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For the STEM students, what they need is statistics (with a focus on high level Bayesian and statistical learning theory, not just frequentist regression tricks

by Onavo 2y ago

For the STEM students, what they need is statistics (with a focus on high level Bayesian and statistical learning theory, not just frequentist regression tricks) and differential equations. Then they can build AI. AI, or specifically deep neural network enabled machine learning, isn't some sort of magical black box solution with no weaknesses. (I will however admit that it is the best universal function approximator that we currently know of) Otherwise you end up with an uneducated public whose main education is from Hollywood and ChatGPT. You need to start from high school, the AP classes need to be revamped. Currently they are focused on purely frequentist statistics. Frequentist statistics is great for most empirical sciences like biology. The formulas are mostly plug and play and even pure life science people with no mathematical talent can wield them without trouble. The problem is that they are very far from statistical learning. Here's the current AP stats curriculum, it is meant to be equivalent to Stat 1. https://library.fiveable.me/ap-stats https://library.fiveable.me/ap-stats If you want to develop a strong foundation for ML, Unit 6, 7, and 8 ought to be thrown out entirely. The level they are taught at doesn't really teach anything more than plugging formulas. Unit 4.5 (Conditional Probability) and Unit 5 (Sampling) need to be further developed to cover the Bayesian theories, perhaps a segue into graphical models and Markov chains. Generative ML for example interprets likelihood as an information generator (since in the Bayesian formula, it is roughly the "inverse" of conditional probability), unfortunately most stats classes outside of physics and high level ML theory will never mention this. Heck most classically trained statisticians won't ever encounter this idea. But it is the bread and butter of generative AI. Having a vague idea of KL-divergence and what Metropolis-Hastings is coming out of high school is infinitely more useful for their career in ML than knowing how to fiddle with a p-value. You can teach most of these concept without calculus if you simplify some things and replace integrals with their discrete summation versions. Rejection sampling for example is very easy to teach. The Common Core needs a revamp, and perhaps it's time to shift away from the historical focus on calculus/pre-calc as the central tenet of pre-college mathematical teaching.

kubb 2y ago
But that’s how employers understand AI. It’s ChatGPT.
throwaway314155 2y ago
The article is more discussing a sort of tool-level competency that is lacking. This looks more like adding classes to teach how to incorporate generative AI into learning and way less like the very advanced curriculum you're prescribing. Think "how to effectively use a search engine" (or even just typing) classes but for ChatGPT. Believe me, most students of the common core don't know or care about the difference between Bayesian and frequentist statistics. Are you only interested in helping the straight-A students that have better chances getting into Harvard? Did you read the article?
dxbydt 2y ago
Throwing out units 6,7,8 is a horrible, horrible idea. That’s the only useful part of the curriculum. In fact, most of the rest of the sections are not even stat. They are just plain math. Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown.
- Onavo 2y ago
  > Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown. The point is to build intuition, those take time and unless the student is particularly mathematically inclined, you can't rush it. That's why you have to start in high school. Right now, the focus of pre calc is to induce them into calculus through slopes, limits, and derivatives. But a good chunk of high level statistics don't need that to build intuition. For example, we generally teach students y=mx+b in middle school and high school. This is considered a perfectly normal part of math education. It's accepted that the students may not understand the full meaning of linearity and regression at first, but at higher levels the formula would be second nature to them. This is the point I am trying to make about statistical learning (not specifically Bayesian theory in particular, but the key concepts around it). Generative ML and stuff like LLMs require a specific frame of mine and view of the world, and it's best to develop it early. The way we are teaching statistical learning theory, at the lower levels, is essentially dumping a massive bag of tricks on them and hoping for the best. We need to change that approach and start treating it like pre-calc and algebra, something to be taught level by level, with building intuition as a core focus. It's not easy to communicate the idea that "the next word prediction of the LLM (depending on the model) is generally the joint probability of all other words that come before it by sampling from a multidimensional probability distribution" to most 14-16 year olds.
  - dxbydt 2y ago
    I think this is a very constructive proposal. I am definitely on board with it. I don't see why we should shoehorn these topics into ap-stats. That curriculum is entirely based on classical statistics, which is very useful for what it does. But suppose there were an ap-ml, where we have word prediction of LLMs, maybe an attempt to teach multi-dim distributions without calculus (ha! I'm seriously skeptical of that, but its your idea), rejection sampling and a suite of easy to code mcmc recipes - MH, Gibbs, Slice Sampling, Importance Sampling, and a dash of Bayesian theory - if there were such a course, it would be quite popular among the high schoolers I work with. btw, college board does revamp ap curriculum quite often. AP African American Studies was introduced last year. Maybe AP-ML is on the cards.

by Onavo 2y ago

kubb 2y ago

But that’s how employers understand AI. It’s ChatGPT.

throwaway314155 2y ago

The article is more discussing a sort of tool-level competency that is lacking. This looks more like adding classes to teach how to incorporate generative AI into learning and way less like the very advanced curriculum you're prescribing. Think "how to effectively use a search engine" (or even just typing) classes but for ChatGPT. Believe me, most students of the common core don't know or care about the difference between Bayesian and frequentist statistics. Are you only interested in helping the straight-A students that have better chances getting into Harvard? Did you read the article?

dxbydt 2y ago

Throwing out units 6,7,8 is a horrible, horrible idea. That’s the only useful part of the curriculum. In fact, most of the rest of the sections are not even stat. They are just plain math. Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown.

Onavo 2y ago
> Rest of your suggestions are just plain wild. If there is some unicorn high schooler out there who meets your wild template - knows no calculus but knows rejection sampling and MH - I would like to see which foolish employer hires this clown. The point is to build intuition, those take time and unless the student is particularly mathematically inclined, you can't rush it. That's why you have to start in high school. Right now, the focus of pre calc is to induce them into calculus through slopes, limits, and derivatives. But a good chunk of high level statistics don't need that to build intuition. For example, we generally teach students y=mx+b in middle school and high school. This is considered a perfectly normal part of math education. It's accepted that the students may not understand the full meaning of linearity and regression at first, but at higher levels the formula would be second nature to them. This is the point I am trying to make about statistical learning (not specifically Bayesian theory in particular, but the key concepts around it). Generative ML and stuff like LLMs require a specific frame of mine and view of the world, and it's best to develop it early. The way we are teaching statistical learning theory, at the lower levels, is essentially dumping a massive bag of tricks on them and hoping for the best. We need to change that approach and start treating it like pre-calc and algebra, something to be taught level by level, with building intuition as a core focus. It's not easy to communicate the idea that "the next word prediction of the LLM (depending on the model) is generally the joint probability of all other words that come before it by sampling from a multidimensional probability distribution" to most 14-16 year olds.
- dxbydt 2y ago
  I think this is a very constructive proposal. I am definitely on board with it. I don't see why we should shoehorn these topics into ap-stats. That curriculum is entirely based on classical statistics, which is very useful for what it does. But suppose there were an ap-ml, where we have word prediction of LLMs, maybe an attempt to teach multi-dim distributions without calculus (ha! I'm seriously skeptical of that, but its your idea), rejection sampling and a suite of easy to code mcmc recipes - MH, Gibbs, Slice Sampling, Importance Sampling, and a dash of Bayesian theory - if there were such a course, it would be quite popular among the high schoolers I work with. btw, college board does revamp ap curriculum quite often. AP African American Studies was introduced last year. Maybe AP-ML is on the cards.