidth for KDE ('scott' or float).

    n_map : int

        Number of points for KDE evaluation.

    distfunc : str

        Not used currently (placeholder).

    disttype : str

        'cont' for continuous, 'dis' for discrete targets.

    plot : bool

        Whether to plot distribution comparison.

    p : int

        Exponent for penalizing deviations in discrete mode.

    k : int

        Index for saving figures (used in filenames).

    w : array-like or None

        Optional weights per observation.

    scale : bool

        Whether to scale `y` to [0, 1] in continuous mode.

    save : bool

        Whether to save plot as PNG.

    rep : str

        Folder path prefix for saving plots.



    Returns:

    -------

    imb_ratio : float

        imbalance coefficient in percentage.

    """

    y = np.array(y)

    if disttype == 'cont':
        # Continuous target
        if scale:
            y = (y - y.min()) / (y.max() - y.min())

        min_y, max_y = y.min(), y.max()
        map_vals = np.linspace(min_y, max_y, n_map)

        # Weight setup
        weights = (
            np.ones(n_map) if w is None else np.interp(map_vals, y, w,
                                                       left=min(w[y == min_y]),
                                                       right=min(w[y == max_y]))
        )

        kde = gaussian_kde(y, bw_method=bdw)
        kde_vals = kde(map_vals)
        d_best = uniform.pdf(map_vals, loc=min_y, scale=max_y - min_y)

        kde_func = lambda x: np.interp(x, map_vals, kde_vals)
        weight_func = lambda x: np.interp(x, map_vals, weights)

        if w is None:
            integrand = lambda x: max(0, 1 - kde_func(x))
            imb_ratio = round(quad(integrand, min_y, max_y, epsabs=1e-5)[0], 4) * 100
        else:
            num = quad(lambda x: max(0, 1 - kde_func(x)) * weight_func(x), min_y, max_y, epsabs=1e-5)[0]
            den = quad(lambda x: weight_func(x), min_y, max_y, epsabs=1e-5)[0]
            imb_ratio = round(num / den, 4) * 100

        if plot:
            plt.figure(figsize=(10, 5))
            plt.hist(y, bins=100, density=True, color='gray', alpha=0.6, label='Histogram')
            plt.plot(map_vals, kde_vals, label='KDE', color='darkred')
            plt.plot(map_vals, d_best, label='Uniform', color='darkgreen')
            plt.title(f"{imb_ratio:.2f}%", fontsize=16, color='darkred')
            plt.xlabel("Target values")
            plt.ylabel("Density")
            plt.legend()
            if save:
                plt.savefig(f"{rep}imbMetric_dens_{k}.png", bbox_inches='tight')
            plt.show()

        return imb_ratio

    elif disttype == 'dis':
        # Discrete target
        y = y.astype(int)
        map_vals = np.arange(y.min(), y.max() + 1)

        if w is None:
            weights = np.ones_like(map_vals)
        else:
            df_w = pd.DataFrame({'map': y, 'w1': w})
            w_agg = df_w.groupby('map')['w1'].mean().reset_index()
            w_all = pd.DataFrame({'map': map_vals})
            w_all = w_all.merge(w_agg, on='map', how='left').fillna(0)
            weights = w_all['w1'].values

        freqs = pd.Series(y).value_counts(normalize=True).reindex(map_vals, fill_value=0).values
        d_best = np.ones_like(map_vals) / len(map_vals)

        error = np.abs(freqs - d_best) ** p * (freqs < d_best) * weights
        imb_ratio = round(np.sum(error[weights > 0]) / np.sum(d_best * weights), 4) * 100
        if np.isnan(imb_ratio):
            imb_ratio = 100

        if plot:
            df_plot = pd.DataFrame({
                'map': list(map_vals) * 2,
                'freq': list(freqs) + list(d_best),
                'dist': ['Emp'] * len(map_vals) + ['Uni'] * len(map_vals)
            })
            plt.figure(figsize=(10, 5))
            for label, group in df_plot.groupby('dist'):
                plt.bar(group['map'], group['freq'], alpha=0.5, label=label)
            plt.title(f"{imb_ratio:.2f}%", fontsize=16, color='darkred')
            plt.xlabel("Target values")
            plt.ylabel("Frequency")
            plt.legend()
            if save:
                plt.savefig(f"{rep}imbMetric_mass_{k}.png", bbox_inches='tight')
            plt.show()

        return imb_ratio

    return None