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Markov Chains Explained Visually (2014)
- ejlangev 8y agoReally 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.
- rtkwe 8y agoYeah that'd be a really neat application for AR as well, interactive examples displayed around the textbook for the current topic etc.
- joshuamorton 8y agoTake a look at distill.pub (which wsa also featured on the HN frontpage today). Its essentially a Machine Learning Journal with a focus on clarity and visualization, and is therefore interactive and visual. Colah is around on HN and might comment explaining it better.
- zentiggr 8y agoThe Young Lady's Illustrated Primer, pending on next century's Kickstarter equivalent. Integrating Explained Visually into digital coursework flows would be amazing. (Disclaimer: have not taken any online courses recently, so my memories of horrendous archaic information management are wildly outdated I hope.)
- rtkwe 8y agoIs 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.
- stochastic_monk 8y agoYou’d need some kind of higher structure of computing. One method for longer-term dependence is simply expanding the transition matrix and state space, but that’s not unbounded in any meaningful sense. A recurrent neural network approximates unbounded long-term information for general tasks, but I think what you’re looking for in particular is a push-down automaton, while a Markov chain is a finite-state automaton.
- tree_of_item 8y agoSee [0] for a way to make recurrent neural nets in to pushdown nets. [0]: https://arxiv.org/abs/1506.02516 https://arxiv.org/abs/1506.02516
- stochastic_monk 8y agoI’m not an expert in nlp or these augmented models. Could you perhaps compare this to Dyer’s Stack LSTM?
- tree_of_item 8y agoI'm not sure how Dyer's thing works, but I can describe the paper I linked to: A "stack" is a stack of (vector, scalar) pairs (a vector and its "weight"). At each time step, the stack has three inputs: the vector to push, the weight to push it with, and the weight to pop off the stack. Its output is the top 1.0 weight of the stack. The stack's behavior on a time step is divided in to three parts: 1. First, that pop weight is removed from the stack. For example, if you want to remove 0.6 from a stack like [(a, 0.4), (b, 0.4)], you'd remove all of a leaving you with 0.2 to remove from b, so the final stack would be [(b, 0.2)]. 2. The pushed vector is placed on the stack with the given push weight. 3. The top 1.0 of the stack is blended together and returned. For example, a stack like [(a, 0.4), (b, 0.4), (c, 0.8)] would take 0.4 of a, 0.4 of b, and 0.2 of c. This process is differentiable, and you can combine this with the usual recurrent loops to make a recurrent stack machine.
- jihadjihad 8y agoDiscussion from 4 years ago: https://news.ycombinator.com/item?id=8103240 https://news.ycombinator.com/item?id=8103240
- 0xffff2 8y agoAm I the only one who finds it absolutely impossible to read text witch constantly moving animations on the screen?
- Raphmedia 8y agoYou are not alone. That's why there is even a media query for it! https://css-tricks.com/introduction-reduced-motion-media-query/ https://css-tricks.com/introduction-reduced-motion-media-que...
- lewis500 8y agokeeps getting posted and going to the top, almost like HN is a memoryless process... :) glad yall are still enjoying it.
- jld 8y agoDoes anyone know the probabilities of HN moving between states “animated Markov chains article at the top” and “animated Markov chains article not at the top”?
- zentiggr 8y ago[[0.0,1.0],[1.0,0.0]] Had to be said :)
- lillesvin 8y agoI'm certainly glad it was posted this particular time. I've never seen it before and now I learned something today. :)
- 2020-3030 8y agoThere is definitely memory, but HN also has new members. If repeat topics move up to a top location, this probably reflects the number of people who hadn't yet seen the topic. "Not new, but new to you."
- elbear 8y agoEven without new members, not everyone is on all the time, so some people miss stuff like this. Or, even if you've seen it again, you vote it up, because you like it and want others to see it.
- ajeet_dhaliwal 8y agoThis truly awesome, the visualization really helped cement the idea in my mind.
- uoaei 8y agoAnd 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.
- matachuan 8y agoExpand a little then it becomes the probabilistic graphical model.
- ryeguy_24 8y agoThis 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 https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw.
- pseudosudoer 8y ago3Blue1Brown is an incredible example of how math concepts should be introduced. His videos are a fantastic reminder of why math is a form of art.
- thanatropism 8y ago3Blue1Brown is impressive in how it uses visualizations, cute faces, soothing voiceovers, etc. but keeps pulling you down the rabbit hole. So at the end of the video you know that you don't know stuff you either think you knew or didn't know existed. And then you start looking up Wikipedia and just getting lost in the music. This is really really rare. Education as entertainment means that the goal is to get the consumer to feel good about himself, to feel like he learned something. You're getting paid (in money or kudos or whatever) to engage the consumer's narcissism, not his curiosity.
- florabuzzword 8y ago> ...keeps pulling you down the rabbit hole. So at the end of the video you know that you don't know stuff you either think you knew or didn't know existed. And then you start looking up Wikipedia and just getting lost in the music. Education as entertainment means that the goal is to get the consumer to feel good about himself, to feel like he learned something. You're getting paid (in money or kudos or whatever) to engage the consumer's narcissism, not his curiosity. This is a profound observation. I’m not sure it only applies in entertainment. I’ve heard it put other ways, but your version, if applied to education as a whole, might be a pretty big deal. There’s no shortage of evidence, either; from Ivy League campuses to niche interest subcultures. Maybe “narcissism” isn’t the best word, but some sort of similar tension related to confidence seems to be associated with successful educational environments. We commonly attribute it to a one-way causal relationship, but you’re articulating the opposite. Likewise, we are used to acknowledging that ‘not giving up’, or ‘belief in one’s self’ is a necessity, but again you’re making a separate claim. You’re saying, in so many words, the confidence in and of itself defines the will as well as the curiosity. And I can’t argue with it. I want to, but I’m not sure I can.
- geoffreyhale 8y ago@lewis500 is your code for the live visuals publicly available?
- Giho 8y agoIsn't this affected that its difficult to get true random by computers? Its more pseudo random and therefore the chance is not real chance but predictable.
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- Sohcahtoa82 8y agoWhile true, there are cryptographically secure PRNG's that are incredibly difficult (Theoretically impossible) to predict. In any case, unless you're using Markov chains to generate data that needs to be kept secure (Like generating a password that could be pronounced), the predictability of random numbers isn't really relevant.
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- s-shellfish 8y agoThis is very a good depiction of a Markov chain. However, it's always a coin flip on your emotions to anthropomorphize math. Pronouns.
- DoritoChef 8y agoThis 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.
- anonytrary 8y agoThis 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.