My guess is that you'd find a connection that works your particular area to validate the problem. If it's a first level connection that's great, easier to ask :). Otherwise, find a second level connection and get introduced to them. Say that you'd like to discuss some of the problems that they may experience [as a teacher, entrepreneur, etc]. People love to talk about their problems to someone who will listen.
Yes, exactly caw - thanks. I view LinkedIn as one huge convention center, and the worst that can happen is people decline you connection request. If you present an honest and positive tone, people will be more receptive. Then it is possible to PM select connections to review your idea or beta, etc.