Description

Gaussian Process Regression throws a "non-positive definite matrix" error when it shouldn't.

Steps/Code to Reproduce

Without using sklearn, we get no error on the decomposition:

from scipy.linalg import cholesky
import numpy as np
K_ = np.load('./K_18_2.npy')
L_ = cholesky(K_, lower=True)

...returns no error, no exception, no warning.

Doing the same with gaussian process regression imported:

from sklearn.gaussian_process import gpr
from scipy.linalg import cholesky
import numpy as np
K_ = np.load('./K_18_2.npy')
L_ = cholesky(K_, lower=True)

Yields this error:

38 if info > 0:
39 raise LinAlgError("%d-th leading minor of the array is not positive "
---> 40 "definite" % info)
41 if info < 0:
42 raise ValueError('LAPACK reported an illegal value in {}-th argument'

LinAlgError: 113-th leading minor of the array is not positive definite

Get the dataset K_18_2.npy here:

https://keybase.pub/espg/K_18_2.npy

Expected Results

No error is thrown. Can use gpr on the data....

adding to the diagonal doesn't do anything-- and shouldn't be needed anyways for this dataset...

Actual Results

38 if info > 0:
39 raise LinAlgError("%d-th leading minor of the array is not positive "
---> 40 "definite" % info)
41 if info < 0:
42 raise ValueError('LAPACK reported an illegal value in {}-th argument'

LinAlgError: 113-th leading minor of the array is not positive definite

Versions

Impacts at least versions 0.20.x ; not present on 0.19.0 and earlier.

System:
python: 3.6.8 (default, Dec 24 2018, 03:01:30) [GCC 7.3.0]
executable: /nix/store/80qva2zal82njkg4zvb7xg94mnikqksd-python3-3.6.8/bin/python3.6m
machine: Linux-4.4.0-143-generic-x86_64-with-debian-stretch-sid

BLAS:
macros: SCIPY_MKL_H=None, HAVE_CBLAS=None
lib_dirs: /usr/local/intel/compilers_and_libraries_2016.3.210/linux/mkl/lib/intel64
cblas_libs: mkl_rt, pthread

Python deps:
pip: 18.1
setuptools: 40.2.0
sklearn: 0.20.3
numpy: 1.15.1
scipy: 1.1.0
Cython: 0.28.3
pandas: 0.23.4