To get to the probabilities in the top right of the board, you keep applying P(A,B)=P(A|B).P(B) ... eg. A=C3, B=C2 x C1 x M3 x M2 x M1 ... keep applying P(A,B)=P(A|B).P(B) and you will end up with same probabilities as shown on the whiteboard top right of screen for the viewer. Great video!
Sorry, but I still don't get the calculation at the end. The whole video was explained flawlessly but the calculation was left out. I don't understand. If you can please further help. Thankyou.
@@ummerabab8297 Here is some code in python showing the calculations in the output, you'll see that the hidden sequence s->s->h has the highest probability (0.018) ##### code #################### def get_most_likely(): starting_probs={'h' :.4, 's':.6} transition_probs={'hh':.7, 'hs':.3, 'sh':.5, 'ss':.5, } emission_probs = {'hr':.8, 'hg':.1,'hb':.1, 'sr':.2, 'sg':.3, 'sb':.5} mood={1:'h', 0:'s'} # for generating all 8 possible choices using BitMasking observed_clothes = 'gbr' def calc_prob(hidden_states:str)->int: res = starting_probs[hidden_states[:1]] # Prob(m1) res *= transition_probs[hidden_states[:2]] # Prob(m2|m2) res *= transition_probs[hidden_states[1:3]] # Prob(m3|m2) res *= emission_probs[hidden_states[0]+observed_clothes[0]] # Prob(c1|m1) res *= emission_probs[hidden_states[1]+observed_clothes[1]] # Prob(c2|m2) res *= emission_probs[hidden_states[2]+observed_clothes[2]] # Prob(c2|m3) return res #Use BitMasking to generate all possible combinations of hidden states 's' and 'h' for i in range(8): hidden_states = [] binary = i for _ in range(3): hidden_states.append(mood[binary&1]) binary //=2 hidden_states = "".join(hidden_states) print(hidden_states, round(calc_prob(hidden_states),5)) ##### Output ###### sss 0.0045 hss 0.0006 shs 0.00054 hhs 0.000168 ssh 0.018 hsh 0.0024 shh 0.00504 hhh 0.001568
Unbelievable Explanation!! I have referred to more than 10 videos where basic working flow of this model was explained but I must say that rather I'm sure that this is the most easiest explanation one can ever find on youtube , the way of explanation considering the practical approach was much needed and you did exactly that Thanks a ton man !
Glad I found your videos. Whenever I need some explanation for hard things in Machine Learning, I come to your channel. And you always explain things so simply. Great work man. Keep it up.
I have 2 questions: 1. The Markov assumption seems VERY strong. How can we guarantee the current state only depends on the previous state? (e.g., person has an outfit for the day of the week instead of based on yesterday) 2. How do we collect the transition/emission probabilities if the state is hidden?
Wonderful explanation. I hand calculated a couple of sequences and then coded up a brute force solution for this small problem. This helped a lot! Really appreciate the video!
Dear ritvik, I watch your videos and I like the way you explain. Regarding this HMM, the stationary vector π is [0.625, 0.375] for the states [happy, sad] respectively. You can check the correct stationary vector by multiplying it with the transpose of the Transition probability Matrix, then it should result the same stationary vector as result: import numpy as np B = np.array([[0.7, 0.3], [0.5, 0.5]]) pi_B = np.array([0.625, 0.375]) np.matmul(B.T, pi_B) array([0.625, 0.375])
This helped me at the best time possible!! I didn't know jack about the math a while ago, but now I have a general grasp of the concept and was able to chart down my own problem as you were explaining the example. Thank you so much!!
thanks for the video! I've watched two other videos but this one is the easiest to understand HMM and I also like that you added the real-life application NLP example at the end
At 2:13, the lecturer says, "it's not random" whether the professor wears a red/green/blue shirt. Not true. It is random. It's random but dependent on the happy/sad state of the professor. Sorry to nitpick. I definitely enjoyed this video :)
I wish you went through Bayes Nets before coming to HMM. That would make the conditional probabilities so much more easier to understand for HMMs. Great explanation though !! :)
I agree Teaching is an art. You have mastered it. Application to real world scenarios are really helpful. Really feel so confident after watching your videos. Question, How did we get the probabilities to start with? are those arbitrary or followed any scientific method to arrive at those numbers?
Great video to get an intuition for HMMs. Two minor notes: 1. There might be an ambiguity of the state sad (S) and the start symbol (S), which might have been resolved by renaming one or the other 2. About the example configuration of hidden states which maximizes P: I think this should be written as a tuple (s, s, h) rather than a set {s, s, h} since the order is relevant? Keep up the good work! :-)
After watching this it left me with the impression that local maximization of conditional probabilities lead to global maximization of the hidden markov model. Seems too good to be true... I guess the hard part is finding out the hidden state transition probabilities?
appreciate that the professor was a 'she' took me by surprise and made me smile :) also great explanation, made me remember that learning is actually fun when you understand what the fuck is going on
oooh I get it now! Thank you so much :-) you have an excellent way of explaining things and I didn’t feel like there was 1 word too much (or too little)!
Thanks a lot for sharing. It is very clearly explained. Just wondering why the objective we want to optimize is not the conditional probability P(M=m | C = c).
Really crisp explanation. I just have a query. When you say that the mood on a given day "only" depends on the mood the previous day, this statement seems to come with a caveat. Because if it "only" depended on the previous day's mood, then the Markov chain will be trivial. I think what you mean is that the dependence is a conditional probability on the previous day's mood: meaning, given today's mood, there is a "this percent" chance that tomorrow's mood will be this and a "that percent" chance that tomorrow's mood will be that. "this percent" and "that percent" summing up to 1, obviously. The word "only" somehow conveyed a probability of one. I hope I am able to clearly explain.
Ritvik, great videos.. I have learnt a lot.. thx. A quick Q re: HMM. How does one create transition matrix for hidden states when in fact you don't know the states.. thx!
Great video, however I was wondering if the hidden state transitioning probabilities are unknown, is there a way to compute/calculate them based on the observations?
Hey in future videos could you provide an unobstructed view of the board, either at the beginning or end of the video, just for a few seconds? Sometimes it’s helpful to screenshot your notes
Why are we maximizing the joint probability? Shouldn't the task to find the most likely hidden sequence GIVEN the observed sequence? i.e. maximizing the conditional probability argmax P(m1m2m3| c1c2c3)?
Thank you, that was a very clear introduction. They key thing I don't get is where the transition and emission probabilities come from. In a real-world problem, how do you get at those?
In the case of the NLP example with part of speech tagging, the model would need data consisting of sentences that are assigned tags by humans. The problem is that there isn't much of that data lying around.
@ritvikmath Any chance of a follow up video covering some of the algos like Baum-Welch, Viterbi, please? ... i'm sure you could explain them well. Thanks a lot.
Good suggestion! I'll look into it for my next round of videos. Usually I'll throw a general topic out there and use the comments to inform future videos. Thanks!
Thanks! And yes exactly, we can do that. In practice, of course with many time periods and states this gets too expensive so we have more efficient ways to compare them but at the end of the day we are still getting the maximum.
