Markov Chains & Transition Matrices
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- Опубликовано: 10 июн 2024
- Part 1 on Markov Chains can be found here: • Intro to Markov Chains... In part 2 we study transition matrices. Using a transition matrix let's us do computation of Markov Chains far more efficiently because determining a future state from some initial state is nothing more than multiplying by a transition matrix. I show you how to go from a Transition Diagram to a Transition Matrix, the terminology used, and do an example to show you how to compute the probabilities. The use of the transition matrix makes it far easier to compute future states arbitrarily far into the future.
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Best video on Markov Chains. So easy to understand and no unnecessary analogies. Great job!
So crisp. So clean. So clear.
Thank you!
What a video man, what an explanation. I literally understood the concept in one go. Keep it up !!!!!!
Dr Trefor, you're a blessing. Thank you for such clear explanations. They're liquid gold.
THANK YOU! God, i finally understood how to make the damn matrix. My professor is so bad at explaining things and he just goes by the sum version, and doesn't explain things.
This is such a life savior !
I've been watching math videos for a few years and I have to say that your channel is the best. You just teach in a extremely organized and interesting way. Please keep on!
Thank you so much!
Simply excellent explanation. In 6 minutes you made me understood what I tried to study in a week
Dude, you are a magician, the way u explain it ! Seems so easy, and make so much sense, thank you so much ! Please do more part !
OMG! This is the best video on Markov Chains. I just spent 30 mins on reading articles on medium, brilliant, wikipedia, etc and couldn't understand what they meant at all. But 4 mins into this video, I got it!
Crystal clear explanation. Direct and easy to understand. Thank You!
The explanations are easy to understand and the video length is at the sweet spot. Great job!
Looking forward to the rest of the series.
Thank you, glad you're enjoying!
don't know how to thank you sir
this deserves to be paied for
really great job and pure gold
Generally speaking the rows are "from state A" and the columns are "to state B" within the literature (so invert his matrix along the diagonal) and it would have been nice to see the even simpler form of P using eigenvalues and eigenvectors to create AD(A^-1)=P to even better show how this generalises transitions and then shows the rate at which the markov chain converges
Was wondering this lol
Wow. Thank you very much. What a way to make this look so easy. I understood this concept for the first time in my life.
Good, very good. Some people on ytube are just afraid of writing math when ever they are teaching, and just mistify the subject. This is good math indeed.
This guy saving my linear algebra grades
also i just realized that markov chains look like finite state machines
Clear explanation. Well poised and articulated. Makes its interesting, even without illustrating a real life practical example in the video. Also, a true desire to teach.
Give this man an award!
Simple and comprehensive, thank you
Thanks for the lucid explanation!
That was a wonderful explanation of the Markov chain, thank you
Simple and comprehensive.Thank you soooooo much
Spot on delivery Dr, many thanks
I really liked your easy explanation. Thank you.
thank you for your video it is well explained, but at 3:19, the matrix isn't supposed to be the way around? I mean the 0.25 shouldn't be in the place of 0.4? because the rows explain the directions, not the columns?
best explanation I could find on youtube
Thank you!
Awesome , cleared my concept , Thank you !
Very well explained sir! Thank you.
Thank you Dr. Trefor Bazett! 谢谢！
You, Sir, are a Superhero.❤
I liked your explanation it was simple and clear, thank you so much.
Our Markovian hero, thanx
that's what I call a straightforward explanation. Thank's a lot!
This guy gave a 6-minute crash course where I started so confused. my man.
very good explanation. thank you.
Wow, I was writing up my thesis on TMMC application to my little chemical adsorption model and I cannot understand the Maths behind it properly. You saved my life.
GREAT EXPLANATION!
Thank you man! This was so helpful☺️
Incredibly good explanation of Markov Chains. Subscribed!
Welcome aboard!
Brilliant to say the least
Wow! Interesting Topic! Thank You for covering something wonderful!
Glad you enjoyed it!
Your explanation is much better than the Khan's Academy lets say. So detailed and so simple to understand.
Thank you so much!
His video is completely wrong about the matrix positioning
Very nice explanation
Thank you for the lecture. It's easy to understand. Do you have any plan on Non-linear control theory (obeviously in easy way llke you taught now)?.
Awesome video!
very clear. nice work.
omg this video helps me a lot! thanks a ton
Lovely explanation
You just saved me !
Thanks
Brilliant explanation thank you :)
Thank you for this very practical video, I was immediately able to apply this concept, although I didn't immediately understand why multiplying the transition matrix with the current state vector yields the next state vector, but after some further consideration, what this multiplication actually does, it is quite clear, why/how that works.
I cried.
This was very good
Beautiful video Sir..👌👌
Also, the diagonalization of a general two state transition matrix is quite nice, so taking a high power of one is not so bad
Amazing video sirrr......Thank you for video. Loves from India
Lovely. I think even Markov would not be able to explain like that !!! Liked and Subscribed!!!
Thanks for the sub!
So we can apply eigendecomposition to simplify the matrix exponentiation! Thanks Trefor!
Absolutely! That was beyond the scope of this video, but would definitely be the next thing to do.
You had shed lights to people like me who suffered a lot from a college class which takes about 90 min
Beautiful.
Great! very clear and concise, what is the connection of this with turing machines?
Great video, thanks!! Any chance to follow up on this topic? Perhaps look into Markov Models?
Thank you it was usefull
Nice! Even I understood that.
Absolutely clear and concise, thank you!
It worth noting however, that computing the P^n matrix is very computationally expensive, is there a better way to to solve for P^n without having to do the power?
Incredible 🔥
Thank you for confusing me. Great work 👍
I am Almina khatun who also comment on our video sir.......I al ways first
Fantastic!!
Saved me👏
This just blew my mind because it made me realize that the final convergent state of a markov chain is dictated by the transition matrix's eigenvector corresponding to its largest eigenvalue because the repeated multiplication essentially comprises the power method of finding the largest eigenvector/value.
thanks sir
Why would some one dislike your Videos. They must be in a dislike Markov state. I wonder when they will transition Dr Trefor Bazett.
Amazing
Thanks❤
Respect!!!!!!✌✌ >>>Legend👏
I did not see a link to the video you referenced introducing matrix multiplication
Best explanation ever!~!!
Thank you!!
Very nice
wow it just so happens to be that the lecture today included transition matrices! what luck!
nice timing!
How do you find at what value n the S vector will have a given value for x1??
I did not get why we calculate s3 if the system has only two states? What is it Sn? Is it number of transitions? If there are two states then we have 4 transitions?
Does this non-Markovian system turns into a Markovian system if we let n -> Infinity ?
This is an awsome video however I am still confused that is it possible to calculate the transition matrix using only the initial probabilities? Or calculate the initial probabilities using only the transition matrix?
So what if I want to predict a specific state, like If I got students degrees and try to predict the average of degree in next semester!? and can I do it for a particular student.!?
Legend!
great video! there's so much more you can talk about concerning markov chains, this is just the beginning! Like how they can limit to some stationary matrix under certain conditions of the transition matrix P, or even easier ways to calculate P^n (if you decompose it such that P=U D U^-1, where U is the matrix of eigenvectors and D is the matrix of eigenvalues, then P^n = U D^n U^-1, where D is simply the matrix of only eigenvalues^n along it's diagonal). They are very interesting indeed, you have your work laid out for you! XD
Totally! I am thinking of doing some follows we are just scratching the surface here
Thank you, I think I will be able to ace the CS 70 final exam at Berkeley.
This was absolutely brilliant. This video could also be used to explain quantum spin 1/2; just make a and b stand for spin up and spin down
It sounds good, i can apply this to Roulette game! 😅
If we were to line up the probability distributions to = 1 along the rows, rather than the columns that wouldn’t work (keeping the vector unchanged). Is that because of how it’s defined, due to the notation used?
Indeed, it's just a quirk of the definition. If you wanted to do it your way, you'd have to be multiplying with the vector on the left instead, which would be just as good but not as conventional.
When does a Markov chain converge into steady state?
How many steps does it take to converge?
Memory less ness property explained
just wow
Thank you for the video! where can we find the explanation about matrices multiplication? and in addition - isn't the matrix should be in such a way that the rows represent the state we are currently in and the columns the state in the next week? or it doesn't matter?
Thanks!!
I know Im asking the wrong place but does someone know a tool to get back into an instagram account?
I stupidly forgot the login password. I love any help you can offer me
@Emiliano Terrell instablaster ;)
@Thaddeus Keanu Thanks so much for your reply. I got to the site thru google and Im trying it out atm.
Looks like it's gonna take a while so I will get back to you later with my results.
@Thaddeus Keanu it worked and I actually got access to my account again. I'm so happy!
Thank you so much you really help me out !
@Emiliano Terrell glad I could help :)
love from nepal
thank you for your videos . if you will explain the logic behind it and not the matrix structure / equation structure perspective it will be much easier to understand. also first video is not on the list
at 3:32, I think the row in the matrix should add up to 1. am I correct? Thanks!
Columns add up to 1.0. Not the rows.
I derived this before knowing what it was
Nice video. Would the diagonalization of this matrix speed up our process of find the solution at k'th step ?
Absolutely. That is actually the planned third video in this series I might make at some point.
@@DrTrefor Really looking forward for your series ahead. I hope you connect the dots ahead with important applications in physics, biology etc. and also with Markov chain Monte Carlo (MCMC) method. :-)
This Markov process feels vaguely quantum mechanical to me, the idea of probabilities spreading out over time over multiple states.
At first I thought the result won't always add up to 1, but it can be easily shown that if both columns of the P matrix and of course the one column of the S matrix add up to 1, the product's column will also add up to 1.