I am using a Hidden Markov Model to classify market regimes. For example, I train it on some asset returns and I get bullish and bearish regimes (2 hidden states). Visually inspecting the results tells me what hidden state corresponds to which market environment. However, the classification is unstable in the sense that each retraining of the Hidden Markov Model can result in hidden state 1 either meaning bullish or bearish. Without visual inspection you can never be sure.
The way I see HMM in this context is that they are an unsupervised learning / clustering technique especially suited for time series problems.
My question is if there are good ways to automatically interpret hidden states. I could of course look at the statistics of the classified samples and infer from that whether a state is bullish or bearish but I don't like that approach too much. Also, if there are more hidden states, e.g. corresponding to mean-reverting, trending, etc. environments, there should be a way to figure out what these hidden states mean or describe.
The only way I see at the moment is summarizing the statistics of each "cluster" and using these statistics (e.g. low standard deviation, positive returns) to label this state.