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/.
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