Markov Chains: Recurrence, Irreducibility, Classes | Part - 2
ฝัง
- เผยแพร่เมื่อ 1 พ.ย. 2020
- Let's understand Markov chains and its properties. In this video, I've discussed recurrent states, reducibility, and communicative classes.
#markovchain #datascience #statistics
For more videos please subscribe -
bit.ly/normalizedNERD
Markov Chain series -
• Markov Chains Clearly ...
Facebook -
/ nerdywits
Instagram -
/ normalizednerd
Twitter -
/ normalized_nerd
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:)
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!
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?
Very good precised explanation with nice animation. Thank you for your video. Please make more for solving numericals and implementation of practical scenario.
Thanks for the video. Now I can understand whenever I hear Markov chain!
Amazing explanation! Can you also please explain the periodicity of a state in a Markov chain?
why this video has views only on thousands? it needs to be in millions!
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.
Your videos are really helpful dada❤
Great videos!
Would you consider making video/s on Queueing theory for stochastic models please?
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?
Love the explaination!
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
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!
Can't believe that Indian is at it's prime. Ek number explanation 🔥🔥🔥
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.
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
Amazing video again 👍
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?
very good video
I am now a fan! New subscriber !
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 ?
You are a very good math professor, thanks a lot!
Thanks a lot!!
Love your videos! Very clearly explained
Thanks mate!
Your channel is a great resource! Thanks!
Glad you think so!
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 😂🙏🏻
Great one
Amazing content for ML and Data Science people. Keep up Bro. Will share it with my ML comrades.
Much appreciated! Please do :D
gr8 vdo...
class 1(state 0 ) and class 3 (state 3)...cant communicate with others, how are they communicative classes???
Very clearly explained! Yes would be useful if there are more videos..
Sure!
Love the videos. Can't wait to get you to 100k subs!
Keep supporting 😁
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.
Great video, is the source code available somewhere?
Amazing animation! Thank you.
My pleasure!
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?
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%
Looks like Stat Quest Channel BAM!!!
Clearly Explained!!!
Haha...He's a legend!
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 😢
Subscribed, awesome stuff dude
Awesome, thank you!
Damn that's a smooth explaination
Thanks!!
Thanks
wow this kind of random walk demo is very helpful
Glad you found this helpful!
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.
Fantastic !!
Many thanks!
thank yo u so much, amazing videos!!!
You're very welcome!
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"?
please upload more in detail for properties and applications
Video coming soon :)
yes more please.
Working on it!
¿What books to learn statistics, prob and markov chain?
Element of Statistical Learning (Springer)
Markov Chains by J.R. Norris
🥺🥺🥺thanq
Basically these are the strongest connected components.
Right you are...strongly connected components
Notes for my future revision.
*New Terminologies*
Transient states.
Recurrence state.
Reducible Markov chain.
Irreducible Markov chain.
Communicating Classes.
you are awsome
Thanks a lot! :D
discrete time markov chains and continuous time markov chains please
Suggestion noted!
More 🤩....
Sure!
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
Facecam kobe asbe?
Ota deri ache 😅
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
osu?
i love you
❤❤❤
Add some music
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.