Comment by notafraudster | Hacker News Reader

Comment by notafraudster | Hacker News Reader

"If you want to scrape the surface, a course in elementary statistics would be fine. If you want a deep conceptual understanding, you’ll probably want to know how the formula for residual sum of squares in derived, which you can learn in most courses on advanced statistics."

This is an extremely shallow claim. The basics of regression rely on, let's see, understanding the normal and t distributions (each of which is described in papers far beyond an undergraduate statistics degree). To understand how the rules of probability empirically map to outcomes, you need a good understanding of the Central Limit Theorem (and thus the Squeeze Theorem, Continuous Mapping Theorem, Chebyshev's Inequality / WLLN, etc.) all of which are pretty sophisticated. Congrats, you now know linear regression. What about all the difference variance estimators, their properties under model misspecification, simulation properties of violations of Gauss-Markov, robust standard errors (including more advanced econometric specifications like cluster-robustness, Satterthwaite approximation of degrees of freedom, etc.)

If you're willing to take a textbook's word for it, actually using most data science stuff is as easy as spending an hour on coursera or reading some free web pdf book. Who needs any math skill? Just close your eyes when the book covers math. Like how a mechanic doesn't need to know any physics, the data science user doesn't need to know any math or statistics. If the pretty stars show up in the regression table you found the truth.

So, yes, on this level, data science requires a high school or early undergraduate understanding of calculus no more sophisticated than basic algebra, the first few weeks of matrix algebra, and the first few weeks of Calculus 1 and 2.

But on the other hand, to actually understand, prove, and improve on existing techniques requires the equivalent of upper division undergraduate mathematics and a graduate education in statistics.

The basics of regression rely on, let's see, understanding the normal and t distributions (each of which is described in papers far beyond an undergraduate statistics degree).

Every stats program I know of teaches each of these concepts quite rigorously, and I can't imagine a stats program without them.

I agree with your broader claim that to actually improve on existing techniques requires graduate education, but understanding existing techniques is well within the reach of most college students.

I missed your reply contemporaneously. Of course undergrad stats programs introduce the normal/t distributions; but often in either a matter-of-fact way (the normal PDF is ...) or in a sort of intuitive way (think of t as a normal distribution, but punishing ourselves for the additional uncertainty of needing to estimate...), but rarely in a beginning to end way. I'm not critiquing this as pedagogy, although I think a lot of students get bombarded with poorly motivated distributions that aren't well connected to a broader problem class. But that being said, I think we teach students how to characterize distributions rather than how to prove or derive them from first principles.

I don't think most undergraduate stats programs deal with the dart-board derivation of the normal distribution, or read Gosset's original t paper, and moment generating functions are rarely discussed.

Here's an example of a fairly elementary question I don't think a stats undergrad would learn without self-guided study: You run a linear regression. One or more of your outcomes or regressors has a skewed distribution. Standard errors are often motivated under CLT claims of normal convergence. Suppose convergence is poor in your finite-sample. What are the consequences of this for your estimates and standard errors in terms of nominal coverage, bias, and consistency?

It's possible an undergraduate class would cover Gauss-Markov and mention violations of normality, and maybe get into mitigations via transforming parameters... but to actually deep dive into the skills necessary to self-verify the kinds of consequences observed in the data you have? Nah.

I mention this because it's a question that first came up to me in a graduate regression class and I was not well prepared for it, and now when I teach statistics undergrads I don't think they would be.

Never mind any kind of analytic result, the notion of really digging in and running the kind of MC simulation required to get empirical results is typically a fourth year undergraduate topic.

there's a salty purist like you listing buzzwords from casella and berger in every thread. your brethren in the data structures threads are those repping CLRS or taocp. and yet data science as an industry marches on (not to say anything of dev).

>prove, and improve on existing techniques

how many "data scientists" in industry are proving or improving existing techniques in their day to day?

>Like how a mechanic doesn't need to know any physics

this is absolutely correct since, you know, they're able to provide value for customers by fixing their cars

i would say that this is exactly what elitism looks like: you take a look at someone that's successful but under different terms than you yourself see fit, and claim it's not genuine success.

There's a huge difference. If I ask "why is this model applicable to this situation?" or even "is this model applicable to this situation?" then I want the practitioner to have the ability to provide and understand the answer. Yes, data science as an industry, but that's because wrong answers are largely undetectable.

If I roll out the treatment cell of an experiment but shouldn't have, because I didn't account for within-client correlation, the world marches on and the business thinks they are making data driven decisions. They'll never know they left millions on the table. Or maybe I'm right for the wrong reasons and I was merely more confident than I should have been and the world still marches on oblivious because there are very very few correction mechanisms.

The academic math types with no ML experience don't fare much better than the no-math practitioners with experience from what I've seen. They generally have terrible mental models of how the math behaves when applied to real data.

IME the competent data scientist needs to have a high-level understanding of the concepts underlying ML (stats, optimization, central limit theorem) and to be comfortable reading math to understand the low-level details when they are relevant. In addition to actually understanding the ML techniques they're using obviously.

On top of that, I would rather work with someone who can code well than a pure mathematician with a ton of experience proving theorems (and no coding ability). Outside of a few industry research jobs, the cost:benefit ratio of making substantial theoretical breakthroughs in most everyday ML work doesn't justify a lot of time doing theoretical proofs.

The person you're replying to isn't talking about "theoretical breakthroughs", he's talking about a basic ability to interpret and detect errors in your model.

These are abilities that "data scientists" do, indeed, lack.

My impression of working closely with data-scientists is that what you describe comes more from experience, than from purely theoretical knowledge of the math behind. Ideally it's both, but if having to choose, I'd rather bet on someone who did it already a dozen times and knows what to expect.

>there's a salty purist like you listing buzzwords from casella and berger in every threa

That cracked me up lol. I was hired as a data science at big tech with only some high level data science skills. I first learned to write productuon quality code. I then (and now) am working through Casella Berger, I'm 1/3 through. It's hard! I've had to stop and brush up on math a lot. I love learning theoretical stats, I feel it makes me a better data scientist. But I also know I've worked with phd data scienctists who worked through all of C&B but couldn't code, and they weren't as valuable as the more self-taught code-first data scientists (at least on my team).

I had never heard of Casella & Berger (but I'm the salty guy on the data structures threads going on about how great TAOCP is). I looked it up on Amazon and it looks interesting and like exactly what I've been looking for, but there's no "look inside this book" or even a table of contents on there. Before I pick it up, how much math background would I probably need to be able to penetrate it? I'm up on calculus and linear algebra, but I only took one statistics course as an undergrad 25 years ago.

there's a pdf floating around - for me it's the first hit when i search casella berger on google

>I'm up on calculus and linear algebra, but I only took one statistics course as an undergrad 25 years ago.

it is a serious graduate math stats book but i personally don't consider it a graduate math book (because it does not use measure theory). it is proof focused because it's used for foundational grad stats classes (i.e. prep for quals) but the proofs aren't that hard to follow (if you've had a good calculus class [epsilon-delta definition of limits]).

some of the exercises are brutal algebraically though. good things there's a solutions manual floating around :)

> some of the exercises are brutal algebraically though

This is definitely true, and I wouldn't recommend this book to anyone unless they considered this a feature. For me, it was/is a feature, because I suck at algebra, and this is helpful.

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