On Linux distros, you can use third party repositories which add to the system ones and allow you to install more ercent versions of some packages. They have to be handled with a bit of care but they’re quite useful to have new software.
The Ubuntu MATE developers have a special repository that can upgrade the desktop on 16.04 to a more recent version (1.18). The repo is there: https://launchpad.net/~ubuntu-mate-dev/+archive/ubuntu/xenial-mate
If you want to upgrade your desktop, add the repo and upgrade like this in a terminal:
sudo add-apt-repository ppa:ubuntu-mate-dev/xenial-mate
sudo apt-get update
sudo apt-get dist-upgrade
Note that it only upgrades the desktop itself, the apps in general will still be the old ones from the 16.04 repos. If you want newer apps, you’ll have to install a more recent version of Ubuntu MATE (17.04). With a LTS version (14.04, 16.04, future 18.04…) you can keep it for up to five years but you have older apps. With a regular version (currently 17.04), you have to upgrade your system every six monthes (next version is 17.10 in october) but you have more recent apps.