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What course did you study to get this knowledge?

by zump 10y ago

AlexCoventry 10y ago
Any course on the mathematics of Bayesian inference will introduce you to the necessary tools.
murbard2 10y ago
AlexCoventry is right, these are "the mathematics of Bayesian inference", to unpack a bit my recommendation is: - Get a strong grip on linear algebra and euclidean spaces. You should be able to have an intuitive feel for the key theorems (e.g. Cayley-Hamilton, the Spectral theorem) and should be comfortable proving them (at least once). The point isn't that you need to check that they're correct (they are), but if you can prove them, it means you've learned a certain amount of prerequisite knowledge and gained enough familiarity with the topic. They aren't just theorems you apply, they make sense and you understand the intuition behind them. - Get the same feel for multivariate calculus. The intuition there is generally easier to acquire than for linear algebra, but you need to be comfortable with the mechanics of it. Learn to prove your results rigorously, but also to quickly derive formulas by treating infinitesimals as variables, like a physicist. - Study integration, measures, distributions and the fundamentals of probability. If the course talks about sigma-algebras, you're in the right place. Finally study Baseyian statistics, Monte-Carlo Integration, Markov-Chain Monte-Carlo, some information theory You don't need that level of rigor and that level of fundamentals to do machine learning. Some linear algebra, some calculus and some probability theory that you pick along the way will generally do. However, I think if you're interested in ML it is worth the effort because it will make most of the math seamless. This is a lot of math to learn, but it's not particularly "advanced" math. The underlying intuitions are relatively concrete and a lot of the procedures are relatively mechanical.
- zump 10y ago
  Thanks for the wonderful reply. How long do you estimate it took for you to get to the level you are now?
  - murbard2 10y ago
    That's hard to answer because there wasn't a precise point where I started and that's not the only thing I've been studying in my life, and I've studied a lot of this while working full time jobs which didn't really require this knowledge (constructive procrastination ftw). I started getting interested in sequential Monte-Carlo methods around 2008 while working at a hedge-fund and I think I had a pretty solid grasp by 2011. But I started with solid math fundamentals, so picking it up wasn't too troublesome. I think a talented high-schooler could learn this topic in three to four years by studying it (and nothing else) intensively. I think it tends to happen more organically in general. You become proficient along the way, it's more of a lifelong thing. I think every piece you'll learn will be valuable and useful on its own.

What course did you study to get this knowledge?

by zump 10y ago

What course did you study to get this knowledge?

AlexCoventry 10y ago

Any course on the mathematics of Bayesian inference will introduce you to the necessary tools.

murbard2 10y ago

AlexCoventry is right, these are "the mathematics of Bayesian inference", to unpack a bit my recommendation is: - Get a strong grip on linear algebra and euclidean spaces. You should be able to have an intuitive feel for the key theorems (e.g. Cayley-Hamilton, the Spectral theorem) and should be comfortable proving them (at least once). The point isn't that you need to check that they're correct (they are), but if you can prove them, it means you've learned a certain amount of prerequisite knowledge and gained enough familiarity with the topic. They aren't just theorems you apply, they make sense and you understand the intuition behind them. - Get the same feel for multivariate calculus. The intuition there is generally easier to acquire than for linear algebra, but you need to be comfortable with the mechanics of it. Learn to prove your results rigorously, but also to quickly derive formulas by treating infinitesimals as variables, like a physicist. - Study integration, measures, distributions and the fundamentals of probability. If the course talks about sigma-algebras, you're in the right place. Finally study Baseyian statistics, Monte-Carlo Integration, Markov-Chain Monte-Carlo, some information theory You don't need that level of rigor and that level of fundamentals to do machine learning. Some linear algebra, some calculus and some probability theory that you pick along the way will generally do. However, I think if you're interested in ML it is worth the effort because it will make most of the math seamless. This is a lot of math to learn, but it's not particularly "advanced" math. The underlying intuitions are relatively concrete and a lot of the procedures are relatively mechanical.

zump 10y ago
Thanks for the wonderful reply. How long do you estimate it took for you to get to the level you are now?
- murbard2 10y ago
  That's hard to answer because there wasn't a precise point where I started and that's not the only thing I've been studying in my life, and I've studied a lot of this while working full time jobs which didn't really require this knowledge (constructive procrastination ftw). I started getting interested in sequential Monte-Carlo methods around 2008 while working at a hedge-fund and I think I had a pretty solid grasp by 2011. But I started with solid math fundamentals, so picking it up wasn't too troublesome. I think a talented high-schooler could learn this topic in three to four years by studying it (and nothing else) intensively. I think it tends to happen more organically in general. You become proficient along the way, it's more of a lifelong thing. I think every piece you'll learn will be valuable and useful on its own.