As I completed over fifty Python projects, the importance of understanding the fundamental principles of statistical models resurfaced. 

"One bit of advice: it is important to view knowledge as sort of a semantic tree -- make sure you understand the fundamental principles, i.e. the trunk and big branches, before you get into the leaves/details or there is nothing for them to hang on to." – Elon Musk

For instance, I read An Introduction to Statistical Learning  from cover to cover and came across the familiar concept – Euler’s number, e. While the formula itself is relatively straightforward,

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 I wanted to understand its applications and semantics in terms I could fully appreciate. The most familiar example I came across was this:  

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 I began inspecting why this limit equaled e. Why do those offsetting elements (i.e. denominator and exponent n) yield a convergent sequence? I dwelled on this concept for several days. After digesting the concept of the natural number e, I moved on to the probability density function.

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 Once I understood the aforementioned concepts, the limitations of many statistical/financial models (e.g. Black-Scholes) became apparent and I realized how often I had incorrectly used them. As machine learning gets widely accepted, such inadvertent errors will likely become increasingly common as most enterprises simply import and treat models as black boxes. Machine learning is incredibly powerful but I believe we can more effectively harness its power if we better understand the fundamentals behind the algorithms. 

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