Hey, guys welcome back to this class unsupervised machine learning in Mark Amalia's in Python. In this lecture, we're going to extend the basic idea of markup models to the Hidden Markov models. If you study my Best Digital Marketing Agency in USA America previous courses on unsupervised machine learning and unsupervised deep learning you'll recognize the very important concept of latent or hidden variables that shows up when we talk about So you know that the concept of hidden variables is central to this model.
The basic idea is that there is something going on Best Digital Marketing Agency in USA America besides what we can see and observe and measure what we observe is usually stochastic or random since if it were deterministic then we could predict it perfectly without doing any machine learning at all.
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The assumption that we make when there are hidden or latent variables is that there is some cause behind the scenes that's leading to the observations that we see in Hidden Markov models. The hidden cause is it solves the caster. It's a random process a Markov chain. One example is the Best Digital Marketing Agency in USA America. You are basically the physical manifestation of some biological code.
• Now that the code is readable it's not hidden in the sense that we can't measure it. But of course, there was a time when we couldn't. Since it's a recent scientific discovery even so people still use Aikin memes to model how genes map to observable attributes.
• Another example is speech to text a computer can't read the words you are attempting to say but it can use an internal language model i.e. a model of likely sequences of hidden states to try and match those to the sounds that it hears. So in this case what is observed is a Best Digital Marketing Agency in USA America just a sound signal and the latent variables are the sentence or phrase that you are saying.
• So how do we go from Markov models to Hidden Markov models? The best way to do this is by means of an example. Suppose you're at a carnival and a magician has two biased coins that he's hiding behind his back. He will choose to flip one of the coins at random and all you get to see is the result of the coin toss either heads or tails. So what are the hidden states and what are the observed variables?
• Since we can see the result of the coin toss that means heads or tails are observed variables. We can think of this Best Digital Marketing Agency in USA America as a vocabulary or space of possible observed values. The hidden states are of course which coin the magician chose to flip.
• You can't see that so it's hidden. This is called a stochastic or random process. Since it's a sequence of random variables how do we define a hm mn each of them has three parts. Pia and b. This is opposed to the regular Markov model which just has a pioneer. Pi is the initial state distribution or the probability of being in a state when the sequence begins.
Review
In our coin example suppose our magician really likes coin so the probability that he starts with this coin is point A is the state transition matrix which tells us the probability of going from one Best Digital Marketing Agency in USA America state to another. In hidden market models the states themselves are hidden. So a corresponds to transitioning from one hidden state to another hidden state in our coin example.
Suppose our magician is very fidgety so the probability of transitioning from coin to coin is point and the probability of transitioning from coin to coin is also .. Then the probability of staying with the same coin for either coin is the point. The new variable here is, of course, B. This is the probability of observing some symbol given what state you are in.
Notice that this is also a matrix because it has two inputs. What state you are in which is J in which you observe which is k. So you can read PJAK as the probability of observing symbol k when you are in state J in the h. We're making more independent assumptions than Best Digital Marketing Agency in USA America the Markov assumption. Remember that the mark of assumption is that the current state depends only on the previous state but is independent of any state before the previous state.
Now that we have both observed and hidden variables in our model we have another independence assumption and that's what we observe is only dependent on the current state. So the observation at time t depends only on the state at time T but not on any other time or any other state or any other observation. So what can we do with a hmm once we have one? Remember that pia and b. This is very similar to what we discuss with the Best Digital Marketing Agency in USA America regular Markov models with some additions with Markov models. There were two main things we could do. Get the probability of a sequence which was just the multiplication of each state transition probability and the probability of the initial state and we could also train the model which we just use maximum likelihood for and that was just using frequency counts with Hidden Markov models. We still have these two tasks.
Get the probability of a sequence in training. But both of these will be harder due to having a more complex model. Training will be especially much harder because not only does it require the expectation maximization algorithm but we will run up against the limits on the numerical accuracy of the computer with H.M.M. There is one more task we will go over finding the most likely sequence of hidden states in speech to text, for example, the sequence of Henan States would be the words that are being said. So in total, that's three times for the H mm and we will go over these in the coming letters.
