如何用hmmlearn解决基础HMM问题：聚焦问题1与问题3

Let's start by breaking down the three fundamental core problems that are central to working with Hidden Markov Models (HMMs):

• Problem 1 (Likelihood): Given an HMM defined as λ=(A,B) — where A represents the state transition probability matrix, and B is the observation emission probability matrix — plus an observation sequence O, calculate the likelihood probability P(O|λ).
• Problem 2 (Decoding): Given an observation sequence O and the HMM λ=(A,B), find the optimal hidden state sequence Q that most accurately explains the observed data.
• Problem 3 (Learning): Given an observation sequence O and the predefined set of HMM states, learn the model's parameters (matrices A and B) to best fit the observed sequence.

For this discussion, we're focusing specifically on Problem 1 and Problem 3. When it comes to Problem 1, the go-to efficient solution is the Forward Algorithm. This method avoids the exponential complexity of brute-force approaches by iteratively computing the probability of being in each state at every time step, conditioned on the observations up to that point, to arrive at the overall likelihood P(O|λ).

内容的提问来源于stack exchange，提问作者Anna