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Running
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L4
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# import matplotlib.pyplot as plt
import numpy as np
def smooth_mapping(
confidence: float,
true_threshold=0.95,
false_threshold=0.40,
target_conf=0.60,
target_prob=0.78,
p_min=0.01,
p_max=0.99,
steepness_factor=0.7, # New parameter: 0-1 range, lower = less steep
) -> float:
"""Map confidence to probability using a sigmoid function with adjustable steepness.
Args:
confidence: Input confidence score
true_threshold: Upper threshold (0.78)
false_threshold: Lower threshold (0.40)
target_conf: Target confidence point (0.60)
target_prob: Target probability value (0.78)
p_min: Minimum probability (0.01)
p_max: Maximum probability (0.99)
steepness_factor: Controls curve steepness (0-1, lower = less steep)
"""
if confidence <= false_threshold:
return p_min
if confidence >= true_threshold:
return p_max
# Calculate parameters to ensure target_conf maps to target_prob
# For a sigmoid function: f(x) = L / (1 + e^(-k(x-x0)))
# First, normalize the target point
x_norm = (target_conf - false_threshold) / (true_threshold - false_threshold)
y_norm = (target_prob - p_min) / (p_max - p_min)
# Find x0 (midpoint) and k (steepness) to satisfy our target point
x0 = 0.30 # Midpoint of normalized range
# Calculate base k value to hit the target point
base_k = -np.log(1 / y_norm - 1) / (x_norm - x0)
# Apply steepness factor (lower = less steep)
k = base_k * steepness_factor
# With reduced steepness, we need to adjust x0 to still hit the target point
# Solve for new x0: y = 1/(1+e^(-k(x-x0))) => x0 = x + ln(1/y-1)/k
adjusted_x0 = x_norm + np.log(1 / y_norm - 1) / k
# Apply the sigmoid with our calculated parameters
x_scaled = (confidence - false_threshold) / (true_threshold - false_threshold)
sigmoid_value = 1 / (1 + np.exp(-k * (x_scaled - adjusted_x0)))
# Ensure we still hit exactly p_min and p_max at the thresholds
# by rescaling the output slightly
min_val = 1 / (1 + np.exp(-k * (0 - adjusted_x0)))
max_val = 1 / (1 + np.exp(-k * (1 - adjusted_x0)))
# Normalize the output
normalized = (sigmoid_value - min_val) / (max_val - min_val)
return p_min + normalized * (p_max - p_min)
def main():
# Visualize the function
x = np.linspace(0, 1, 1000)
y = [smooth_mapping(xi) for xi in x]
plt.figure(figsize=(10, 6))
plt.plot(x, y, "r-", label="Mapping Function", linewidth=2)
# Add vertical lines for thresholds
plt.axvline(x=0.40, color="b", linestyle="--", label="False Threshold (0.40)")
plt.axvline(x=0.95, color="g", linestyle="--", label="True Threshold (0.95)")
# Add horizontal lines for probability limits
plt.axhline(y=0.01, color="r", linestyle=":", alpha=0.5)
plt.axhline(y=0.99, color="g", linestyle=":", alpha=0.5)
plt.grid(True, alpha=0.3)
plt.xlabel("Confidence Score")
plt.ylabel("Mapped Probability")
plt.title("Confidence to Probability Mapping (Matching Red Line)")
plt.legend()
plt.ylim(-0.05, 1.05)
plt.savefig("calibration.png")
# Print some example values
test_values = [0.4, 0.425, 0.6, 0.85, 0.9]
for val in test_values:
print(f"Confidence {val:.3f} → Probability {smooth_mapping(val):.3f}")
if __name__ == "__main__":
main()
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