Point process model for Bayesian inference with persistence diagrams.
Project description
bayes_tda
This module contains classes to implement a marked Poisson process model for Bayesian inference with persistence diagrams. The model relies on mixed Gaussian assumptions. For a full description of the model, please refer to https://arxiv.org/abs/1901.02034.
Installation
Use the package manager pip to install bayes_tda.
pip install bayes_tda
Classes
Class name | Description | Methods |
---|---|---|
WedgeGaussian | Gaussian density restricted to upper half of $\mathbb{R}^2$. | eval |
Prior | Mixed Gaussian prior intensity. | eval |
Posterior | Mixed Gaussian posterior intensity. | eval |
Usage
from bayes_tda import *
import matplotlib.pyplot as plt
import numpy as np
x = [0,0] # a point in birth-persistence coordinates
wg = WedgeGaussian(mu = [0,0], sigma = 1) # Gaussian densities restricted to the upper half plane
d = wg.eval(x) # evaluates the Gaussian density at x
means = np.array([[0,0],[6,6]])
ss = [1,1]
ws = [1,1]
pri = Prior(weights = ws,mus = means, sigmas = ss)
d_pri = pri.eval(x)
b = np.linspace(0,10,50)
p = np.linspace(0,10,50)
B,P = np.meshgrid(b,p)
Z = list()
for ind in range(len(P)):
l = list()
for i in range(len(P)):
l.append(pri.eval([B[ind][i],P[ind][i]]))
Z.append(l)
plt.style.use('seaborn-white')
plt.contourf(B,P,Z, 20, cmap = 'twilight')
plt.colorbar()
plt.show()
noise = Prior(weights = [0], mus = [[30,30]], sigmas = [10])
post = Posterior(prior = pri,clutter = noise,Dy = [[1,5],[5,1]], sy = 1)
peval = post.eval(x)
Z = list()
for ind in range(len(P)):
l = list()
for i in range(len(P)):
l.append(post.eval([B[ind][i],P[ind][i]]))
Z.append(l)
plt.style.use('seaborn-white')
plt.contourf(B,P,Z, 20, cmap = 'twilight')
plt.colorbar()
plt.show()
Reporting Bugs
Report any bugs by opening an issue at https://github.com/coballejr/bayes_tda/.
License
Project details
Release history Release notifications | RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
bayes_tda-0.2.tar.gz
(4.8 kB
view hashes)