Actually all these models are just variations of well known statistical models (or can be derived as such). For instance support vector machines is the same as logistic regression with a slightly different loss function and regularization. Clustering is also a well know subject of statistics (in machine learning often referred to as unsupervised machine learning). Deep learning is 'just' stacking different models on top of each other hoping to capture more abstract concepts. Very cool but at this point there is not a good mathematical explanation why this works so well.
A lot of stuff is the same between machine learning and statistics with different terminology. With machine learning often more focussing on the practical side rather the theoretical side (or the real probabilities).
It's good to cross pollinate and learn from each other. Such as the machine learning field learning to create better models with Bayesian statistics, and statisticians learning from models like support vector machines.
I also look forward to more mathematicians and statisticians exploring deep learning, and finding more rigorous scientific explanations why they work so well (and this can help us making them even better).
(I come from an Econometrics background, but wrote my master these about machine learning).