I think as well it really depends where you are coming from / what your background is. The reason i say this is i have recently gone through a similar transition into machine learning 'from scratch' except once i got there i realised i knew more than i thought. My academic background is in psychology / biomedical science which involved a LOT of statistics. From my perspective once i started getting into the field i realised there are a lot of things i already knew from stats with different terms in ML. It was also quite inspiring to see many of the eminent ML guys have backgrounds in Psychology (for instance Hinton) meaning i felt perhaps a bit more of an advantage on the theoretical side that many of my programming peers don't have.
I realise most people entering the field right now have a programming background so will be coming at things from an opposite angle. For me i find understanding the vast majority of the tests and data manipulation pretty standard undergraduate stuff (using python / SK Learn is incredible because the library does so much of the heavy lifting for you!). Where i have been struggling is in things that an average programmer probably finds very basic - it took me 3 days to get my development environment set up before i could even start coding (solved by Anaconda - great tool and lessons learned). Iterating over dictionaries = an nightmare for me (at first anyway, again getting better).
I think (though i may be biased) it's easier to go from programming to ML rather than the other way around because so much of ML is contingent on having decent programming skills. If you have a decent programming skill set you can almost 'avoid' the math component in a sense due to the libraries available and support online. There are some real pluses to ML compared to traditional statistics - i.e. tests that are normally ran in stats to check you are able to apply the test (i.e. shape of the data: skewness / kurtosis, multicollinearity etc) become less of an issue as the algorythms role is to deliver an output given the input.
I would still recommend some reading into the stats side of things to get a sense of how data can be manipulated to give different results because i think this will give you a more intuitive feel for parameter tuning.
This book does not look very relevant but it's actually a really useful introduction to thinking about data and where the numbers we hear about actually come from
In conclusion if you can programme and have a good attitude towards learning and are diligent with efforts I think this should be a simple transition for you.
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