如何在 Python 中生成日志均匀分布？

Question

在给定最小值和最大值的情况下，我无法在 Python 中找到一个内置函数来生成对数均匀分布（R 等效项为 here），例如：loguni[n, exp(min), exp( max), base] 返回在 exp(min) 和 exp(max) 范围内均匀分布的 n 对数。

我找到的最接近的是numpy.random.uniform。

Answer 1

来自http://ecolego.facilia.se/ecolego/show/Log-Uniform%20Distribution：

在对数均匀分布中，假设对数变换后的随机变量是均匀分布的。

这样

logU(a, b) ~ exp(U(log(a), log(b))

因此，我们可以使用numpy 创建一个对数均匀分布：

def loguniform(low=0, high=1, size=None):
    return np.exp(np.random.uniform(low, high, size))

如果你想选择不同的基础，我们可以定义一个新的函数如下：

def lognuniform(low=0, high=1, size=None, base=np.e):
    return np.power(base, np.random.uniform(low, high, size))

编辑：@joaoFaria's answer 也是正确的。

def loguniform(low=0, high=1, size=None):
    return scipy.stats.reciprocal(np.exp(low), np.exp(high)).rvs(size)

Answer 2

我相信scipy.stats.reciprocal 是您想要的发行版。
来自文档：

倒数的概率密度函数为：

f(x, a, b) = \frac{1}{x \log(b/a)}

对于 a 0

reciprocal 将a 和b 作为形状参数。

Answer 3

from random import random
from math import log

def loguniform(lo,hi,seed=random()):
    return lo ** ((((log(hi) / log(lo)) - 1) * seed) + 1)

您可以使用特定的种子值进行检查：lognorm(10,1000,0.5) 返回 100.0

Answer 4

这是一个：

只需使用提供的.rvs() 方法：

class LogUniform(HyperparameterDistribution):
    """Get a LogUniform distribution.
    For example, this is good for neural networks' learning rates: that vary exponentially."""

    def __init__(self, min_included: float, max_included: float):
        """
        Create a quantized random log uniform distribution.
        A random float between the two values inclusively will be returned.
        :param min_included: minimum integer, should be somehow included.
        :param max_included: maximum integer, should be somehow included.
        """
        self.log2_min_included = math.log2(min_included)
        self.log2_max_included = math.log2(max_included)
        super(LogUniform, self).__init__()

    def rvs(self) -> float:
        """
        Will return a float value in the specified range as specified at creation.
        :return: a float.
        """
        return 2 ** random.uniform(self.log2_min_included, self.log2_max_included)

    def narrow_space_from_best_guess(self, best_guess, kept_space_ratio: float = 0.5) -> HyperparameterDistribution:
        """
        Will narrow, in log space, the distribution towards the new best_guess.
        :param best_guess: the value towards which we want to narrow down the space. Should be between 0.0 and 1.0.
        :param kept_space_ratio: what proportion of the space is kept. Default is to keep half the space (0.5).
        :return: a new HyperparameterDistribution that has been narrowed down.
        """
        log2_best_guess = math.log2(best_guess)
        lost_space_ratio = 1.0 - kept_space_ratio
        new_min_included = self.log2_min_included * kept_space_ratio + log2_best_guess * lost_space_ratio
        new_max_included = self.log2_max_included * kept_space_ratio + log2_best_guess * lost_space_ratio
        if new_max_included <= new_min_included or kept_space_ratio == 0.0:
            return FixedHyperparameter(best_guess).was_narrowed_from(kept_space_ratio, self)
        return LogUniform(2 ** new_min_included, 2 ** new_max_included).was_narrowed_from(kept_space_ratio, self)

如果您也感兴趣，原始项目还包括一个 LogNormal 分布。

来源：

• Neuraxle，一种超参数调整和机器学习管道框架，https://www.neuraxio.com/en/neuraxle/stable/api/neuraxle.hyperparams.distributions.html#neuraxle.hyperparams.distributions.LogUniform

许可证：

• Apache 许可证 2.0，版权所有 2019 Neuraxio Inc.

Answer 5

from neuraxle.hyperparams.distributions import LogUniform

# Create a Log Uniform Distribution that ranges from 0.001 to 0.1: 
learning_rate_distribution = LogUniform(0.001, 0.1)

# Get a Random Value Sample (RVS) from the distribution: 
learning_rate_sample = learning_rate_distribution.rvs()

print(learning_rate_sample)

示例输出：

0.004532

这是使用Neuraxle。

Answer 6

更好的方法不是直接从对数均匀生成样本，而是应该创建对数均匀密度。

用统计学来说，这是一个倒数分布，它已经存在于 SciPy 中：scipy.stats.reciprocal。例如，要构建一个 10^{x~U[-1,1]} 的示例，您可以：

rv = scipy.stats.reciprocal(a=0.1,b=10)
x = rv.rvs(N)

另外，我编写并使用以下代码对任何scipy.stats-like (frozen) random-variable 进行对数转换

class LogTransformRV(scipy.stats.rv_continuous):
    def __init__(self,rv,base=10):
        self.rv = rv
        self.base = np.e if base in {'e','E'} else base
        super(LogTransformRV, self).__init__()
        self.a,self.b = self.base ** self.rv.ppf([0,1])

    def _pdf(self,x):
        return self.rv.pdf(self._log(x))/(x*np.log(self.base)) # Chain rule

    def _cdf(self,x):
        return self.rv.cdf(self._log(x)) 

    def _ppf(self,y):
        return self.base ** self.rv.ppf(y)

    def _log(self,x):
        return np.log(x)/np.log(self.base)

Answer 7

SciPy v1.4 包含一个 loguniform 随机变量：https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.loguniform.html

使用方法如下：

from scipy.stats import loguniform

rvs = loguniform.rvs(1e-2, 1e0, size=1000)

这将创建均匀分布在 0.01 和 1 之间的随机变量。通过可视化对数标度直方图可以最好地展示这一点：

无论基数如何，这种“对数缩放”都有效； loguniform.rvs(2**-2, 2**0, size=1000) 还产生对数均匀随机变量。更多详细信息在loguniform 的文档中。