fuz

fuz is a library for probability fusion, allowing the merging of distribution functions in a principled manner.

with fuz, you can do things like bayesian evidence updating, optimal bayesian ranking, and fuzzy logic.

highlights

• pooling
  • linear, multiplicative, geometric, holder ...etc.
• fuzzy logic extension to distribution functions
• numerical integration in logarithmic space for stability
• NaN and logarithmic complex number handling
• distribution tools

upcoming features

• wider compatibility with narwhals
  • dataframes, functions, samples ...etc.
• initial gpu support with jax
• more documentation 😹

demos

check out the marimo demos at:

• ch1. bernoulli to beta
• ch2. to infinity

quickstart

pip install fuz

distributions

import fuz.dists as fd
a = fd.Beta(5,4)
a.stats

b = fd.beta_from_mode_trials(0.9,10)
d = fd.Dirichlet([3,6,2])

logarithmic manipulation

import numpy as np
from fuz.log import complex_lsub, lsimp_irreg

a = np.log([[1,np.nan],[3,4]])
b = np.log([[3,2],[6,1]])
print(complex_lsub(a,b))

x = np.linspace(0,1,1025)
b = fd.beta_from_mu_k(0.3,9)
c = fd.beta_from_mode_k(0.3,9)
y = b.logpdf(x) * c.logcdf(x)
np.exp(lsimp_irreg(y,x))

note - integrating y here gives you the win rate of b over c. see the demo folder for more.

fuzzy logic

import fuz.logic as fzl

x = np.linspace(0,1,1025)
b = fd.beta_from_mode_var(0.7,0.01)
c = fd.beta_from_mu_var(0.7,0.01)
b_negpdf = fzl.negf(b.pdf)
negb_and_c = fzl.ands(x, b_negpdf(x), c.pdf(x))

pooling

ranking

more

see demo folder (pip install marimo first) for more usage.

other

the official pronunciation of fuz is a fugued function of fuzzy fusion 😉

abstract

fuz is a python library for fusion of probability distributions, bayesian evidence updating and ranking, fuzzy logic, operations in logarithmic space, and more. fuz includes several original contributions, including a performant bayesian averaging/ranking algorithm that is mathematically optimal, equations for determining whether one pdf "wins" over another, and multiple demonstrations of equivalence. these include the equivalence of simple kalman filtering, bayesian updating, and multiplicative (upco) pooling, the equivalence of mode-parameterization of beta and dirichlet distributions to optimal bayesian averaging, useful limits as the dirichlet $\alpha_0$ approaches infinity, and various equivalences for discrete distributions.

acknowledgements

thanks to jane liou for her useful insights and support!