title: How to make future prediction with Hidden Markov Models
body: <p>I have many sequences of variable length. For these I want to train a Hidden Markov Model that I want to use later to predict possible continuations of (partial) sequences. I have found two ways to predict the future using HMMs so far:</p>
  
  <p>1) Hallucinate continuations and get the likelihood for that continued sequence. Pick the one with the highest likelihood as your prediction. This method requires explicit knowledge of the possible values for continations.</p>
  
  <p>2) Use the Viterbi algorithm with the (partial) sequence to obtain the most likely hidden-state-sequence. Take the emission distribution of the last hidden state in this sequence and predict e.g. the mean of that distribution (which often is Gaussian).</p>
  
  <p>Now my question is: Are there any other, possibly more principled, ways to predict the future using HMMs?</p>
  
  <p>Thanks!</p>