98 lines
3.1 KiB
Python
98 lines
3.1 KiB
Python
import math
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from typing import Tuple, Dict
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from functools import cache
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import torch
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import torch.distributions as dist
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from torch import exp
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F1: Dict[float, float] = {}
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F2: Dict[float, float] = {}
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CDF: Dict[float, float] = {}
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lookup_count = 0
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def get_lookup_count():
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global lookup_count
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return lookup_count
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@cache
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def calc_cdf(alpha: float) -> Tuple[float, float, float]:
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normal = dist.Normal(0, 1)
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cdf_alpha = normal.cdf(torch.tensor(alpha)).item()
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pdf_alpha = exp(normal.log_prob(torch.tensor(alpha))).item()
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f1 = alpha * cdf_alpha + pdf_alpha
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f2 = alpha ** 2 * cdf_alpha * (1 - cdf_alpha) + (
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1 - 2 * cdf_alpha) * alpha * pdf_alpha - pdf_alpha ** 2
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return cdf_alpha, f1, f2
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def max_gaussian(mu1, sigma1, mu2, sigma2) -> Tuple[float, float]:
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global lookup_count
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global F1
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global F2
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global CDF
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"""
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Returns the combined max gaussian of two Gaussians represented by mu1, sigma1, mu2, simga2
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:param mu1: mu of the first Gaussian
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:param sigma1: sigma of the first Gaussian
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:param mu2: mu of the second Gaussian
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:param sigma2: sigma of the second Gaussian
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:return: mu and sigma maximized
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"""
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# we assume independence of the two gaussians
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#print(mu1, sigma1, mu2, sigma2)
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#normal = dist.Normal(0, 1)
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sigma_m = math.sqrt(sigma1 ** 2 + sigma2 ** 2)
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alpha = round((mu1 - mu2) / sigma_m, 2)
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cdf_alpha, f1_alpha, f2_alpha = calc_cdf(alpha)
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mu = mu2 + sigma_m * f1_alpha
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sigma = math.sqrt(sigma2 ** 2 + (sigma1 ** 2 - sigma2 ** 2) * cdf_alpha + sigma_m ** 2 * f2_alpha)
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#sigma = math.sqrt((mu1**2 + sigma1**2) * cdf_alpha + (mu2**2 + sigma2**2) * (1 - cdf_alpha) + (mu1 + mu2) * sigma_m * pdf_alpha - mu**2)
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return mu, sigma
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def min_gaussian(mu1, sigma1, mu2, sigma2) -> tuple[float, float]:
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"""
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Returns the combined min gaussian of two Gaussians represented by mu1, sigma1, mu2, simga2
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:param mu1: mu of the first Gaussian
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:param sigma1: sigma of the first Gaussian
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:param mu2: mu of the second Gaussian
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:param sigma2: sigma of the second Gaussian
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:return: mu and sigma minimized
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"""
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try:
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normal = dist.Normal(0, 1)
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sigma_m = math.sqrt(sigma1 ** 2 + sigma2 ** 2)
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alpha = (mu1 - mu2) / sigma_m
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cdf_alpha = normal.cdf(torch.tensor(alpha)).item()
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pdf_alpha = exp(normal.log_prob(torch.tensor(alpha))).item()
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pdf_alpha_neg = exp(normal.log_prob(torch.tensor(-alpha))).item()
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mu = mu1 * (1 - cdf_alpha) + mu2 * cdf_alpha - pdf_alpha_neg * sigma_m
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sigma = math.sqrt((mu1**2 + sigma1**2) * (1 - cdf_alpha) + (mu2**2 + sigma2**2) * cdf_alpha - (mu1 + mu2) * sigma_m * pdf_alpha - mu**2)
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return mu, sigma
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except ValueError:
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print(mu1, sigma1, mu2, sigma2)
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def beta_mean(alpha, beta):
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return alpha / (alpha + beta)
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def beta_std(alpha, beta):
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try:
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return math.sqrt((alpha * beta) / ((alpha * beta)**2 * (alpha + beta + 1)))
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except ZeroDivisionError:
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print(alpha, beta)
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def gaussian_ucb1(mu, sigma, N) -> float:
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return mu + math.sqrt(2 * math.log(N) * sigma)
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