If I understand correctly you are in the predictive analytics space so potential clients are using Big Data in some way. If this is so Linked In is probably the best social media platform for inbound lead generation.
If this is true then there are only a few options that have been successful for others. I have listed them in order of potential success rates the best will be last in the list.
1. Hire an intern to develop your connections and publish relevant content in posts and in relevant group forums.
2. Hire someone with technical skills to run automated software that - a. automatically visits other Linked in profiles (a percentage will then look at your profile and your marketing message) and b. regularly sends out invitations to connect and sends direct messages on a regular basis to your 1st level connections. And publish relevant content in posts and in relevant group forums.
3. Outsource these activities.
Simply handing this off to a outsourcing group without regular interaction from you company is unlikely to product a positive result. If you are looking at outsourcing the more involved you and your team are the more likely a positive outcome.
I hope this helps.
Biz Builder Mike