What are some applications of unsupervised HMMs? Supervised HMMs can be applied to many problems like POS tagging and OCR (optical character recognition).
I've learned that HMMs can be trained unsupervisedly using EM (Baum-Welch algorithm), what are some example applications of this unsupervised approach?
 A: Hidden Markov Models in general (both supervised and unsupervised) are heavily applied to model sequences of data. Baum-Welch algorithm which is a special case of EM algorithm is widely used in speech processing and bioinformatics. For instance, it is commonly used to predict the location of a gene in a particular chromosome, for speech recognition, structure analysis of videos and even in cryptanalysis, it is used to estimate the parameters of HMMs in deciphering noisy information or even ciphertexts.
In general, suppose you have a given set of observed sequences $\mathcal{O}= \{x_1, x_2,...x_n\}$ (could be speech recordings, sequences nucleotides, amino acids ... etc) and you are interested in analyzing the sequence based on your Hidden Markov Model. However, the solution to your analysis is meaningful only if the HMM can properly model the sequence of interest. Thus the important question is the reasonable choice for HMM parameters for the given sequence. This is where Baum-Welch algorithm is useful. Although there is no ideal way to estimate the parameters from a limited number of observed sequences, Baum-Welch algorithm lets you do it in a locally optimal way. The same can be accomplished using the segmental k-means algorithm (which is an extension of Viterbi algorithm) which differs from Baum-Welch algorithm in the optimization step.
For an interesting (unintuitive) case study, you can take a look at this paper [1] which compares the performance of supervised and unsupervised learning for modelling intentional process of humans. Their results demonstrate that supervised learning performs poorly because it introduces inherent human's biases, provides unreliable results in the absence of ground truth ...etc. On the other hand unsupervised learning performs better and requires lower human effort (for data labelling).
[1]: Ghazaleh Khodabandelou, Charlotte Hug, Rebecca Deneckere, Camille Salinesi. Supervised vs. Unsupervised
Learning for Intentional Process Model Discovery. Business Process Modeling, Development,
and Support (BPMDS), Jun 2014, Thessalonique, Greece. pp.1-15, 2014,
