| """
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| imbalance_coefficient.py
|
|
|
| Provides a function `imb_coef` to quantify imbalance in regression targets
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| for both continuous and discrete settings. It estimates the deviation of the
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| empirical distribution from the uniform distribution using KDE or frequency analysis.
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|
|
| Author: Samuel Stocksieker
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| License: MIT or CC-BY-4.0
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| Date: 2025-08-06
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| """
|
|
|
| import numpy as np
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| import pandas as pd
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| import matplotlib.pyplot as plt
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| from scipy.stats import gaussian_kde, uniform
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| from scipy.integrate import quad
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|
|
|
|
| def imb_coef(
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| y,
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| bdw='scott',
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| n_map=100_000,
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| distfunc='pdf',
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| disttype='cont',
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| plot=False,
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| p=1,
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| k=1,
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| w=None,
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| scale=True,
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| save=False,
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| rep='',
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| ):
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| """
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| Computes an imbalance coefficient for a target variable in regression tasks.
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|
|
| Parameters:
|
| ----------
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| y : array-like
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| Target variable (continuous or discrete).
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| bdw : str or float
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| Bandwidth for KDE ('scott' or float).
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| n_map : int
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| Number of points for KDE evaluation.
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| distfunc : str
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| Not used currently (placeholder).
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| disttype : str
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| 'cont' for continuous, 'dis' for discrete targets.
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| plot : bool
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| Whether to plot distribution comparison.
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| p : int
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| Exponent for penalizing deviations in discrete mode.
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| k : int
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| Index for saving figures (used in filenames).
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| w : array-like or None
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| Optional weights per observation.
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| scale : bool
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| Whether to scale `y` to [0, 1] in continuous mode.
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| save : bool
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| Whether to save plot as PNG.
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| rep : str
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| Folder path prefix for saving plots.
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|
|
| Returns:
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| -------
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| imb_ratio : float
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| imbalance coefficient in percentage.
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| """
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|
|
| y = np.array(y)
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|
|
| if disttype == 'cont':
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|
|
| if scale:
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| y = (y - y.min()) / (y.max() - y.min())
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|
|
| min_y, max_y = y.min(), y.max()
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| map_vals = np.linspace(min_y, max_y, n_map)
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|
|
|
|
| weights = (
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| np.ones(n_map) if w is None else np.interp(map_vals, y, w,
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| left=min(w[y == min_y]),
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| right=min(w[y == max_y]))
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| )
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|
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| kde = gaussian_kde(y, bw_method=bdw)
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| kde_vals = kde(map_vals)
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| d_best = uniform.pdf(map_vals, loc=min_y, scale=max_y - min_y)
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|
|
| kde_func = lambda x: np.interp(x, map_vals, kde_vals)
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| weight_func = lambda x: np.interp(x, map_vals, weights)
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|
|
| if w is None:
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| integrand = lambda x: max(0, 1 - kde_func(x))
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| imb_ratio = round(quad(integrand, min_y, max_y, epsabs=1e-5)[0], 4) * 100
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| else:
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| num = quad(lambda x: max(0, 1 - kde_func(x)) * weight_func(x), min_y, max_y, epsabs=1e-5)[0]
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| den = quad(lambda x: weight_func(x), min_y, max_y, epsabs=1e-5)[0]
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| imb_ratio = round(num / den, 4) * 100
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|
|
| if plot:
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| plt.figure(figsize=(10, 5))
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| plt.hist(y, bins=100, density=True, color='gray', alpha=0.6, label='Histogram')
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| plt.plot(map_vals, kde_vals, label='KDE', color='darkred')
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| plt.plot(map_vals, d_best, label='Uniform', color='darkgreen')
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| plt.title(f"{imb_ratio:.2f}%", fontsize=16, color='darkred')
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| plt.xlabel("Target values")
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| plt.ylabel("Density")
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| plt.legend()
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| if save:
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| plt.savefig(f"{rep}imbMetric_dens_{k}.png", bbox_inches='tight')
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| plt.show()
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|
|
| return imb_ratio
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|
|
| elif disttype == 'dis':
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|
|
| y = y.astype(int)
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| map_vals = np.arange(y.min(), y.max() + 1)
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|
|
| if w is None:
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| weights = np.ones_like(map_vals)
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| else:
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| df_w = pd.DataFrame({'map': y, 'w1': w})
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| w_agg = df_w.groupby('map')['w1'].mean().reset_index()
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| w_all = pd.DataFrame({'map': map_vals})
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| w_all = w_all.merge(w_agg, on='map', how='left').fillna(0)
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| weights = w_all['w1'].values
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|
|
| freqs = pd.Series(y).value_counts(normalize=True).reindex(map_vals, fill_value=0).values
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| d_best = np.ones_like(map_vals) / len(map_vals)
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|
|
| error = np.abs(freqs - d_best) ** p * (freqs < d_best) * weights
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| imb_ratio = round(np.sum(error[weights > 0]) / np.sum(d_best * weights), 4) * 100
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| if np.isnan(imb_ratio):
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| imb_ratio = 100
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|
|
| if plot:
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| df_plot = pd.DataFrame({
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| 'map': list(map_vals) * 2,
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| 'freq': list(freqs) + list(d_best),
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| 'dist': ['Emp'] * len(map_vals) + ['Uni'] * len(map_vals)
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| })
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| plt.figure(figsize=(10, 5))
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| for label, group in df_plot.groupby('dist'):
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| plt.bar(group['map'], group['freq'], alpha=0.5, label=label)
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| plt.title(f"{imb_ratio:.2f}%", fontsize=16, color='darkred')
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| plt.xlabel("Target values")
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| plt.ylabel("Frequency")
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| plt.legend()
|
| if save:
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| plt.savefig(f"{rep}imbMetric_mass_{k}.png", bbox_inches='tight')
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| plt.show()
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|
|
| return imb_ratio
|
|
|
| return None
|
|
|
