Fastgam

Fastgam is a Python package for constructing fast additive models.

Installation

You can install the package via pip:

pip install fastgam

Minimal example

In this example, we try to learn an additive model with $d = 5$ effects, with a regularity $s = 2$. The data satisfies

• $Y = f(X_1, \dots, X_5) + \varepsilon$,
• $f(x_1, \dots, x_5) = \sum_{j=1}^5 (\exp(x_j/(j+1))-1)$,
• $\varepsilon \sim \mathcal N(0, 1)$.

import numpy as np
from fastgam import FastGAM

d = 5
s = 2
N = 10**2
N_val = 1000

lambda_N_list = [10**(-i/3) for i in range(10)]

x_train = np.random.uniform(size=(d, N))
f_train = np.zeros(N)
for i in range(d):
    f_train += np.exp(x_train[i]/(i+1)) - 1
y_train =  (f_train + np.random.normal(size=N)).astype(np.complex128)

x_val = np.random.uniform(size=(d, N_val))
f_val = np.zeros(N_val)
for i in range(d):
    f_val += np.exp(x_val[i]/(i+1)) - 1
y_val =  (f_val + np.random.normal(size=N_val)).astype(np.complex128)


lambda_n=N**(-(2*s)/(2*s+1))
m = 1+ int(N**(1/(2*s+1))/d)
threshold = lambda_n/10

model = FastGAM(d)
model.fit_grid(x_train, y_train, x_val, y_val,lambda_N_list, m, threshold)

N_test = 10**4
x_test = np.random.uniform(size=(d, N_test))
f_test = np.zeros(N_test)

for i in range(d):
    f_test += np.exp(x_test[i]/(i+1)) - 1
y_test =  f_test.astype(np.complex128)

model.predict(x_test)
model.mse(y_test)