gammy 0.4.0

Generalized additive models with a Bayesian twist

Gammy – Generalized additive models in Python with a Bayesian twist

A Generalized additive model is a predictive mathematical model defined as a sum of terms that are calibrated (fitted) with observation data.

Generalized additive models form a surprisingly general framework for building models for both production software and scientific research. This Python package offers tools for building the model terms as decompositions of various basis functions. It is possible to model the terms e.g. as Gaussian processes (with reduced dimensionality) of various kernels, as piecewise linear functions, and as B-splines, among others. Of course, very simple terms like lines and constants are also supported (these are just very simple basis functions).

The uncertainty in the weight parameter distributions is modeled using Bayesian statistic with the help of the superb package BayesPy.

Documentation

A detailed documentation of the package can be found in https://malmgrek.github.io/gammy.

Installation

The package is found in PyPi.

pip install gammy

Quick glance

Let's try to estimate the MATLAB function from pseudo-random samples that are corrupted with pseudo-random noise.

import matplotlib.pyplot
import numpy as np

import gammy
from gammy.arraymapper import x


# Simulate data
n = 100
input_data = 6 * np.vstack((np.random.rand(n), np.random.rand(n))).T - 3
y = (
    gammy.peaks(input_data[:, 0], input_data[:, 1]) + 4 
    + 0.3 * np.random.randn(n)
)

# Fit a model
gp = gammy.ExpSquared1d(
    grid=np.arange(-3, 3, 0.1),
    corrlen=0.5,
    sigma=4.0,
    energy=0.9
)
model = gammy.models.bayespy.GAM(
    # Define a bivariate Gaussian Process prior with a
    # Kronecker structure
    gammy.Kron(gp(x[:, 0]), gp(x[:, 1])) + gammy.Scalar()
).fit(input_data, y)

err = model.predict(input_data) - y  # Prediction error
err.mean()
# 1.00842e-08
err.std()
# 0.739

# Noise std estimated by the model
np.sqrt(model.inv_mean_tau)
# 0.913

Plot generated with gammy.plot.validation_plot:

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