Show HN: Markov chains explained visually
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Re: Show HN: Markov chains explained visually
#2Very nice! I've never had to work with Markov chains but I've read about them and they seem to pop up in lots of places.
Nice and simple and interactive explanation.
Re: Show HN: Markov chains explained visually
#3This is fantastic. I have encountered markov chains in my career and always thought of them as a black box. This simple visualization makes it so easy to understand what has previously been so hard for me. Thank you.
Re: Show HN: Markov chains explained visually
#4Beautiful. I had seen Markov chains mentioned before, but had not looked them up. Skimming the wikipedia page made sense (it's a state machine with transitions determined by probabilities instead of defined events), but I would not have had an intuitive understanding of why they are useful. The explanation mid-way down about modeling the distribution of sunny and rainy days really made it click for me.
Re: Show HN: Markov chains explained visually
#5This is really nice.
Minor nit #1: https://www.dropbox.com/s/2meqa8hhen9ztba/Screenshot%202014-... Seems like the graph visualization is sticking to the wrong coordinates (dragging it to the left doesn't help; it moves back to the center)
Minor nit #2. I'd love to see a visualization of the "probability mixing" interpretation of markov chains and stationary distributions, which is what PageRank is really about. That is, it'd be really nice to have a visualization of the fact that Markov chains are ultimately memoryless (it eventually doesn't matter in which state you start for the distribution of events). I think it could be done by exchanging "probabilities conditioned on the past", which is most easily done by multiplying the entire probability vector by the stochastic matrix and visualizing that.
Re: Show HN: Markov chains explained visually
#6Presumably in the B row it should read "P(A|B)" and "P(B|B)"
Re: Show HN: Markov chains explained visually
#7Beautiful. I had seen Markov chains mentioned before, but had not looked them up. Skimming the wikipedia page made sense (it's a state machine with transitions determined by probabilities instead of defined events), but I would not have had an intuitive understanding of why they are useful. The explanation mid-way down about modeling the distribution of sunny and rainy days really made it click for me.
The explanation mid-way down about modelling the distribution of sunny and rainy days really made it click for me.
Another very easy to understand is language. Say, I give you a small text. You could create a small state machine containing the possible transitions between words. You could also compute probabilities (estimated from the text) of going from one word to another (e.g the -> text vs. the -> possible, etc), and you'll have a Markov chain.
Of course, this is a very weak model of language, and usually in such models probabilities are modelled on at least the previous two states. But it turns out to be very useful in practice, e.g. you can compute the fluency of different formulations of the same semantics.
Re: Show HN: Markov chains explained visually
#8Great! It would be nice to be able to stop the animations though, they are distracting while you are trying to read the text.
The sunny/rainy probability example is perfect as a scenario.
Re: Show HN: Markov chains explained visually
#9This is really great, but could you put in a bit how some transition matrices aren't markov (e.g. [0 1; 1 0]) and the convergence criterion where you can take M^n n->infinity and get the occupancy of the states?
Re: Show HN: Markov chains explained visually
#10Very nice concept; a mvp
Just on first glance: 1. first diagram and others, ball jumps from beginning of BtoA arc to B without sliding along the arc.
2. second diagram box was no P(B|B). That is boxes are mislabeled.
3. strange, but arcs are sometimes at an angle. It appears to happen if they are scrolled to, but no if drawn on the initial screen.
4. while the R S on the next diagram does settle to a steady state, it starts with random Rs and Ss marching across at random rates.
Good Start!