Mathematics of Data Science

Data science is always a very overloaded term ever since it took off way back in the 2010s. One of, if not the most, durable definition of this that likely can also be the most valuable because it’ll probably land your jobs(even today) is being able to make decisions from looking at data that have an team wide(good IC like job security) scope at the least and company wide scope(very rich).

Building that intuition is incredibly difficult. It can be learned if one likes to solve and think about problems that way. Like for example you can get quite far with knowing how to use linear regression(for example coefficients of linear regression can be determined using a deterministic algorithm using linear algebra yet knowing the assumptions of linear expected value and constant or variance is more useful as is the knowledge of what probability model to use to define the random variable(hmm are these Bernoulli events or poison)).

How to do sampling(like using reservoir sampling when you have an infinite sample count e.g in a long running crowd sourced survey to not over or under sample buckets for calibration).

Or just rule of thumbs like how # of samples needed for moving decimal point on significance varies roughly as inverse of sqrt of N and probably much more in case of interacting factors.

I would like a book on that :)

I always starts with students by explaining how our intuition breaks in high-dimensions (spikiness, volumes,...) and how that carries when fitting/training models or searching optimization space.

It's a very important fundamental for modern data-science, to give one intuition about stochastic gradient descent, high-dimensional models, ... And this book starts with just that. I'm hooked. Thanks for sharing.

See this older hacker news thread as well: https://news.ycombinator.com/item?id=45116849 A Random Walk in 10 Dimensions (2021)