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Suppose I am continuously getting labeled observations, each one of which is type A or type B. I want to continuously update my belief of the probability that the next object will be of type A (or B). This should involve formulating a transition rule, something of the form: "Given that my current belief is that Pr{next object is type A} = p, and the last observation was X, my new Pr{next object A} = p' ". So the idea is continuously updating my belief based on the recent event(s), and the belief(s) I had when they happened. How do I get started? What is the simplest technique? What should I start looking into? Thanks
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A very simple technique might be to use a n-gram model and to update the counts of the model while observing the sequence. |
You could look into hidden markov models
Hidden Markov models are probably the way forward. A bit more simplistic are Kalman filters, which apply only to the Gaussian case.
Is this online learning? Can you be a bit more explicit about what problem you're trying to reduce to this scenario? Is this a homework question?
Yes, it is online problem. No, it is not homework, it is industry.
So have you tried any of a large family of online learning algorithms for classification? Perceptron, SGD, winnow.. ? There are fast implementations out there, most notably vowpal wabbit. If that does not solve your problem, what does?
Ultimately, the output should not be discrete. Even if I describe the problem in terms of discrete states, my current outcome should be continuous(possible through probabilities of what state I am currently in).
It is easy to predict probabilities in online learning.
Can you be more precise, please? How would I use perceptron for this kind of situation, or SGD, for the matter of fact?
It looks like your problem is more of a hidden Markov model anyway. Well, if you know the emission and transition probabilities you can just multiply them and normalize.