我在 GPFlow 中构建了一个自定义的 Matern32 内核，以对一些计算成本很高的矩阵值进行操作，这些矩阵值包含我的数据点之间的“距离”：
import numpy as np
import tensorflow as tf
import gpflow
dat_mat = np.load('example_matrix.npy')
dat_diag = tf.constant(np.diag(dat_mat),dtype=tf.float64)
dat_mat = tf.constant(dat_mat,dtype=tf.float64)
def sub_mat(A,A2):
global dat_mat
A = tf.cast(A,tf.int32)
A2 = tf.cast(A2,tf.int32)
K_rows = tf.gather_nd(dat_mat, A)
K_rows = tf.transpose(K_rows)
K_mat = tf.gather_nd(K_rows, A2)
K_mat = tf.transpose(K_mat)
return tf.cast(K_mat, tf.float64)
class Matern32_RBF(gpflow.kernels.Kernel):
global dat_mat, dat_diag
def __init__(self):
super().__init__(input_dim=1, active_dims=[0])
self.var = gpflow.Param(1.0, transform=gpflow.transforms.Exp())
self.mag = gpflow.Param(1.0, transform=gpflow.transforms.Exp())
@gpflow.params_as_tensors
def K(self, A, A2=None):
if A2 is None:
A2=A
K_mat = sub_mat(A,A2)
z = np.sqrt(3)*K_mat*self.var
return self.mag*(1+z)*tf.math.exp(-z)
def Kdiag(self, A):
A=tf.cast(A,tf.int32)
K_diag = tf.cast(tf.gather_nd(dat_diag, A),tf.float64)
z = np.sqrt(3)*K_diag*self.var
return self.mag*(1+z)*tf.math.exp(-z)
此自定义内核是为二进制分类任务实现的（附加示例数据文件）：
Y=np.loadtxt('example_data.csv', usecols=1)
len_dataset = len(Y)
#These x-values only refer to the rows of my computed distance matrix
X=np.array(range(len_dataset))
X=X.astype(int)
X=X.reshape(-1,1)
Y=Y.reshape(-1,1)
k = Matern32_RBF()
#Data_set split
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, Y, random_state=1)
custom_config = gpflow.settings.get_settings()
custom_config.numerics.jitter_level = 1e-3
opt = gpflow.train.ScipyOptimizer()
model = gpflow.models.VGP(X_train, y_train, likelihood=gpflow.likelihoods.Bernoulli(), kern=k)
with gpflow.settings.temp_settings(custom_config):
opt.minimize(model)
运行上述返回以下错误：
Traceback (most recent call last):
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1334, in _do_call
return fn(*args)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1319, in _run_fn
options, feed_dict, fetch_list, target_list, run_metadata)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1407, in _call_tf_sessionrun
run_metadata)
tensorflow.python.framework.errors_impl.InvalidArgumentError: Cholesky decomposition was not successful. The input might not be valid.
[[{{node VGP-cb46397c-6/Cholesky}}]]
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "trial.py", line 64, in
opt.minimize(model)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/training/scipy_optimizer.py", line 89, in minimize
**kwargs)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/training/external_optimizer.py", line 175, in minimize
optimizer_kwargs=self.optimizer_kwargs)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/training/external_optimizer.py", line 436, in _minimize
result = scipy.optimize.minimize(*minimize_args, **minimize_kwargs)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/scipy/optimize/_minimize.py", line 601, in minimize
callback=callback, **options)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/scipy/optimize/lbfgsb.py", line 335, in _minimize_lbfgsb
f, g = func_and_grad(x)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/scipy/optimize/lbfgsb.py", line 285, in func_and_grad
f = fun(x, args)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/scipy/optimize/optimize.py", line 300, in function_wrapper
return function((wrapper_args + args))
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/scipy/optimize/optimize.py", line 63, in call
fg = self.fun(x, *args)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/training/external_optimizer.py", line 398, in loss_grad_func_wrapper
loss, gradient = loss_grad_func(x)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/training/external_optimizer.py", line 309, in eval_func
augmented_fetches, feed_dict=augmented_feed_dict)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 929, in run
run_metadata_ptr)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1152, in _run
feed_dict_tensor, options, run_metadata)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1328, in _do_run
run_metadata)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/client/session.py", line 1348, in _do_call
raise type(e)(node_def, op, message)
tensorflow.python.framework.errors_impl.InvalidArgumentError: Cholesky decomposition was not successful. The input might not be valid.
[[node VGP-cb46397c-6/Cholesky (defined at /home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/models/vgp.py:108) ]]
Caused by op 'VGP-cb46397c-6/Cholesky', defined at:
File "trial.py", line 61, in
model = gpflow.models.VGP(X_train, y_train, likelihood=gpflow.likelihoods.Bernoulli(), kern=k)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/core/compilable.py", line 90, in init
self.build()
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/core/node.py", line 156, in build
self._build()
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/models/model.py", line 79, in _build
likelihood = self._build_likelihood()
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/decors.py", line 67, in tensor_mode_wrapper
result = method(obj, *args, **kwargs)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/models/vgp.py", line 108, in _build_likelihood
L = tf.cholesky(K)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/ops/gen_linalg_ops.py", line 767, in cholesky
"Cholesky", input=input, name=name)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/framework/op_def_library.py", line 788, in _apply_op_helper
op_def=op_def)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/util/deprecation.py", line 507, in new_func
return func(*args, **kwargs)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/framework/ops.py", line 3300, in create_op
op_def=op_def)
File "/home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/tensorflow/python/framework/ops.py", line 1801, in init
self._traceback = tf_stack.extract_stack()
InvalidArgumentError (see above for traceback): Cholesky decomposition was not successful. The input might not be valid.
[[node VGP-cb46397c-6/Cholesky (defined at /home/wjm41/.conda/envs/gpenv/lib/python3.6/site-packages/gpflow/models/vgp.py:108) ]]
我已经尝试改变 GPFlow 设置中的抖动级别以及内核参数的初始值，但这并没有解决这个 Cholesky 分解问题。我的自定义内核适用于回归任务，所以我不确定问题出在哪里。我的数据真的很糟糕吗？（示例数据是完整数据集的一小部分 - 请参阅此处了解脚本和数据。）
我正在使用 Python 3.6、GPFlow 1.3.0 和 TensorFlow 1.13.1。任何帮助将非常感激！