Software license compliance, known unknowns

I’m currently working with a Fortune 500 company that has 10k desktops worldwide. My group is responsible for desktop infrastructure so we are the primary area audit comes asking for desktop software license compliance. The problem we have is that people will install and run applications we do not know about, yet we are on the hook for ensuring all desktops have licensed software. The question is: how do you keep track of all software and associated licenses when you don’t control installations or purchasing?