The article is light on details. imo there are two major things your team needs:
1) Programmers that have the needed math skills, or mathematicians with the needed coding skills
2) A distributed ML framework
Solving problem one is not easy but it's straightforward.
Solving problem two is harder. While there are a lot of open source machine learning projects, almost all of them seem to have a focus of being used by a person and not a program. Moreover very few do distributed processing except for mahout (http://mahout.apache.org/). Mahout is promising but the documentation is still thin, and I'm not sure if it's getting momentum in terms of mind share yet.
Aside from algebra to do log or exp division addition and multiplications, you have to be versed in statistics. Most ml problems are solved on statistical bases. Although many of the algorithms have been solved, you still need to grasp the statistics behind it which is a bit more involved than calculating the odds of a die
Yes, many people that I know working on ML do not remember statistics well enough. Some keep their ignorance while relying on mathematicians on-staff (who can't really code), while others either start buying college textbooks or go to night classes. There are too many people who don't understand the algorithms being used.
To work with ML stuff you don't need much. You can just download packages and get experience with how to best pick models, choose features and tweak (hyper)parameters. If you want to work on or understand it then you will need math.
You need a decent understanding of calculus (mid 1800s level, mulitvariate calculus), a more decent understanding of Linear Algebra (1950s ), information theory (1960s), and probability and statistics. With the last having shifted the most from the past due to more recent respect for bayesian methods. Note the years in parenthesis is not to say that nothing new has been used from those areas, more like if you pick up a book on that topic from that year you would be pretty well covered for the purposes of ML.
Worth having a vague idea of are stuff like PAC learning, topology and computational complexity stuff like Valiant's work on evolvability. If you are doing stuff related to genetic programming then category and type theory have riches to be plundered.
Or if you want to be more hardcore and are looking at very higher dimensional data and reductions on them you might look at algebraic geometry (in particular algebraic varieties) and group theory. So basically the answer to your question is as little or as much math as you want and or depending on the problem and your interests in trying different approaches than the typical toolkits of linear algebra and statistics.
* If you are doing stuff related to genetic programming then category and type theory have riches to be plundered.*
Could you expand this a bit as I don't understand the meaning. Are you saying that if the problem you are working on can be solved with genetic algorithms, then you could blow it away with category and type theory?
I don't have a vested interest in either, I am just curious. Thanks.
1) Programmers that have the needed math skills, or mathematicians with the needed coding skills
2) A distributed ML framework
Solving problem one is not easy but it's straightforward.
Solving problem two is harder. While there are a lot of open source machine learning projects, almost all of them seem to have a focus of being used by a person and not a program. Moreover very few do distributed processing except for mahout (http://mahout.apache.org/). Mahout is promising but the documentation is still thin, and I'm not sure if it's getting momentum in terms of mind share yet.