TorchLevy

TorchLevy is python package that provides torch-based pdf, score calculation and sampling of symmetric alpha stable distribution.

Setup

pip install git+https://github.com/UNIST-LIM-Lab/torchlevy.git 

Simple Tutorial Code

import torch
from torchlevy import LevyStable, stable_dist

alpha = 1.7
x = torch.randn(size=(3, 200, 200))

# likelihood
likelihood = stable_dist.pdf(x, alpha)

# score function
score = stable_dist.score(x, alpha)

# x10 faster version of levy_stable.rvs()
sample = stable_dist.sample(alpha, beta=0, size=(3, 200, 200))

Performance

• Result from time_compare.py

RTX 3090 + AMD EPYC 7702

	sampling	score	likelihood
scipy	9.055s	58.837s	14.714s
torchlevy	0.009s (x1000 faster)	0.026s (x2000 faster)	0.003s (x4000 faster)

mac mini M1

	sampling	score	likelihood
scipy	1.843s	12.668s	3.188s
torchlevy	0.370s (x5 faster)	0.029s (x400 faster)	0.008s (x400 faster)

Gaussian + Levy Tutorial Code

import torch
from torchlevy import LevyGaussian

x = torch.randn(size=(3, 200, 200))

# score of gaussian+levy via fourier transform
levy_gaussian = LevyGaussian(alpha=1.7, sigma_1=1, sigma_2=1)
score = levy_gaussian.score(x)

import torch
from torchlevy import levy_gaussian_score

alpha = 1.8
x = torch.linspace(-10, 10, 100)
sigma1 = torch.ones(x.size()) * 0.5
sigma2 = torch.ones(x.size()) * 0.5

y = levy_gaussian_score(x, alpha=alpha, sigma1=sigma1, sigma2=sigma2)