How can you encourage a person to invite you to an event that you were not previously invited to without making them feel like you have to invite them?

I heard that inviting yourself places it’s rude but I would really like to get involved in some parties and social outings but I never get invited. So how can I, if I know of parties and other events going on that is not open to the general public, encourage a person who is hosting or going to that event to invite me out of their own free will. I don’t want the person to feel like they have to invite me I just want them to remember that I exist and decide to invite me out of their own free will because they think I’ll be a good addition and not because they feel sorry for me or they don’t want to upset me.