GPs on Non-Euclidean Input Spaces

GPs on non-Euclidean input spaces have become more and more relevant in recent years. fvgp can be used for that purpose as long as a cvalid kernel is provided. Of course, if mean functions and noise functions are also provided, they have to operate on these non-Euclidean spaces.

In this example, we run a small GP on words. It’s a proof of concept, the results are not super relevant

#install the newest version of fvgp
#!pip install fvgp==4.2.0

import numpy as np
import matplotlib.pyplot as plt
from fvgp import GP
from dask.distributed import Client
%load_ext autoreload
%autoreload 2

#making the x_data a set will allow us to put any objects or structures into it.
x_data = [('hello'),('world'),('this'),('is'),('fvgp')]
y_data = np.array([2.,1.9,1.8,3.0,5.])


from fvgp.gp_kernels import *
def string_distance(string1, string2):
    difference = abs(len(string1) - len(string2))
    common_length = min(len(string1),len(string2))
    string1 = string1[0:common_length]
    string2 = string2[0:common_length]
    
    for i in range(len(string1)):
        if string1[i] != string2[i]:
            difference += 1.

    return difference


def kernel(x1,x2,hps,obj):
    d = np.zeros((len(x1),len(x2)))
    count1 = 0
    for string1 in x1:
        count2 = 0
        for string2 in x2:
            d[count1,count2] = string_distance(string1,string2)
            count2 += 1
        count1 += 1
    return hps[0] * matern_kernel_diff1(d,hps[1])
    



my_gp = GP(x_data,y_data,init_hyperparameters=np.ones((2)), gp_kernel_function=kernel, info = False)

bounds = np.array([[0.001,100.],[0.001,100]])
my_gp.train(hyperparameter_bounds=bounds)

print("hyperparameters: ", my_gp.get_hyperparameters())
print("prediction : ",my_gp.posterior_mean(['full'])["f(x)"])
print("uncertainty: ",np.sqrt(my_gp.posterior_covariance(['full'])["v(x)"]))

hyperparameters:  [1.43431191 0.40010055]
prediction :  [2.74004694]
uncertainty:  [1.19762762]

/home/marcus/Coding/fvGP/fvgp/gp.py:261: UserWarning: hyperparameter_bounds not provided. They will have to be provided in the training call.
  warnings.warn("hyperparameter_bounds not provided. "
/home/marcus/Coding/fvGP/fvgp/gp.py:301: UserWarning: No noise function or measurement noise provided. Noise variances will be set to 1% of mean(y_data).
  self.likelihood = GPlikelihood(self.data.x_data,