EM Algorithm
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- เผยแพร่เมื่อ 25 ก.ค. 2024
- This is, what I hope, a low-math oriented introduction to the EM algorithm. The example I use is from a coin toss, but can be generalized to any example that uses two treatments in which there is data for success or failure. In coin toss terms: two coins and each yields a different average number of heads.
The only video I watched many times to understand EM algo concept.
A very SIMPLE explanation that is not easy to represent.
A really clear and easy-understanding illustration and this really saves my life, thank you, sir.
This is the best EM explanation on TH-cam so far. Thanks!
Perfect explanation deserves spreading! I really like this video that contains no equations but explains the theory so clearly!
Finally a clear explanation with examples of EM algorithm. Great job!
Best example ever for understanding EM, thanks so much!
very nice, simple and clear example. thank you!
Very good explanation, clear and easy to understand. Thanks!
Wow! this was so well presented and explained! Thanks a ton!
Excellent tutorial thank you so much for posting!
Thank you for this awesome explanation. Helped me a lot!
This has really cleared up my EM concept upto an extent.
Excellent work!
This is the best explanation ever!!
great explanation! thanks!
Great example - thanks!
begs to wonder why lecturers cant themselves prepare simple diagrams and visuals like this to assist with the learning.. Well explained thank you
Thanks a lot !! It helped a lot in my master thesis project !
This was really helpful. Thanks man!
Thank you very much very, a great explanation
Thanks very much! This video is very helpful for me.
Thank you! Great video :)
Thanks a lot. This has helped me a lot.
Good Example.. Thanks for explaining it :)
Thanks !! Gr8 video.
thank you so much,sir
For this example, we are not looking for which coin produced which output. Nor which coin is more likely (between A and B) to have produced the output. Instead, we are interested in figuring out what is the P(h) of the two coins, giving that we assume there were two coins flipped, that resulted these 5 rows of output. (where each row is the result of picking on of the two coins randomly and flipping it 10 times).
loved it!
Very well prepared and explained, thanks.
There were two minor mistakes in this video: 1) 0.55 was 0.5 and the little 5 was the number for footnote ;-)
2) When you went back some slides to show the distribution of having 5 heads, that graph was showing the distribution for 15 coins, while you were talking about a single coin.
Thanks again, keep up the great work.
Nice Explanation.
I read the Nature article but explanation of binomial distribution was not explained explicitly. This is a very helpful video.
thank you
thanks a lot.
Yey, i understand at the end!!
I own you my exam. You are my saviour. Best explanation ever!!!
I am wondering where is the argmax part in updating the two old parameters? I mean the maximu likelihood part.
thanks alot
Thank you for the simple and clear explanation. My question is does it always converge to the same values independent of our initial setting. Are there global and local optimals and what even is the criteria for those optimals? Thank you
EM guarantees to find a local maximum. So depending on the initial choice of thetas you get different convergence
Great! Thank you! I understood the intuition of the EM algorithm! What if you don't know how many times you've thrown the coin consequently? (e.i. you don't know u had 5 rounds of 10 coin tosses..it might have been from one of the coins or both... that is the HMM model)
best ever man, love from india ,
I don't understand why in 23:48 T=0.45x5 tails= 2.2 tails, shoudn't it be (1-0.45)*5 tails?
maplecoin111 No, the 0.45 is the likelihood that Coin A was tossed, but in that toss 5 coins came up as H and 5 as T. so, you multiply the likelihood of that coin being coin A(0.45) by the number of heads (5); then multiply the likelihood of that coin being coin A (still 0.45) by the number of tails (5). It was a coincidence that it came up as the same number.
Thank you Francisco Iacobelli. This helped me to understrand the principle. I have a question. How much the initial guess of the parameters usually affects the final parameter estimates?
this really depends on the problem. Generally, a good initial guess should be better than a random one, and sometimes you have no choice but to start with a random guess. depending on the problem, the "learning" speed may be faster or slower.
I guess it is a trial and error kind of problem is at hand. some people do not wait for the algorithm to converge, but instead they put a fixed number of iterations assuming the solution is "good enough".
Francisco Iacobelli
thanks for your reply!
Can someone explain to me why, at 23:34, we are multiplying 0.45 * 5 and 0.55 * 5?
My understanding:
- 0.45 is the probability that the first coin was tossed with the assumption that coin A has a 60% chance of being heads.
-0.55 is the probability that the first coin was tossed with the assumption that coin B has a 50% chance of being heads.
We observed 5 H and 5 T in this case. What does it mean we are "estimating likely number of heads and tails? Why does a 0.45 probability it was the coin A give us 2.2 heads and 2.8 tails? The sum of this is only 5 coins observed...
I'm also confused regarding this. Please let us know if you figure it out.
I am also stumbling upon this. I am not sure whether I understood it, but I'll share my thoughts anyway. When you look into the figure of the paper at 24:15 you see the table where the results (2,2H; 2,2T for A and 2,8H, 2,8T for B) are displayed. All together sum up to ten coins (2,2 + 2,8)*2=10. So I think, these numbers represent the expected heads and tails from each coin respectively we can expect if we observe 10 tosses and don't know which coin was used.
how is expected number of heads is .45*5 ?
Isn't it that for binomial (n,p) expected number of success is np , so shouldn't it be .45*10 ?
I am wondering if it is a coincidence that the EM solutions are consistent with the given thetas. From the 5 (10 times each) tosses, we could see that, in general, the coins are skewed to head ( 33 heads v.s 17 heads). For example, if we random choose theta_1=0.5, thera_2=0.6 at the beginning, we would come to the solution theta_1=0.52, and theta_2=o.8, moreover, if we random choose theta_1=0.55, theta_2=0.55, would we obtain some solution like theta_1=0.65, theta_2=0.65 at the end?
(1)Its a clustering algorithm. It does not provide correct label for each cluster. So it is just a coincidence. (2) The same parameters should not be chosen, since updates becomes the same, so the converged parameters.
mistyped? thetaB=0.5^5 (20:35)
i couldn't understand how result 0.6 and 0.55 appear p/s elaborate it
This video is good but the mouse was blinking all time. it was distracting
6:25 toin cosses
Avijeet Kartikay I know :P
Which random variable refers to z (latent variable) or missing variable in this example?
Is it the coin to be A or B?
Is this correct: PA(h)^h(1-PA(h))^10-h
0.6(5)^5(1-0.6(5))^10-5 is this correct?
No, it is 0.6 ^ 5 (1 - 0.6) ^ 10 - 5
22:40
Thank you for your video. I understand the computation but I still have some confusions about EM. I ask you some questions and hope you can answer me:
1. Take the first toss to be an example, I agree the number 0.45 for A and 0.55 for B and the coin B is highly probable to be picked. But the next step, I don't understand the essence of calculating the new theta{A}, theta{B}. Why did you do like that? I understand the calculation but I don't know why I have to do that.
2. The theta{A} and theta{B} increase or decrease following by a monotonous function or not?
Thank you!
Thanks dude! But TBH i'd be more focused if your cursor hadn't trembled that much..
The Video in Hindi explains it much better... and I don't even speak Hindi.
I thought EM stands for Expectation Maximization
I am sory sir.. I dont understand the 0.6 and 0.5 coming from where.. With best wishes
Can i download the slides??
Wow, I am confused even more now. 🙄
While this definitely helped, goddamn was it’s hard to sit through. The unnecessary and confusing "examples" regarding marketing strategy in the beginning, the cursor that just fucks around all the time, the shitload of mistakes you made and then corrected.
Also people watch out: If you are confused by his results around 24.16, so was I. That is because in the first column he assumes the probability of coin B to throw a head is 0.55, while on the subsequent tests he assumes that it is 0.5. Basically he switches the probability of Coin B from 20.43 (which was a typo) but doesn't correct it in the first row.
Man, I really hope for people after me that you'll make a streamlined version of this.
Thank you! Great video :)