Optimise custom gaussian processes kernel in scikit using gridsearch

问题

I'm working with Gaussian processes and when I use the scikit-learn GP modules I struggle to create and optimise custom kernels using gridsearchcv. The best way to describe this problem is using the classic Mauna Loa example where the appropriate kernel is constructed using a combination of already defined kernels such as RBF and RationalQuadratic. In that example the parameters of the custom kernel are not optimised but treated as given. What if I wanted to run a more general case where I would want to estimate those hyperparameters using cross-validation? How should I go about constructing the custom kernel and then the corresponding param_grid object for the grid search?

In a very naive way I could construct a custom kernel using something like this:

def custom_kernel(a,ls,l,alpha,nl):
    kernel = a*RBF(length_scale=ls) \
    + b*RationalQuadratic(length_scale=l,alpha=alpha) \
    + WhiteKernel(noise_level=nl)
    return kernel

however this function can't of course be called from gridsearchcv using e.g. GaussianProcessRegressor(kernel=custom_kernel(a,ls,l,alpha,nl)).

One possible path forward is presented in this SO question however I was wondering if there's an easier way to solve this problem than coding the kernel from scratch (along with its hyperparameters) as I'm looking to work with a combination of standard kernels and there's also the possibility that I would like to mix them up.

回答1:

So this is how far I got. It answers the question but it is really really slow for the Mauna Loa example however that's probably a difficult dataset to work with:

from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.model_selection import GridSearchCV
from sklearn.gaussian_process.kernels import ConstantKernel,RBF,WhiteKernel,RationalQuadratic,ExpSineSquared
import numpy as np
from sklearn.datasets import fetch_openml

# from https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_co2.html
def load_mauna_loa_atmospheric_co2():
    ml_data = fetch_openml(data_id=41187)
    months = []
    ppmv_sums = []
    counts = []

    y = ml_data.data[:, 0]
    m = ml_data.data[:, 1]
    month_float = y + (m - 1) / 12
    ppmvs = ml_data.target

    for month, ppmv in zip(month_float, ppmvs):
        if not months or month != months[-1]:
            months.append(month)
            ppmv_sums.append(ppmv)
            counts.append(1)
        else:
            # aggregate monthly sum to produce average
            ppmv_sums[-1] += ppmv
            counts[-1] += 1

    months = np.asarray(months).reshape(-1, 1)
    avg_ppmvs = np.asarray(ppmv_sums) / counts
    return months, avg_ppmvs

X, y = load_mauna_loa_atmospheric_co2()

# Kernel with parameters given in GPML book
k1 = ConstantKernel(constant_value=66.0**2) * RBF(length_scale=67.0)  # long term smooth rising trend
k2 = ConstantKernel(constant_value=2.4**2) * RBF(length_scale=90.0) \
    * ExpSineSquared(length_scale=1.3, periodicity=1.0)  # seasonal component
# medium term irregularity
k3 = ConstantKernel(constant_value=0.66**2) \
    * RationalQuadratic(length_scale=1.2, alpha=0.78)
k4 = ConstantKernel(constant_value=0.18**2) * RBF(length_scale=0.134) \
    + WhiteKernel(noise_level=0.19**2)  # noise terms
kernel_gpml = k1 + k2 + k3 + k4
gp = GaussianProcessRegressor(kernel=kernel_gpml)

# print parameters
print(gp.get_params())

param_grid = {'alpha': np.logspace(-2, 4, 5),
              'kernel__k1__k1__k1__k1__constant_value': np.logspace(-2, 4, 5),
              'kernel__k1__k1__k1__k2__length_scale': np.logspace(-2, 2, 5),
              'kernel__k2__k2__noise_level':np.logspace(-2, 1, 5)
              }
grid_gp = GridSearchCV(gp,cv=5,param_grid=param_grid,n_jobs=4)
grid_gp.fit(X, y)

What helped me was to initialise the model first as gp = GaussianProcessRegressor(kernel=kernel_gpml) and then use the get_params attribute in order to get a list of the model hyper parameters.

Finally I note that in their book Rasmussen and Williams appear to have used Leave one out cross validation to tune the hyperparameters.

来源：https://stackoverflow.com/questions/58938819/optimise-custom-gaussian-processes-kernel-in-scikit-using-gridsearch

标签

python-3.x

machine-learning

scikit-learn

regression

gridsearchcv