This issue should be "easy" if you are already familiar with:

• travis configuration
• bash scripting
• docker

We need to add the following line in our .travis.yml:

sudo: required

services:
  - docker

more details in Using Docker in Builds.

Here is a minimalistic script that could put in build_tools/travis/docker_test.sh:

# This test script is mean to be executed with 'docker run' using one of the manylinux images
set -e
export PATH=/opt/python/cp36-cp36m/bin:$PATH
pip install numpy scipy cython nose pytest
cd /io
pip install -e .
pytest -l sklearn

This script can used to launch the test with (for 32 bit linux):

docker run --rm -v`pwd`:/io quay.io/pypa/manylinux1_i686 \
    bash /io/build_tools/travis/docker_test.sh

This command should be launched from the scikit-learn folder such that the -v flag mount the scikit-learn source folder of the host into the /io folder inside the container.

The above test script should be improved to specify the version number of python, numpy scipy and cython with environment variables defined in .travis.yml (that should be passed via the -e flag of the docker command).