41–50 of 96 posts
Edit 1: Also, P(A|B) reads "P(A|A)".
Edit 2: Not trying to be too nitpicky, though. It's a really nice visualization. Really excited about the growing use of d3 to visualize algorithms. Is this inspired by Mike Bostock's post by that title?
I created a Markov chain generator: https://gist.github.com/grant/561834963dc526495c45 var numNodes=10;var roundNum=100;var a=[];for(var i=0;i roundNum)/roundNum;connections[j]=randNum;sum+=randNum}connections=connections.map(function(e){var t=e (1/sum);t=Math.round(t roundNum)/roundNum;return t});sum=connections.reduce(function(e,t){return e+t});connections[numNodes-1]+=1-sum;connections[numNodes-1]=Math.round(conne…
This is at a tangent, but I'm a fresh CS undergrad and this simple explanation really hooked me. So my question is, where can I find more of this stuff? MOOCs are tough to manage with university, but if I wanted to learn more about these mathematical concepts presented in an interesting way, where should I start looking? I'm a tad bit indecisive about how good I am with CS theory but I know if I took the leap and mas…
That's pretty cool. The markov chain diagrams seem very similar (identical?) to deterministic finite automota. Would it be correct or incorrect to say that a Markov Chain can be thought of as a DFA where the changes in state are determined by probability?
I've seen Markov chains applied to language generation - producing sentences that make sense grammatically but not literally. Anyone know what the connection is here? I think I have an idea but would like to see if it gets independently verified by someone else.
There are complicated ways of doing this, but the naïve way is as follows: First you need a corpus of text that's grammatically correct Each node in the chain is a word or piece of punctuation. Each word has a certain probability of being followed by every other word in the corpus, including itself. There are a few different ways to start the sentence. One approach is to start from the node for the punctuation mark "…
The first lecture by Jack I listened to was given in the spring of 1954 in a seminar in functional analysis. A brilliant array of lecturers had been expounding throughout the spring term on their pet topics. Jack's lecture dealt with stochastic processes. Probability was still a mysterious subject cultivated by a few scattered mathematicians, and the expression "Markov chain" conveyed more than a hint of mystery. Jack started his lecture with the words, "A Markov chain is a generalization of a function." His perfect motivation of the Markov property put the audience at ease. Graduate students and instructors relaxed and followed his every word to the end.
Beuatiful visualizations.
he said, "imagine god is sitting around emitting DNA sequences. She has sevearl 4-sided biased dice, rolls one of the 4-sided die, BAM, emit an A! Again, roll the die, BAM, emit a A! Roll again, BAM, emit a T! Now, imagine god is a fickle person, and between rolls, decides to roll a die to decide which of the biased die to roll.
For some reason, that helped.
Beautiful. 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.
http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pd...
There's a bunch of fun stuff that suddenly becomes possible.
It's gently distressing that by far the most use that Markov chains have seen so far is to generate English-like gibberish text to beat spam filters.