How do I generate Log Uniform Distribution in Python?

Question

I could not find a built-in function in Python to generate a log uniform distribution given a min and max value (the R equivalent is here), something like: loguni[n, exp(min), exp(max), base] that returns n log uniformly distributed in the range exp(min) and exp(max).

The closest I found though was numpy.random.uniform.

Answer 1

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

In a loguniform distribution, the logtransformed random variable is assumed to be uniformly distributed.

Thus

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

Thus, we could create a log-uniform distribution using numpy:

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

If you want to choose a different base, we could define a new function as follows:

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

EDIT: @joaoFaria's answer is also correct.

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

Answer 2

SciPy v1.4 includes a loguniform random variable: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.loguniform.html

Here's how to use it:

from scipy.stats import loguniform

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

This will create random variables evenly spaced between 0.01 and 1. That best shown by visualizing the log-scaled histogram:

This "log-scaling" works regardless of base; loguniform.rvs(2**-2, 2**0, size=1000) also produces log-uniform random variables. More details are in loguniform's documentation.

Answer 3

I believe the scipy.stats.reciprocal is the distribution you want.
From the documentation:

The probability density function for reciprocal is:

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

for a <= x <= b and a, b > 0

reciprocal takes a and b as shape parameters.

Answer 4

from random import random
from math import log

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

You can check this using a specific seed value: lognorm(10,1000,0.5) returns 100.0

Answer 5

Here is one:

Simply use the .rvs() method provided:

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)

The original project also includes a LogNormal distribution if that also interests you.

Source:

• Neuraxle, a Hyperparameter Tuning and Machine Learning Pipelines Framework, https://www.neuraxio.com/en/neuraxle/stable/api/neuraxle.hyperparams.distributions.html#neuraxle.hyperparams.distributions.LogUniform

License:

• Apache License 2.0, Copyright 2019 Neuraxio Inc.

Answer 6

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)

Example output:

0.004532

This is using Neuraxle.

Answer 7

A better approach would be instead of directly generating a sample from a log-uniform, you should create the log-uniform density.

In statistics speak, that is a reciprocal distribution which is already in SciPy: scipy.stats.reciprocal. For example, to build a sample that is 10^{x~U[-1,1]}, you would do:

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

Alternatively, I wrote and use the following code to take the log-transform of any scipy.stats-like (frozen) random-variable

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)