Updated results, hebrew, abstract, intro, etc.

content/method/figures/roll_aoc_roc.py

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+"""
+ROC curve illustration for ROLL-AOC.
+
+Shows how ROLL-AOC converts the single-threshold ROLL into AUC optimization:
+- ROC curve traced by sweeping threshold τ
+- 10 evenly-spaced FPR sample points (as ROLL evaluates in miniature)
+- Green shaded region = AUC (area under curve, what we maximize)
+- Red shaded region  = AOC = 1 − AUC (area over curve, the loss we minimize)
+- Vertical segments  = per-threshold loss 1 − TPR(αᵢ), one per sampled FPR
+
+Run from the thesis root:
+    nix develop --command python3 content/method/figures/roll_aoc_roc.py
+"""
+
+import numpy as np
+import matplotlib
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+from scipy.stats import norm
+
+OUT_DIR = "content/method/figures"
+
+# --- Parameters (same distributions as roll_principle.py) ------------------
+mu0, sig0 = 0.0, 1.00
+mu1, sig1 = 1.5, 1.00
+
+# --- ROC curve -------------------------------------------------------------
+# Sweep τ from high to low → FPR rises from 0 to 1
+tau_grid = np.linspace(norm.ppf(0.9999, mu0, sig0),
+                       norm.ppf(0.0001, mu0, sig0), 3000)
+fpr_curve = 1.0 - norm.cdf(tau_grid, mu0, sig0)
+tpr_curve = 1.0 - norm.cdf(tau_grid, mu1, sig1)
+
+# Pin endpoints so the fill covers the full unit square correctly
+fpr_full = np.concatenate([[0.0], fpr_curve, [1.0]])
+tpr_full = np.concatenate([[0.0], tpr_curve, [1.0]])
+
+auc = float(np.trapezoid(tpr_full, fpr_full))
+
+# --- 10 sample FPR points: αᵢ = i/11 for i = 1…10 ------------------------
+n_samples = 10
+alpha_s = np.array([(i / (n_samples + 1)) for i in range(1, n_samples + 1)])
+tpr_s   = np.interp(alpha_s, fpr_full, tpr_full)
+
+# --- Palette (matches roll_principle.py) -----------------------------------
+C_POS   = "#CC6633"   # ROC curve (positive-class colour)
+C_GREEN = "#44AA77"   # AUC fill
+C_RED   = "#BB3333"   # AOC fill / vertical segments
+C_DOT   = "#333333"   # sample dots
+
+# ── Figure ─────────────────────────────────────────────────────────────────
+fig, ax = plt.subplots(figsize=(4.8, 4.4))
+
+# Random-classifier diagonal
+ax.plot([0, 1], [0, 1], color="#AAAAAA", linestyle="--",
+        linewidth=0.9, zorder=1, label="Random classifier")
+
+# AUC — green fill under ROC curve
+ax.fill_between(fpr_full, 0, tpr_full,
+                color=C_GREEN, alpha=0.25, zorder=2,
+                label=rf"AUC $\approx$ {auc:.2f}  (maximize)")
+
+# AOC — red fill above ROC curve
+ax.fill_between(fpr_full, tpr_full, 1.0,
+                color=C_RED, alpha=0.22, zorder=2,
+                label=r"AOC $= 1-\mathrm{AUC}$  (minimize)")
+
+# ROC curve itself
+ax.plot(fpr_full, tpr_full, color=C_POS, linewidth=2.0, zorder=3,
+        label="ROC curve")
+
+# Per-threshold loss segments: vertical from TPR(αᵢ) up to 1
+for a_i, t_i in zip(alpha_s, tpr_s):
+    ax.plot([a_i, a_i], [t_i, 1.0],
+            color=C_RED, linewidth=1.0, alpha=0.55, zorder=4)
+
+# Sample dots on the ROC curve
+ax.scatter(alpha_s, tpr_s,
+           color=C_DOT, s=35, zorder=5,
+           label=r"Sampled $\alpha_i$ (ROLL evaluations)")
+
+# --- Axes / labels ---------------------------------------------------------
+ax.set_xlabel(r"FPR $(\alpha)$", fontsize=9)
+ax.set_ylabel(r"TPR", fontsize=9)
+ax.set_xlim(0.0, 1.0)
+ax.set_ylim(0.0, 1.0)
+ax.set_aspect("equal")
+ax.tick_params(labelsize=8)
+ax.spines[["top", "right"]].set_visible(False)
+ax.legend(fontsize=7.5, loc="lower right", framealpha=0.88)
+
+fig.tight_layout()
+fig.savefig(f"{OUT_DIR}/roll_aoc_roc.pdf", bbox_inches="tight")
+fig.savefig(f"{OUT_DIR}/roll_aoc_roc.png", bbox_inches="tight", dpi=180)
+print(f"Saved to {OUT_DIR}/roll_aoc_roc.{{pdf,png}}")
+print(f"AUC = {auc:.4f}  AOC = {1-auc:.4f}")