The problem, that the installation freezes, has been fixed by the Ubuntu 18.04.2 LTS version. It comes with the 4.18 kernel by default and lets you install Ubuntu without any problem. However, after installation, it still freezes after attempting to log in.
To fix this, you have to boot your the Linux kernel with the
nomodeset option. Here's what you do:
Follow this instruction on how to boot your Linux kernel with the
Log into your computer (It will be in 800x400 pixel mode)
Enter the terminal with
Install the latest Nvidia driver. It occurred to me, that it's easier to install the driver from the
graphics-drivers repository than from Nvidia directly. To find out the latest driver version, go to the Nvidia drivers page and type in your GPU information (GTX1070, Linux-64bit). Right now it is version
430. Then run:
sudo add-apt-repository ppa:graphics-drivers/ppa
sudo apt-get update
sudo apt-get install nvidia-driver-430
(if the last step failed, try
sudo apt-get install nvidia-430)
Now reboot your computer and you should be set. Validate the driver installation by running
nvidia-smi in a terminal.