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我想使用 GPflow 中使用版本 2 实现的高斯过程回归执行一些多元回归。安装pip install gpflow==2.0.0rc1

下面是一些示例代码，它生成一些 2D 数据，然后尝试使用 GPR 对其进行拟合，最后计算真实输入数据和 GPR 预测之间的差异。

最终，我想扩展到更高的维度并针对验证集进行测试以检查过度拟合并尝试使用其他内核和“自动相关性确定”，但了解如何使其工作是第一步。

谢谢！

以下代码片段将在 jupyter notebook 中运行。

import gpflow
import numpy as np
import matplotlib
from gpflow.utilities import print_summary

%matplotlib inline
matplotlib.rcParams['figure.figsize'] = (12, 6)
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def gen_data(X, Y):
    """
    make some fake data.
    X, Y are np.ndarrays with shape (N,) where
    N is the number of samples.
    """

    ys = []
    for x0, x1 in zip(X,Y):
        y = x0 * np.sin(x0*10)
        y = x1 * np.sin(x0*10)
        y += 1
        ys.append(y)
    return np.array(ys)


# generate some fake data
x = np.linspace(0, 1, 20)
X, Y = np.meshgrid(x, x)

X = X.ravel()
Y = Y.ravel()

z = gen_data(X, Y)

#note X.shape, Y.shape and z.shape
#are all (400,) for this case.

# if you would like to plot the data you can do the following
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(X, Y, z, s=100, c='k')


# had to set this 
# to avoid the following error
# tensorflow.python.framework.errors_impl.InvalidArgumentError: Cholesky decomposition was not successful. The input might not be valid. [Op:Cholesky]
gpflow.config.set_default_positive_minimum(1e-7)

# setup the kernel

k = gpflow.kernels.Matern52()


# set up GPR model

# I think the shape of the independent data
# should be (400, 2) for this case
XY = np.column_stack([[X, Y]]).T
print(XY.shape) # this will be (400, 2)

m = gpflow.models.GPR(data=(XY, z), kernel=k, mean_function=None)

# optimise hyper-parameters
opt = gpflow.optimizers.Scipy()

def objective_closure():
    return - m.log_marginal_likelihood()

opt_logs = opt.minimize(objective_closure,
                        m.trainable_variables,
                        options=dict(maxiter=100)
                       )


# predict training set
mean, var = m.predict_f(XY)

print(mean.numpy().shape)
# (400, 400)
# I would expect this to be (400,)

# If it was then I could compute the difference
# between the true data and the GPR prediction
# `diff = mean - z`
# but because the shape is not as expected this of course
# won't work.
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1 回答 1

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的形状z必须是(N, 1)，而在您的情况下是(N,)。但是，这是 GPflow 中缺少的检查，而不是您的错。

于 2020-02-10T10:59:02.307 回答