How to pronounce “markov” in English

Markov had shattered Nekrasov's argument, and he knew it.

So Markov set out to prove that dependent events could also follow the law of large numbers, and that you can still do probability with dependent events.

Then Markov broke the string into overlapping pairs, that gave him four possible combinations, vowel-vowel, consonant-consonant,

So Markov had shown that the letters were dependent.

So Markov had built a dependent system, a literal chain of events, and he showed that it still followed the law of large numbers,

And Markov himself seemingly didn't care much about how it might be applied to practical events.

as Markov did like a 200 pound kid and they injected a similarly sized pallet of rice and it was the pig to see if it

- But to Markov, Nekrasov was delusional.

But when Markov actually counted, he found vowel-vowel pairs only show up 6% of the time, way less than if they were independent.

the exact split Markov had counted by hand.

With this Markov chain, as it came to be known, he found a way to do probability with dependent events.

By using Markov chains, Page and Brin had built a better search engine, and they called it PageRank.

He went back to Markov's original idea of predicting text, but instead of just using vowels and consonants, he focused on individual letters.

But the beautiful thing Markov and others found is that for many of these systems you can ignore almost all of that.

He used Markov chains, Monte Carlo sampling techniques.

and so it ends its Markov chain, or it can strike another uranium-235 atom, triggering a fission event and releasing two or three more neutrons

So now we can run this Markov chain and see what happens.

So there are some systems where Markov chains don't work, but for many other dependent systems, they offer a way of doing probability.

So we used something called Markov state models that was also developed at Standford mainly.

- His intellectual nemesis on the socialist side was Andrey Markov, also known as Andrey The Furious.

And this was the idea that sparked Nekrasov and Markov's feud.

So to test this, Markov turned to a poem at the heart of Russian literature, "Eugene Onegin" by Alexander Pushkin.

Well, Markov knew that if you pick a random starting point, there is a 43% chance that it'll be a vowel.

Many of these processes could be modeled using Markov chains.

What von Neumann realized is that you needed a Markov chain.

And it wouldn't be the last time Markov chain based method changed the course of human affairs.

- And at the heart of this trillion dollar algorithm is a Markov chain, which only looks at the current state to predict what's going to happen next.

And it's this memoryless property that makes Markov chains so powerful because it's what allows you to take these extremely complex systems

So you can think of card shuffling as a Markov chain where each deck arrangement is a state, and then each shuffle is a step.

You can discover how large language models actually work from basic Markov chains to complex neural networks, or dig into the math behind this shuffling question.

I was one of the pioneers of hierarchical hidden Markov models in the '80s and '90s and used that for speech recognition, and today, that is the dominant technique in

remember the famous umbrella murder in 1978 where you Markov standing at a

So what they realized is that we can model the web as a Markov chain.

whether that's genetic algorithms, like Markov chains.

And this is no coincidence, the algorithms that make these predictions are based on Markov chains.

- But today's large language models don't treat all those tokens equally, because unlike simple Markov chains, they also use something called attention,

- As one paper put it, "Problem-solving is often a matter of cooking up an appropriate Markov chain."

But all the evidence suggests that it really was this determination to show up Nekrasov that led Markov to do the work.

And these days, with computers, and algorithms like Markov chain Monte Carlo, and large data, and whatnot, they're actually on the ascendant in statistics.

The best example I can give you is this Bulgarian dissident, Georgi Markov.

And they wrote their watershed synthesis, now called MCMC for Markov chain-Monte Carlo, very, very fast 'cause they were scared other people would put the pieces together, too.

rice and pellet embedded in the tip of that umbrella and and KGB actually did him in and and Markov

Each one has its own probability, and you can represent these probabilities with a mathematical tool called a Markov chain.

If you combine that with a much bigger search window so it can point much further back in memory, then you get the Lempel Ziv Markov chain algorithm, or LZMA.

It was first proven by Jacob Bernoulli in 1713, and it was the key concept at the heart of probability theory right up until Markov and Nekrasov.

Do people think it was like a mic drop moment and like, "Oh, Nekrasov's out, like, Markov's the man"?

- And any system like this where we have a feedback loop, will become hard to model using Markov chains.

Bayes, Gibbs sampling, Monte Carlo, Markov chains, iterations.

It's 60 or 80 pages on Bayes, Markov