Markov Chains Explained Visually (2014)

This is a phenomenal example of how to teach math. You can go through theory, formulas and proofs all day long (yes, sometimes rigor is needed), but this type of teaching is sticky. It takes a lot more time to display information in the way the author has done, but it reaps massive benefits for those trying to learn. In my mind, math is about concepts and there is no reason why we can't start teaching math like this.

Amazing work. The collective intelligence of the world has just gone up.

Another amazing example of visual math lectures, https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw.

This really drives home a sentiment I've acquired during the course of my college education: CS/Math is often considered "hard", but I feel that's just because we've struggled with getting good visual/verbal communicators to dedicate their lives to CS/Math education. I really feel that when explained properly (and the definition of "properly" sometimes need to be adapted from person to person), topics like Gibbs Sampling or Fourier Transforms or Backpropagation aren't topics that should take entire weeks of self-study to grasp in 2018. Yes, they require some math background, but there's some strong intuition behind them. Maybe I'm just slow or thick in the skull.

Discussion from 4 years ago: https://news.ycombinator.com/item?id=8103240

keeps getting posted and going to the top, almost like HN is a memoryless process... :)

glad yall are still enjoying it.

And Hidden Markov Models (HMMs) are just ones where the symbols are emitted upon interaction with an edge of the graph instead of the node. The nodes are still the "states" of the system, but in general you can't know which state the model is in just by observing the symbols emitted by the edges as there may be equivalent structures in the graph associated with different states.

Really great visualization here, kudos to the author. Really makes is clear what's going on. Made me think that things like this could be useful in textbooks as well if they were more digital. Maybe in the next few years there will be a better way to integrate this kind of stuff into courses, I guess today they could always happen in lectures.

This is how we were taught it in our Linear 2 class; the professor used static pictures via chalkboard, but it was still super helpful. I feel like most of the benefit is gained in drawing the graph and talking about "hopping between states". Animating it might help some people who think more mechanically.

Is there a standard way to build markov chains with deeper memory than just the current state? For example in the rainy sunny markov chain our rainy probability should/could decrease as the number of rainy days in a row increases. In a pure state machine this would require an infinite number of states for SS...SSS and RR...RRR.

This truly awesome, the visualization really helped cement the idea in my mind.