UNHaP on simulated univariate Hawkes processes

This example demonstrates inference performed by UNHaP on univariate Hawkes processes simulated with a truncated gaussian kernel.

# Authors: Guillaume Staerman <guillaume.staerman@inria.fr>
#          Virginie Loison <virginie.loison@inria.fr>
#          Thomas Moreau <thomas.moreau@inria.fr>
#
# License: MIT

Let us first define the parameters of our model. %% Imports

import numpy as np
import matplotlib.pyplot as plt

from fadin.utils.utils_simu import simu_marked_hawkes_cluster, custom_density
from fadin.utils.utils_simu import simu_multi_poisson
from fadin.solver import UNHaP
from fadin.utils.functions import identity, linear_zero_one
from fadin.utils.functions import reverse_linear_zero_one, truncated_gaussian
from fadin.utils.vis import plot

baseline = np.array([0.3])
baseline_noise = np.array([0.05])
alpha = np.array([[1.45]])
mu = np.array([[0.4]])
sigma = np.array([[0.1]])

delta = 0.01
end_time = 10000
seed = 0
max_iter = 20000
batch_rho = 200

def simulate_data(baseline, baseline_noise, alpha, end_time, seed=0):
    n_dim = len(baseline)

    marks_kernel = identity
    marks_density = linear_zero_one
    time_kernel = truncated_gaussian

    params_marks_density = dict()
    # params_marks_density = dict(scale=1)
    params_marks_kernel = dict(slope=1.2)
    params_time_kernel = dict(mu=mu, sigma=sigma)

    marked_events, _ = simu_marked_hawkes_cluster(
        end_time,
        baseline,
        alpha,
        time_kernel,
        marks_kernel,
        marks_density,
        params_marks_kernel=params_marks_kernel,
        params_marks_density=params_marks_density,
        time_kernel_length=None,
        marks_kernel_length=None,
        params_time_kernel=params_time_kernel,
        random_state=seed,
    )

    noisy_events_ = simu_multi_poisson(end_time, [baseline_noise])

    random_marks = [np.random.rand(noisy_events_[i].shape[0]) for i in range(n_dim)]
    noisy_marks = [
        custom_density(
            reverse_linear_zero_one,
            dict(),
            size=noisy_events_[i].shape[0],
            kernel_length=1.0,
        )
        for i in range(n_dim)
    ]
    noisy_events = [
        np.concatenate(
            (noisy_events_[i].reshape(-1, 1), random_marks[i].reshape(-1, 1)), axis=1
        )
        for i in range(n_dim)
    ]

    events = [
        np.concatenate((noisy_events[i], marked_events[i]), axis=0)
        for i in range(n_dim)
    ]

    events_cat = [events[i][events[i][:, 0].argsort()] for i in range(n_dim)]

    labels = [
        np.zeros(marked_events[i].shape[0] + noisy_events_[i].shape[0])
        for i in range(n_dim)
    ]
    labels[0][-marked_events[0].shape[0] :] = 1.0
    true_rho = [labels[i][events[i][:, 0].argsort()] for i in range(n_dim)]
    # put the mark to one to test the impact of the marks
    # events_cat[0][:, 1] = 1.

    return events_cat, noisy_marks, true_rho


ev, noisy_marks, true_rho = simulate_data(
    baseline, baseline_noise.item(), alpha, end_time, seed=0
)

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solver = UNHaP(
    n_dim=1,
    kernel="truncated_gaussian",
    kernel_length=1.0,
    delta=delta,
    optim="RMSprop",
    params_optim={"lr": 1e-3},
    max_iter=max_iter,
    batch_rho=batch_rho,
    density_hawkes="linear",
    density_noise="uniform",
    moment_matching=True,
)
solver.fit(ev, end_time)

sum of marks per channel: tensor([49561.7422])
number of events is: tensor([74591.])
precomput: 0.5620157718658447
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Fitting model...  14.1%
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Fitting model...  17.6%
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Fitting model...  18.1%
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Fitting model...  19.1%
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Fitting model...  20.3%
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Fitting model...  25.1%
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Fitting model...  25.3%
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Fitting model...  26.1%
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Fitting model...  26.3%
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Fitting model...  27.1%
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Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
Fitting model...  28.7%
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Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
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Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
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Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.8%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
Fitting model...  28.9%
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Fitting model...  29.0%
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Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
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Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.0%
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Fitting model...  29.0%
Fitting model...  29.0%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
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Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
Fitting model...  29.1%
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Fitting model...  29.2%
Fitting model...  29.2%
Fitting model...  29.2%
Fitting model...  29.2%
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Fitting model...  29.2%
Fitting model...  29.2%
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Fitting model...  29.2%
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Fitting model...  29.3%
Fitting model...  29.3%
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Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
Fitting model...  29.3%
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Fitting model...  29.4%
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Fitting model...  29.4%
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Fitting model...  29.4%
Fitting model...  29.4%
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Fitting model...  29.4%
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Fitting model...  29.4%
Fitting model...  29.4%
Fitting model...  29.4%
Fitting model...  29.5%
Fitting model...  29.5%
Fitting model...  29.5%
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Fitting model...  29.5%
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Fitting model...  29.5%
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Fitting model...  29.5%
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Fitting model...  29.5%
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Fitting model...  29.5%
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Fitting model...  29.5%
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Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.6%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
Fitting model...  29.7%
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Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.8%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  29.9%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.0%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.1%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.2%
Fitting model...  30.3%
Fitting model...  30.3%
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Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
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Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.3%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.4%
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Fitting model...  30.4%
Fitting model...  30.4%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
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Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
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Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.5%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
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Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.6%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
Fitting model...  30.7%
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Fitting model...  30.8%
Fitting model...  30.8%
Fitting model...  30.8%
Fitting model...  30.8%
Fitting model...  30.8%
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Fitting model...  30.8%
Fitting model...  30.8%
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Fitting model...  30.8%
Fitting model...  30.8%
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Fitting model...  30.8%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
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Fitting model...  30.9%
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Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
Fitting model...  30.9%
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Fitting model...  31.0%
Fitting model...  31.0%
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Fitting model...  31.0%
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Fitting model...  31.0%
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Fitting model...  31.0%
Fitting model...  31.0%
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Fitting model...  31.0%
Fitting model...  31.0%
Fitting model...  31.0%
Fitting model...  31.0%
Fitting model...  31.0%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.1%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.2%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.3%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.4%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.5%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
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Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.6%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
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Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
Fitting model...  31.7%
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Fitting model...  31.8%
Fitting model...  31.8%
Fitting model...  31.8%
Fitting model...  31.8%
Fitting model...  31.8%
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Fitting model...  31.8%
Fitting model...  31.8%
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Fitting model...  31.8%
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Fitting model...  31.8%
Fitting model...  31.8%
Fitting model...  31.9%
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Fitting model...  31.9%
Fitting model...  31.9%
Fitting model...  31.9%
Fitting model...  31.9%
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Fitting model...  31.9%
Fitting model...  31.9%
Fitting model...  31.9%
Fitting model...  31.9%
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Fitting model...  31.9%
Fitting model...  32.0%
Fitting model...  32.0%
Fitting model...  32.0%
Fitting model...  32.0%
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Fitting model...  32.0%
Fitting model...  32.0%
Fitting model...  32.0%
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Fitting model...  32.0%
Fitting model...  32.0%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
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Fitting model...  32.1%
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Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
Fitting model...  32.1%
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Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
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Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
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Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.2%
Fitting model...  32.3%
Fitting model...  32.3%
Fitting model...  32.3%
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Fitting model...  32.3%
Fitting model...  32.3%
Fitting model...  32.3%
Fitting model...  32.3%
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Fitting model...  32.3%
Fitting model...  32.3%
Fitting model...  32.3%
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Fitting model...  32.4%
Fitting model...  32.4%
Fitting model...  32.4%
Fitting model...  32.4%
Fitting model...  32.4%
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Fitting model...  32.4%
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Fitting model...  36.3%
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Fitting model...  37.1%
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Fitting model...  37.3%
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Fitting model...  39.8%
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Fitting model...  39.8%
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Fitting model...  39.8%
Fitting model...  39.8%
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Fitting model...  40.1%
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Fitting model...  40.3%
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Fitting model...  41.0%
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Fitting model...  41.1%
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Fitting model...  41.2%
Fitting model...  41.2%
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Fitting model...  41.3%
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Fitting model...  42.1%
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Fitting model...  42.3%
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Fitting model...  50.1%
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Fitting model...  69.5%
Fitting model...  69.5%
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Fitting model...  69.5%
Fitting model...  69.5%
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Fitting model...  69.6%
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Fitting model...  69.7%
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Fitting model...  70.1%
Fitting model...  70.1%
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Fitting model...  70.2%
Fitting model...  70.2%
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Fitting model...  70.3%
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Fitting model...  70.7%
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Fitting model...  71.1%
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Fitting model...  71.3%
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Fitting model...  72.1%
Fitting model...  72.1%
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Fitting model...  72.2%
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Fitting model...  72.2%
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Fitting model...  72.3%
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Fitting model...  75.1%
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Fitting model...  76.1%
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Fitting model...  77.1%
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Fitting model...  78.1%
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Fitting model...  80.7%
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Fitting model...  81.1%
Fitting model...  81.1%
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Fitting model...  81.2%
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Fitting model...  81.3%
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Fitting model...  81.7%
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Fitting model...  82.0%
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Fitting model...  82.1%
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iterations in  55.329752683639526

<fadin.solver.UNHaP object at 0x7fcce890e700>

print("Estimated baseline is: ", solver.param_baseline[-10:].mean().item())
print("Estimated alpha is: ", solver.param_alpha[-10:].mean().item())
print("Estimated kernel mean is: ", (solver.param_kernel[0][-10:].mean().item()))
print("Estimated kernel sd is: ", solver.param_kernel[1][-10:].mean().item())
print("Estimated noise baseline is: ", solver.param_baseline_noise[-10:].mean().item())
# error on params
error_baseline = (solver.param_baseline[-10:].mean().item() - baseline.item()) ** 2
error_baseline_noise = (
    solver.param_baseline_noise[-10:].mean().item() - baseline_noise.item()
) ** 2
error_alpha = (solver.param_alpha[-10:].mean().item() - alpha.item()) ** 2
error_mu = (solver.param_kernel[0][-10:].mean().item() - 0.5) ** 2
error_sigma = (solver.param_kernel[1][-10:].mean().item() - 0.1) ** 2
sum_error = error_baseline + error_baseline_noise + error_alpha + error_mu + error_sigma
error_params = np.sqrt(sum_error)

print("L2 square errors of the vector of parameters is:", error_params)

Estimated baseline is:  0.30654624104499817
Estimated alpha is:  1.4332163333892822
Estimated kernel mean is:  0.4043726921081543
Estimated kernel sd is:  0.10575250536203384
Estimated noise baseline is:  0.5540191531181335
L2 square errors of the vector of parameters is: 0.5133590602874576

fig, axs = plot(solver, plotfig=False, bl_noise=True, title="UNHaP fit", savefig=None)
plt.show(block=True)