CODEWITHSUNDEEP
machine-learninghidden-markov-modelsprobabilistic-programming
Xristos Timplalexis
Xristos Timplalexis

Reputation: 119

Hidden Markov Model with new, unseen observations

I am trying to use a hidden markov model, but I have the problem that my observations are some triplets of continuous values (temperature, humidity, sth else). This means that I do not know the exact number of my possible observations, as they are not discrete. This creates the problem that I can not define the size of my emission matrix. Considering discrete values is not an option because using the necessary step at each variable, I get some millions of possible observation combinations. So, can this problem be solved with HMM? Essentialy, can the size of the emission matrix change every time that I get a new observation?

Upvotes: 0

Views: 543

Answers (2)

user3103059
user3103059

Reputation:

One approach is to give the new unseen observation an equal probability of been emitted by all the states, or assign them a probability according a PDF if you happen to know it. This at least will solve your immediate problem. Later on, when the state is observed (I assume you are trying to predict states), you may want to reassign the real probabilities to the new observation.

A second approach (the one I like better) is to cluster your observations employing a clustering method. This way, your observations would be the clusters not the real time data. Once you capture your data you assign it to the corresponding cluster and give the HMM the cluster number as an observation. No more "unseen" observations to worry about.

Or you may have to resort to a Continuous Hidden Markov model instead of a discrete one. But this one comes with a lot of caveats.

Upvotes: 0

Tala Warang
Tala Warang

Reputation: 91

I guess you have misunderstood the concept, there is no emission matrix, only transition probability matrix. and it is constant. Concerning your problem with 3 unknown continuous rv. is easier comparing to speech recognition, for example with 39 MFCC continuous rv. but in speech there is the assumption that 39 rv (yours only 3) distributes normal independent, not identical. So if you insist on HMM, then do not change the emission matrix. you're problem still can be solved instead.

Upvotes: 0

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