If you are sure that the program isn't uninstalled, you can navigate to the folder in which Microsoft Office is installed. By default, it should be under : C:\Program Files \Microsoft Office\ Office. In the mentioned folder, you should be able to find all the EXE files from all the Office tools like Word, Excel, Publisher. From there, you should right click on the ones you want to see on desktop and select Send to > Desktop.
This can also be done by performing a right click on desktop > New > Shortcut, navigate to the same location as above, select the Publisher EXE file, click Next, choose a name and click Finish.