Not parent, but I've built my own computers for almost 20 years.
As the articles author himself questions, he should have gotten the marginally more expensive CPU, and definitely the GPU with more RAM.
* The overclockable CPU doesn't just mean that you very easily could get a 10%+ performance boost without much work, but also that you often (depending on your specific chip) can lower the voltage and make it run much cooler/quieter, which is something I increasingly care about if I'm using it a lot.
* He writes that fitting the model in RAM is basically the most important part, but then saves less than a dinner out by basically halving the RAM on the GPU he bought. The chip is otherwise the same though, so performance is only dependent on whether you fill that RAM or not.
* The Noctua D15 the parent mentioned is a CPU cooler where Noctua is a long standing high performant brand, and D15 is a specific model with a 15 inch fan and comparable sized heat sink. There are of course other brands, but I myself also usually end up with Noctuas. The reason it's important is that however fast you can dissipate heat from the cpu/case, the less chance of throttling, and the larger headroom for potential overclocks you get.
Airflow and room for larger heatsinks is also why he recommended not going for an ITX. A linked benefit is again the potential for a quieter system.
I haven't gone much into ML (yet), but I currently have a system with:
* I7 6700K (the difference to I5 6600K being higher base clock and hyperthreading, which is more important to computational work than to gaming, so if you have the money, definitely go for the I7)
* 32GB DDR4 (as author mentioned, RAM is cheap). The clock/timings on RAM isn't really as important, but try to find the best you can find for a given price point.
* An Nvidia GTX 1080: It's not Titan X or Z, but almost, at less price. It definitely blows the budget for a $1000 system, but I agree that the entire 10 series is good.
If the limit is a firm $1000, I would get something like this:
https://pcpartpicker.com/list/XHV9Fd
And if more funds is available, I'd get more storage and RAM, then a better CPU, then a better GPU, then maybe bump the chassis up to an R5 (same brand), possibly another motherboard. In that order. There's always something better, so you compromise based on budget.