laksjdjf · August 28, 2024 01:22 · laksjdjf · Aug 28, 2024
diff --git a/logitsnorm_shift.py b/logitsnorm_shift.py
 import numpy as np
 import matplotlib.pyplot as plt

 def sigmoid(x):
    return 1 / (1 + np.exp(-x))

 def inverse_sigmoid(y):
    return np.log(y / (1 - y))

 # 逆シグモイド関数の微分
 def inverse_sigmoid_derivative(y):
    return 1 / (y * (1 - y))

 def shift_func(x, shift):
    return (x*shift) / (1 + (shift - 1) * x)

 def inverse_shift(y, shift):
    return y / (shift - y * (shift - 1))

 def inverse_shift_derivative(y, shift):
    return shift / (shift - y * (shift - 1))**2

 def gaussian(x):
    return (1 / (np.sqrt(2 * np.pi))) * np.exp(-0.5 * x ** 2)

 # 確率密度関数
 def transformed_pdf(x, shift):
    y = inverse_sigmoid(inverse_shift(x, shift))
    dydx =  inverse_sigmoid_derivative(inverse_shift(x, shift)) * inverse_shift_derivative(x, shift)
    return gaussian(y) * dydx
  
  
 shift = 0.5

 # 確率分布
 y_values = np.linspace(0.01, 0.99, 1000)  # y = 0, 1 に近づくと逆シグモイドが発散するので端を避ける
 pdf_values = transformed_pdf(y_values, shift)

 # サンプリング
 sample_size = 10000
 normal_samples = np.random.normal(0, 1.0, sample_size)
 transformed_samples = shift_func(sigmoid(normal_samples), shift)

 plt.figure(figsize=(12, 6))
 plt.hist(transformed_samples, bins=50, density=True, alpha=0.6, color='g', label="Sampled Histogram")
 plt.plot(y_values, pdf_values, label="Transformed PDF (Sigmoid applied)")
 plt.title(f"shift={shift}")
 plt.xlabel("y")
 plt.ylabel("Density")
 plt.legend()
 plt.grid(True)
 plt.show()
	import numpy as np
	import matplotlib.pyplot as plt

	def sigmoid(x):
	return 1 / (1 + np.exp(-x))

	def inverse_sigmoid(y):
	return np.log(y / (1 - y))

	# 逆シグモイド関数の微分
	def inverse_sigmoid_derivative(y):
	return 1 / (y * (1 - y))

	def shift_func(x, shift):
	return (xshift) / (1 + (shift - 1) x)

	def inverse_shift(y, shift):
	return y / (shift - y * (shift - 1))

	def inverse_shift_derivative(y, shift):
	return shift / (shift - y * (shift - 1))**2

	def gaussian(x):
	return (1 / (np.sqrt(2 * np.pi))) * np.exp(-0.5 * x ** 2)

	# 確率密度関数
	def transformed_pdf(x, shift):
	y = inverse_sigmoid(inverse_shift(x, shift))
	dydx = inverse_sigmoid_derivative(inverse_shift(x, shift)) * inverse_shift_derivative(x, shift)
	return gaussian(y) * dydx


	shift = 0.5

	# 確率分布
	y_values = np.linspace(0.01, 0.99, 1000) # y = 0, 1 に近づくと逆シグモイドが発散するので端を避ける
	pdf_values = transformed_pdf(y_values, shift)

	# サンプリング
	sample_size = 10000
	normal_samples = np.random.normal(0, 1.0, sample_size)
	transformed_samples = shift_func(sigmoid(normal_samples), shift)

	plt.figure(figsize=(12, 6))
	plt.hist(transformed_samples, bins=50, density=True, alpha=0.6, color='g', label="Sampled Histogram")
	plt.plot(y_values, pdf_values, label="Transformed PDF (Sigmoid applied)")
	plt.title(f"shift={shift}")
	plt.xlabel("y")
	plt.ylabel("Density")
	plt.legend()
	plt.grid(True)
	plt.show()