Database

db={"videos":[{"_id":"1","name":"1's Video","status":"complete","privacy":"public"},{"_id":"2","name":"2's Video","status":"complete","privacy":"public"},{"_id":"3","name":"3's Video","status":"complete","privacy":"public"},{"_id":"4","name":"4's Video","status":"complete","privacy":"private"},{"_id":"5","name":"5's Video","status":"flagged","privacy":"public"}],"analytics":[{"_id":"1","user":"1","event":"video_impression","data":{"video":"1"}},{"_id":"2","user":"2","event":"video_impression","data":{"video":"2"}}]}

Query

db.videos.aggregate([{$match:{"status":"complete","privacy":"public"}},{$lookup:{from:"analytics",localField:"_id",foreignField:"data.video",as:"matched_docs"}},{$match:{"matched_docs":{$eq:[]}}}])

Result