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So in this lecture, we will summarize everything we learned in this section.

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The section was about the Markov model and how it can be used for NLP.

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We started this section by learning about the markoff property, although this assumption seems to be

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very restrictive.

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We also learned that it has many applications in fields such as finance, reinforcement learning and

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speech recognition.

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So clearly, although it is very restrictive, it is still very useful.

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The next step was to discuss how a market model is represented mathematically, which also helps us

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understand how to represent one in Python.

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The next step was to look at how to apply the markup model for applications in NLP.

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Now, you may not yet realize this, but what you learned in this section is just the start of a potentially

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long journey.

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In fact, what you have learned does not end here.

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We learned in this section that the basic idea is that we want to predict the future from the past.

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That is, we want to predict X of T given X of T minus one x of T minus two and so forth.

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With Markov models, it turns out that we cut this off that X of T minus one.

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However, this need not be the case.

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One thing we can do is to simply add more terms when we use one pass value.

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It's called First Order Markov.

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When we use to pass values, it's called Second Order, Markov and so forth.

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Despite the simplicity of this idea, you will find that it appears again and again in machine learning,

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even at the most advanced levels.

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One example of this is with a time series analysis.

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A common way to build a forecasting model is to try and learn a function that maps previous values to

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the next value.

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This can be a linear function, a neural network, a random forest and so forth.

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Another direction we can go is to use more complex architectures.

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We'll keep working with text, but we'll use more powerful models that can yield more complex dependencies

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between the pass values and the next value.

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One example of this is with recurrent neural networks, although that sounds complicated when using

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Arden's for NLP, you can do useful things only by training your model to predict the next value from

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previous values.

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In fact, the story still doesn't end here.

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The most powerful NLP models we have today called Transformers are also trained to do this exact same

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thing.

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Transformers might sound intimidating, but behind the scenes, all they have been trying to do is predict

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the next word from previous words.

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So again, although this is a very simple idea, it's also very powerful and it's the foundation for

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the current state of the art.