> It's more than fancy linear regression.

I am not an expert, but it seems to me that "big data algorithms" are actually simpler and require less ingenuity than classical statistics. Just look at a difference between frequentist and bayesian approaches in statistics. In frequentist methods, you need to choose model wisely, you're constrained what you can model, and there are many different models with different assumptions. With bayesian methods, you just represent any distribution somehow and do the calculation on those. Less assumptions for the models, more general models, but at the expense of more computations.