Would a computer science degree be the best major for an entrepreneur interested in machine learning, or is being self-taught and/or taking a few classes as electives fine?
If you are an entrepreneur, then it means you are running the business. Which means that you are also responsible for funding it and hiring people. Which means you could technically hire yourself. You only need a degree (generally speaking) because you want to work for someone else who requires a degree.
From my experience with college and getting a degree is that the pros are this:
Structure & discipline - If you have not developed enough structure and discipline, you will most likely fail at trying to run your own business.
Networking - Schools are great for connecting with other people on the same path as you.
If you have the funding on your own, or know how to get it, and plan on running/owning the business, being self taught might be sufficient as long as you have the structure and discipline to be really good at learning on your own.