There are a lot of big names in the field, the ones that come to my mind. I will comment that these names are really only representative of the academic track. Data Science outside of academia is very different (and since I'm pretty much just out of undergrad, don't know anyone in that area). This is necessarily a very compressed and subjective list. There are a large number of very, very good researchers that I have omitted whose career paths may be more relevant. Similarly you should recognize that a lot of ML / Data Science work is domain specific. There is a lot of good work by database people, astronomers, computational biologists, etc that is omitted here. Also I have omitted many younger researchers who are currently making big contributions to the field. Of particular note is the omission of much statistical work. There are many statisticians of note that I have not mentioned primarily because I have tried to confine this to more ML. However there is a lot of important stats in high-dimensional data, Friedman and so on are responsible for a lot of the theory of the lasso, and high dimensional PCA. If people have a specific interest outside of this please write.
Vladimir Vapnik (NYU) & Alexey Chervonenkis - Responsible for SVMs and VC-dimensions, SVMs + kernels dominated machine learning in the 90s and the last decade. VC-dimension is still one of the cornerstones of advanced theory in statistical machine learning. Most of their findings are summed up in the book Statistical Learning Theory by Vapnik, but it's a REALLY dense tome and probably isn't the most enlightening source on these topics.
Michael Jordan (UCBerkeley) - Very big name in statistics, runs a huge research lab in Berkeley.
Yoshua Bengio (UMontreal), Yann LeCun (Facebook), Geoffrey Hinton (Google) - Are the three biggest names in deep learning. Virtually all researchers in Deep Learning are their students.
Andrew Ng (Stanford) - Hugely cited, director of Baidu's silicon valley AI lab, founder of coursera. He's a big name in the field, but to be honest I can't think of anything special from him. He does seem to have a large background in Deep learning because that's what he does with Baidu (they poached him from google).
Leslie Valiant (Harvard) - developed probably approximately correct learning model.
Tom Mitchell (CMU) - Has been in the field for a long time. Lots of work. In my opinion the most interesting work he's done is the NELL project,
http://rtw.ml.cmu.edu/rtw/ essentially they built a web crawler that continuously scrapes the web and learns relationships (I was thinking of trying something similar with a dynamic neural network)
Daphne Koller (Stanford) - Probably best known for probabilistic graphical models (course on coursera + 1000 page book), does a lot of work on bioinformatics.
Sebastian Thrun - Probably the closest to non-academic I can think of. Still a professor at Stanford but has done a lot of work in automation, self-driving cars etc.
Pedro Dominigos (UWashington)
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