I've been having some problem with compiz causing lock ups in 16.04 lately. You should try Marco as your window manager for a while to see if that alleviates the problem. Also, you should enable Ctrl+Alt+Backspace to get out of a freeze, which is more preferred than powering down.
https://ubuntu-mate.community/t/enable-ctrl-alt-backspace/12971?u=steven
As @BrokenCanoe has already pointed out, this should be in the support section of the forum. However, I hope this helps you stabilize your system. Ubuntu Mate 16.04 is not perfect, but is still a good daily driver IMO.