182 lines
6.8 KiB
Python
182 lines
6.8 KiB
Python
"""
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Comparison of density estimators on real model output scores.
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For each class (negative / positive) plots four curves against the empirical CDF:
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- ECDF — ground truth step function
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- KDE (ISJ) — Gaussian-kernel KDE with Improved Sheather-Jones bandwidth
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- Gaussian fit — MLE normal distribution
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- Beta fit — sigmoid-transformed scores fitted with Beta MLE, CDF
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mapped back to the original logit axis
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Data: test split of a ROLL model trained on the glass0 dataset.
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Run from the impl directory (KDEpy lives in that flake):
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cd impl && nix develop --command python3 ../thesis/content/method/figures/density_fit_comparison.py
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"""
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import sys, pickle
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from pathlib import Path
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import numpy as np
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import matplotlib
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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from scipy.stats import norm, beta as sp_beta
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from scipy.special import expit
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from KDEpy import FFTKDE
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from KDEpy.bw_selection import silvermans_rule, improved_sheather_jones
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# Resolve paths relative to this script's location so the script runs from anywhere.
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_HERE = Path(__file__).resolve().parent # .../thesis/content/method/figures
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_THESIS = _HERE.parents[2] # .../thesis
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_IMPL = _THESIS.parent / "impl" # .../impl
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sys.path.insert(0, str(_IMPL)) # pickle needs 'import src.experiment' → impl/src/experiment.py
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# ── Config ──────────────────────────────────────────────────────────────────
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RESULT_PKL = _IMPL / "results/glass0/2026-07-08-22-25/roll/0/test-res.pkl"
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OUT_DIR = _HERE
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SPLIT = "test"
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C_NEG = "#4477AA"
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C_POS = "#CC6633"
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plt.rcParams.update({
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"text.usetex": False,
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"mathtext.fontset": "cm",
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"pdf.fonttype": 42,
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})
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# ── Load data ────────────────────────────────────────────────────────────────
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with open(RESULT_PKL, "rb") as f:
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ep = pickle.load(f)
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res = ep.split_results[SPLIT]
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yh = res.yh.astype(np.float64) # raw logit scores
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y = res.y
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scores_neg = yh[y == 0]
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scores_pos = yh[y == 1]
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print(f"Loaded {SPLIT} split: {len(scores_neg)} negatives, {len(scores_pos)} positives")
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print(f"Score range: [{yh.min():.3f}, {yh.max():.3f}]")
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# ── Helpers ──────────────────────────────────────────────────────────────────
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def ecdf(scores):
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"""Return (x, p) for a step-function ECDF."""
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s = np.sort(scores)
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p = np.arange(1, len(s) + 1) / len(s)
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return s, p
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def _kde_pdf(scores, x_grid, h):
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pdf = FFTKDE(kernel="gaussian", bw=h).fit(scores).evaluate(x_grid)
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dx = x_grid[1] - x_grid[0]
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cdf = np.cumsum(pdf) * dx
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cdf /= cdf[-1]
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return cdf
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def kde_isj_cdf(scores, x_grid):
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"""ISJ bandwidth; Silverman fallback on failure."""
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data = scores[:, np.newaxis].astype(np.float64)
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try:
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h = float(improved_sheather_jones(data))
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except Exception:
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h = float(silvermans_rule(data))
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return _kde_pdf(scores, x_grid, h)
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def kde_silverman_cdf(scores, x_grid):
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h = float(silvermans_rule(scores[:, np.newaxis].astype(np.float64)))
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return _kde_pdf(scores, x_grid, h)
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def gauss_cdf(scores, x_grid):
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loc, scale = norm.fit(scores)
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return norm.cdf(x_grid, loc, scale)
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def beta_cdf(scores, x_grid):
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"""Fit Beta in sigmoid space; evaluate CDF back on the logit x_grid."""
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s01 = expit(scores).clip(1e-6, 1 - 1e-6)
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a, b, _, _ = sp_beta.fit(s01, floc=0, fscale=1)
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return sp_beta.cdf(expit(x_grid), a, b)
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# ── Shared x-grid (covers both classes with a small margin) ──────────────────
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margin = 0.5
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x_lo = yh.min() - margin
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x_hi = yh.max() + margin
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x_grid = np.linspace(x_lo, x_hi, 2048)
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# ── Compute all curves ───────────────────────────────────────────────────────
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neg_ecdf_x, neg_ecdf_p = ecdf(scores_neg)
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neg_cdf_kde = kde_isj_cdf(scores_neg, x_grid)
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neg_cdf_silverman = kde_silverman_cdf(scores_neg, x_grid)
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neg_cdf_gauss = gauss_cdf(scores_neg, x_grid)
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neg_cdf_beta = beta_cdf(scores_neg, x_grid)
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pos_ecdf_x, pos_ecdf_p = ecdf(scores_pos)
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pos_cdf_kde = kde_isj_cdf(scores_pos, x_grid)
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pos_cdf_silverman = kde_silverman_cdf(scores_pos, x_grid)
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pos_cdf_gauss = gauss_cdf(scores_pos, x_grid)
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pos_cdf_beta = beta_cdf(scores_pos, x_grid)
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# ── Plot ─────────────────────────────────────────────────────────────────────
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fig, (ax0, ax1) = plt.subplots(
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2, 1, figsize=(5.5, 4.8), sharex=True,
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gridspec_kw={"height_ratios": [1, 1]},
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)
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fig.subplots_adjust(hspace=0.08)
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def _plot_class(ax, color, ecdf_x, ecdf_p,
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cdf_isj, cdf_silverman, cdf_gauss, cdf_beta, label_prefix):
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ax.step(ecdf_x, ecdf_p,
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color=color, lw=1.0, alpha=0.55, where="post",
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label="ECDF")
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ax.plot(x_grid, cdf_isj,
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color=color, lw=1.8, linestyle="-",
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label="KDE (ISJ)")
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ax.plot(x_grid, cdf_silverman,
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color=color, lw=1.4, linestyle="-.",
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label="KDE (Silverman)")
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ax.plot(x_grid, cdf_gauss,
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color=color, lw=1.4, linestyle="--",
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label="Gaussian")
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ax.plot(x_grid, cdf_beta,
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color=color, lw=1.6, linestyle=":",
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label="Beta")
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ax.set_ylabel("CDF", fontsize=9)
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ax.set_yticks([0.0, 0.25, 0.50, 0.75, 1.0])
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ax.set_yticklabels(["0", ".25", ".5", ".75", "1"], fontsize=7.5)
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ax.tick_params(labelsize=8)
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ax.spines[["top", "right"]].set_visible(False)
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ax.text(0.97, 0.05, label_prefix,
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transform=ax.transAxes, fontsize=8,
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ha="right", va="bottom", color=color)
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_plot_class(ax0, C_NEG,
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neg_ecdf_x, neg_ecdf_p,
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neg_cdf_kde, neg_cdf_silverman, neg_cdf_gauss, neg_cdf_beta,
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r"Negative class ($y=0$)")
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_plot_class(ax1, C_POS,
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pos_ecdf_x, pos_ecdf_p,
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pos_cdf_kde, pos_cdf_silverman, pos_cdf_gauss, pos_cdf_beta,
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r"Positive class ($y=1$)")
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ax0.legend(fontsize=7.5, loc="upper left", framealpha=0.88)
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ax1.set_xlabel(r"Score $f_\theta(\mathbf{x})$", fontsize=9)
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ax0.set_xlim(x_lo, x_hi)
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for path_suffix in ("pdf", "png"):
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kw = {"bbox_inches": "tight"}
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if path_suffix == "png":
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kw["dpi"] = 180
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fig.savefig(OUT_DIR / f"density_fit_comparison.{path_suffix}", **kw)
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print(f"Saved to {OUT_DIR}/density_fit_comparison.{{pdf,png}}")
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