Multimodal Exponentially Modified Gaussians

Quick Facts

• multiple asymmetric Gaussian distributions for the univariate case
• optional oscillation term for wave approximations
• based on analytical derivation
• accepts numpy as well as torch data types

Kick Start

Below is a code excerpt for fitting multi-modal skewed Gaussian distributions:

from multimodal_emg import gaussian_envelope_model, emg_envelope_model, emg_wave_model
from multimodal_emg.regression.derivatives import gaussian_jac, emg_jac, oemg_jac

# multimodal optimization
p_star, result = multimodal_fit(
    data,
    features = [[1, 24, 2, 0],[.5, 48, 3, -1]], # amplitude, location, spread, skew
    components = 2,
    x = x,
    fun = emg_envelope_model,
    jac_fun = emg_jac,
)

print(p_star)

import matplotlib.pyplot as plt
plt.plot(result)
plt.show()

Oscillating Regression

The oscillation regression can be found in the accompanied Jupyter Notebook which yields the below result:

Citation

@inproceedings{Hahne:2022,
    author = {Christopher Hahne},
    title = {Multimodal Exponentially Modified Gaussian Oscillators},
    booktitle= {2022 IEEE International Ultrasonics Symposium (IUS)},
    address={},
    month={Okt},
    year={2022},
    pages={1-4},
}

Acknowledgment

This research is funded by the Hasler foundation under project number 22027.