Markov Chains: Recurrence, Irreducibility, Classes | Part - 2
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- Опубліковано 8 лют 2025
- Let's understand Markov chains and its properties. In this video, I've discussed recurrent states, reducibility, and communicative classes.
#markovchain #datascience #statistics
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why this video has views only on thousands? it needs to be in millions!
Can't believe that Indian is at it's prime. Ek number explanation 🔥🔥🔥
This is really nice for the beginners to understand the basic properties of markov chain. It would be great if your video could go further to the hidden markov chain and factorial markov chain:)
You are a very good math professor, thanks a lot!
Thanks a lot!!
Very catchy! I request you to make more such videos on markov chains with these kinds of awesome representations!! Markov chains were a dread to me previously.. your videos are too cool!
Definitely will do!
Great to see high-quality educational channels like 3Blue1Brown coming from India. Btw, what software do you use to create the animations?
It's a python library named manim, created by Grant Sanderson!
Are you sure about that comparison?
@@abhirajarora7631i mean grant is sanderson is 3b1b, so it's bound to be similar
@@abhirajarora7631 Normalised Nerd will reach that level in future dw
Absolutely brilliant, clear explanation!
Your videos are really helpful dada❤
Amazing content for ML and Data Science people. Keep up Bro. Will share it with my ML comrades.
Much appreciated! Please do :D
Your channel is a great resource! Thanks!
Glad you think so!
Very good precised explanation with nice animation. Thank you for your video. Please make more for solving numericals and implementation of practical scenario.
Looks like Stat Quest Channel BAM!!!
Clearly Explained!!!
Haha...He's a legend!
Thanks for the video. Now I can understand whenever I hear Markov chain!
This is excellent info well presented. Thank Yoyu
Bro we need more videos. Don't wait for comments just do it 🙏🙏❤❤
Very clearly explained! Yes would be useful if there are more videos..
Sure!
Why don't our teachers teach like this , was hating maths few mins ago, till I turned this video ,Thank you so for this much-needed video 🥺, Now I kinda want to do PhD instead in this 😂🙏🏻
I am now a fan! New subscriber !
Thanks for the videos. Helped me a lot. Would appreciate if you upload a video for complete in depth mathematical analysis of the Marco chain and its stationary probability.
Amazing explanation! Can you also please explain the periodicity of a state in a Markov chain?
5:46 - "Between any of these classes, we can always go from one state to the other." But how can we do that if two of the classes are self-contained? Do you mean that we can always move between states within each class?
"we can always move between states within each class" This is what I meant.
@@NormalizedNerd thanks
I also think it is a bit hard to understand why it can be called a communication class when 1 cannot reach 0.
Love the videos. Can't wait to get you to 100k subs!
Keep supporting 😁
At @2:36 : I beg to differ. There is a non-zero probability that once I go from State 2 to State 1; I would continue to be in State 1 forever. In this case, we are not *bound * to come back to State 2 ever again. So I wouldn't say the probability of ever coming back to State 2 from State 2 is *1*.
(Or am I missing something here?)
There isn’t a probability we’ll stay at state 1 forever. We can go from state 1 to state 1 again once twice or a billion times but we will come back to state 2 eventually.
Love the explaination!
great video man
In a certain way, this video was less about Markov chains themselves and more about the underlying directed graphs. Using different language to describe the same things, the communicating classes are called “strongly connected components”, and you can form a “condensation graph” (which is a directed acyclic graph) by collapsing these communicating states.
Amazing video again 👍
Hello, dumb question. Shouldn't state 2be transient also. I mean, there is a extremely small chance (but not zero), that in a random walk we go from state 2 to state 1 and then we keep looping through state 1 forever, hence not coming back to state 2? No? Thanks love your vids.
Thank you so much
2:48 Sir, how come state 2 is recurrent state? It is possible that after reaching state 1, it keeps on looping back to state 1 forever, it is not "bound" to come back to state 2 from 1.
Recurrent state just means that after going from state to state infinitely, you will reach a giving state also infinitely. Generally, for very large numbers, 2 will be reached. 0, if we ran the transitions infinitely, would have a finite occurrence, a specific amount before it left state 0 and unable to return
No, because recurrence at 1 isn't with probability 1. So, provided you wait long enough, you will eventually leave state 1.
Love your videos! Very clearly explained
Thanks mate!
Damn that's a smooth explaination
Thanks!!
I don't quite understand the part where 2 is also a recurrent state in the first example. If the definition of the recurrent state is where the probability of returning back to that state is =1 (i.e. guaranteed), wouldn't 2 be a transient state since there is the possible case where 1 goes back to itself only ad infinitum?
Yes that s true, I think he doesn't define well enough the two different cases
I think there is a mistake at 2:56? 2 is not a recurrent state because after we leave 2, the chance of going back to 2 is less than 1 when 1 recurse itself. Only 1 is a recurrent state because after we leave 1, it's 100% that we will come back to 1. Can someone confirm that?
I was thinking the same thing, but I suppose if you consider an infinite number of steps, eventually the probability of going back to 2 approaches 100%
wow this kind of random walk demo is very helpful
Glad you found this helpful!
Great one
Thanks
Notes for my future revision.
*New Terminologies*
Transient states.
Recurrence state.
Reducible Markov chain.
Irreducible Markov chain.
Communicating Classes.
Amazing animation! Thank you.
My pleasure!
Great brother 👌👌
So, if the stationary distribution has all non zero values, the chain will be irreducible ?
(Since all states can communicate with each other)
And Reducible if any of the states has 0 value in stationary distribution ?
very good video
Subscribed, awesome stuff dude
Awesome, thank you!
Thank you for your video. But I am confused, you said Sum of Outgoing Probabilities Equals 1, but in the first example, the sum of outgoing probabilities of state 0 is less than 1?
🥺🥺🥺thanq
Is there a video on No U-Turn Sampler (NUTS)? Thanks
thank yo u so much, amazing videos!!!
You're very welcome!
gr8 vdo...
class 1(state 0 ) and class 3 (state 3)...cant communicate with others, how are they communicative classes???
Fantastic !!
Many thanks!
Good presentation but I have a doubt in the end. How can we go from any state to any other state after transformation to similar states?
Great video. Just one observation; state 1 is NOT recurrent. A state cannot be recurrent and transient at the same time. The probability of never visiting state 0 again is greater than 0 so by definition it can't be recurrent. To be recurrent all paths leading out of the state has to eventually lead back to that state but that's no the case for state 0. I'm I missing something?
Great videos!
Would you consider making video/s on Queueing theory for stochastic models please?
please upload more in detail for properties and applications
Video coming soon :)
You could have explained why what is the utility of simplifying markov chains into irreducible and what is the math difference when considering them separated.
"...why what is the utility"?
Basically these are the strongest connected components.
Right you are...strongly connected components
yes more please.
Working on it!
Thank you for your channel and all your videos. I had a question watching this video: How does this relate to the definition of Markov chain which you provided in part one which said the probability of the future state only depends on the current state?
How did you use Manim to represent the random walk by blinking effect? Could you share the portion of that code? I started learning manim recently but couldn't manage to do that.
I created a custom manim object to create the graphs (markov chains). Then I'm just walking through the vertices and edges. The blinking effect is just creating a circle and fading it immediately.
@@NormalizedNerd I see. It will be great if you could share the custom object codes.
If we have state space {0,1,2,3}
And given Matrix then how to find the pij(n)? Please explain this 😢
you are awsome
Thanks a lot! :D
discrete time markov chains and continuous time markov chains please
Suggestion noted!
¿What books to learn statistics, prob and markov chain?
Element of Statistical Learning (Springer)
Markov Chains by J.R. Norris
Great video, is the source code available somewhere?
Hang on, if you define transient state as 'the probably of a state returning to itself is less than 1', then in the first example, would state 2 not also be a transient state? Reason being, there could be a random walk, in which you go from state 2 to state 1, and then state 1 keeps looping back on itself infinitely, never going back to state 2. Then the probability of state 2 returning to itself is less than 1, given there is a random walk in which it does not return to itself.
The probability of state 1 returning to itself infinitely is 0. It is bound to return to 2 at some point.
In all random walks that go on forever, we will go back to 2 if we start there.
Found this math concept from Numb3rs and got curious
More 🤩....
Sure!
Saw video 1
I will be honest, was ready to find another video when heard the Indian accent. But then saw high upvote/downvote and stayed, and don't regret it!
Haha
Facecam kobe asbe?
Ota deri ache 😅
No wonder it's called the Gambler's Ruin. 🤣
osu?
i think it's heal my light depression, thank you
I paused the video @1:00 minute mark to tell you it is NOT DUCKING GOOD TO REFER TO STATE A B AND C WHILE THE F-ING PICTURE SAYS STATE 1 2 and 3. FFS, ok now I will watch the rest of it but I think this will be a waste of time just from this start, I can tell you cant explain crap.
A and B are definition variables, like generalized variables you find in books so you can use it in any example.
i love you
❤❤❤
Add some music
Why?
No