Issue 1:
test_extract_xi failing for MB_PYTHON_VERSION=3.6 PLAT=i686 and MB_PYTHON_VERSION=3.7 PLAT=i686

https://travis-ci.org/MacPython/scikit-learn-wheels/jobs/525429182

https://travis-ci.org/MacPython/scikit-learn-wheels/jobs/525429184

Issue 2:
I'm re-posting the issue

#12273

as its owner no longer works on scikit-learn.

Here is a code snippet, fitting 2-cluster Gaussian data (blue) in 1-d with well-separated means. Fitting with mean_concentration_prior set to 0.001 (orange), BayesianGaussianMixture finds the 2 clusters nicely. However, with mean_concentration_prior set to 35, we can clearly see the 2 clusters biased towards mean_prior, which is by default the sample mean of the data.

The documentation states

| mean_precision_prior : float | None, optional.

| The precision prior on the mean distribution (Gaussian).

| Controls the extend to where means can be placed. Smaller (LARGER??)

| values concentrate the means of each clusters around mean_prior.

| The value of the parameter must be greater than 0.

| If it is None, it's set to 1.

while running the code, it seems larger values of mean_precision_prior concentrate the prior around mean_prior.

import numpy as _N
from sklearn.mixture import BayesianGaussianMixture
import matplotlib.pyplot as _plt

# generate data - 2-component Gaussian mixture
N1 = 220
N2 = 380

X = _N.empty((N1+N2, 1))
X[0:N1, 0] = 0.1*_N.random.randn(N1)
X[N1:N1+N2, 0] = 5 + 0.1*_N.random.randn(N2) # 2nd cluster well separted from 1st.

# max # of components for finite approx of Dirichlet process
n_components = 4

# example - setting dof_prior and cov. prior to reasonable value
# still produces very wide

# [dof_prior, cov_prior, mean_prec_prior]
prm_sets = [[0.1, 0.1, 0.001],
[0.1, 0.1, 35.]]

# Documentation for mean_prec_prior says small value concentrates around
# mean prior. In this case, I expect the 1st param set to not be able
# to fit the 2 clusters which are well separated.
# However running code shows the opposite.
# Therefore, I believe the documentation should say
# LARGER values concentrate the means of each clusters around `mean_prior`

# | mean_precision_prior : float | None, optional.
# | The precision prior on the mean distribution (Gaussian).
# | Controls the extend to where means can be placed. Smaller (LARGER??)
# | values concentrate the means of each clusters around `mean_prior`.
# | The value of the parameter must be greater than 0.
# | If it is None, it's set to 1.

fig = _plt.figure(figsize=(7, 4))
i_subpl = 0

random_state = 10
BNS=140

# bins for histogram
xbns = _N.linspace(-1, 6, BNS+1)
xms = 0.5*(xbns[0:-1] + xbns[1:])
dx = _N.diff(xbns)[0]

for prm in prm_sets:
i_subpl += 1

occ_cnts, bnsx = _N.histogram(X[:, 0], bins=xbns)

bgm = BayesianGaussianMixture(\
n_components=n_components,\
################ priors
weight_concentration_prior_type="dirichlet_process",\
weight_concentration_prior=0.9,\
degrees_of_freedom_prior=prm[0],\
covariance_prior=_N.array([prm[1]]),\
mean_precision_prior=prm[2],\
################ priors
reg_covar=0, init_params='random',\
max_iter=1500,\
random_state=random_state, covariance_type="diag")

bgm.fit(X)

pcs = bgm.means_.shape[0]

mns_r = bgm.means_.T.reshape((1, pcs))
isd2s_r= bgm.precisions_.T.reshape((1, pcs))
sd2s_r = bgm.covariances_.T.reshape((1, pcs))
xms_r = xms.reshape((BNS, 1))

A = (bgm.weights_ / _N.sqrt(2*_N.pi*sd2s_r)) * dx
occ_x = _N.sum(A*_N.exp(-0.5*(xms_r - mns_r)*(xms_r - mns_r)*isd2s_r), axis=1)
fig.add_subplot(1, 2, i_subpl)
_plt.ylim(0, 0.15)
_plt.plot(xms, occ_cnts/(X.shape[0]))
_plt.plot(xms, occ_x)
_plt.title("[%(dof).1f, %(cov).1f, %(prc).3f]" % {"dof" : prm[0], "cov" : prm[1], "prc" : prm[2]})

_plt.suptitle("[dof prior, cov prior, mn prec prior]")
_plt.savefig("prior_effect.png")

>>> import sklearn; sklearn.show_versions()

System:
python: 3.7.1 (default, Dec 14 2018, 13:28:58) [Clang 4.0.1 (tags/RELEASE_401/final)]
executable: /Users/arai/miniconda2/envs/py37/bin/python
machine: Darwin-14.5.0-x86_64-i386-64bit

BLAS:
macros: SCIPY_MKL_H=None, HAVE_CBLAS=None
lib_dirs: /Users/arai/miniconda2/envs/py37/lib
cblas_libs: mkl_rt, pthread

Python deps:
pip: 18.1
setuptools: 40.6.3
sklearn: 0.20.3
numpy: 1.15.4
scipy: 1.1.0
Cython: 0.29.2
pandas: 0.24.1