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.
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.
In my experience Data Science looks very little like it used to a few years ago, and the priority skill these days is good strong understanding of the basics and very good sense of judgement. To me, statistics is the absolute number one priority for any data scientist. You need to fully and deeply understand just basic concepts in statistics in order to translate what you see into action and do what you’re really there to do which is to prevent screwing up and acting on the wrong information or what’s more likely the wrong interpretation of the information.
For me the most valuable skill I have is a lot of experience applying and learning about Bayesian statistics: what it is (the beginning parts of Jaynes Probability Theory were not useful practically but deeply significant in helping me understand what it means and where it comes from), seeing lots of probabilistic models in the wild, playing around with them in both personal and professional worlds. Some people play video games, I love building hierarchical models. The nice thing is that in addition to it being very expressive It’s also just so much easier, such an intuitive way to avoid footguns because it just requires you to conceptualize one small bit at a time. When you’re done you get the inference for free with lots of charming stops along the pareto frontier between rigor and compute. Variational inference, expectation maximization, EM, Laplace. You can understand all of them with just a few concepts. Plus marginalization is just so unbelievably elegant to me. What is so surprising and beautiful to me is that Bayesian inference and marginalization are so useful and practical today. That being said there are plenty of unintuitive surprises, which is also a plug to not just understand the math but the theory and fundamentals to know how to interpret what you’re doing and seeing.
Also again this is still a great guide with lots of super important stuff (SVD/PCA linear algebra and linear regression (so much reward from just understanding linear regression from multiple perspectives)), no doubt. But if you really truly understand the basics you don’t need to worry about graph Laplacians (though highly highly recommend it’s also beautiful). Because more and more you can outsource the question of which method is ideal to a deep research agent that will read and understand arxiv for you. But you still have to audit it which means just really understanding the fundamentals is so crucial nowadays.
That and valuing speed and practicality. Strongest discriminator between someone junior and someone senior is recognizing when to reach for something simple and when you need to bring out bigger guns.
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)
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 :)
For me the most valuable skill I have is a lot of experience applying and learning about Bayesian statistics: what it is (the beginning parts of Jaynes Probability Theory were not useful practically but deeply significant in helping me understand what it means and where it comes from), seeing lots of probabilistic models in the wild, playing around with them in both personal and professional worlds. Some people play video games, I love building hierarchical models. The nice thing is that in addition to it being very expressive It’s also just so much easier, such an intuitive way to avoid footguns because it just requires you to conceptualize one small bit at a time. When you’re done you get the inference for free with lots of charming stops along the pareto frontier between rigor and compute. Variational inference, expectation maximization, EM, Laplace. You can understand all of them with just a few concepts. Plus marginalization is just so unbelievably elegant to me. What is so surprising and beautiful to me is that Bayesian inference and marginalization are so useful and practical today. That being said there are plenty of unintuitive surprises, which is also a plug to not just understand the math but the theory and fundamentals to know how to interpret what you’re doing and seeing.
Also again this is still a great guide with lots of super important stuff (SVD/PCA linear algebra and linear regression (so much reward from just understanding linear regression from multiple perspectives)), no doubt. But if you really truly understand the basics you don’t need to worry about graph Laplacians (though highly highly recommend it’s also beautiful). Because more and more you can outsource the question of which method is ideal to a deep research agent that will read and understand arxiv for you. But you still have to audit it which means just really understanding the fundamentals is so crucial nowadays.
That and valuing speed and practicality. Strongest discriminator between someone junior and someone senior is recognizing when to reach for something simple and when you need to bring out bigger guns.