In medical research, supervised heterogeneity analysis has important implications. Assume that there are two types of features. Using both types of features, our goal is to conduct the first supervised heterogeneity analysis that satisfies a hierarchical structure. That is, the first type of features defines a rough structure, and the second type defines a nested and more refined structure. A penalization approach is developed, which has been motivated by but differs significantly from penalized fusion and sparse group penalization. 
             Reference: 
             Ren, M., Zhang, Q., Zhang, S., Zhong, T., Huang, J. & Ma, S. (2022). "Hierarchical cancer heterogeneity analysis based on histopathological imaging features". Biometrics, <doi:10.1111/biom.13426>.

Develops algorithms for fitting, prediction, simulation 
  and initialization of the following models
  (1)- hidden hybrid Markov/semi-Markov model, 
  introduced by Guedon (2005) <doi:10.1016/j.csda.2004.05.033>, 
  (2)- nonparametric mixture of B-splines emissions (Langrock et al., 2015
  <doi:10.1111/biom.12282>), 
  (3)- regime switching regression model 
  (Kim et al., 2008 <doi:10.1016/j.jeconom.2007.10.002>) and auto-regressive 
  hidden hybrid Markov/semi-Markov model, 
  (4)- spline-based nonparametric 
  estimation of additive state-switching models  
  (Langrock et al., 2018 <doi:10.1111/stan.12133>)
  (5)- robust emission model proposed by 
  Qin et al, 2024 <doi:10.1007/s10479-024-05989-4>
  (6)- several emission distributions, including mixture of multivariate normal  
  (which can also handle missing data using EM algorithm) and multi-nomial emission 
  (for modeling polymer or DNA sequences)
  (7)- tools for prediction of future state sequence, computing the score of a new sequence,
  splitting the samples and sequences to train and test sets, computing the information measures of 
  the models, computing the residual useful lifetime (reliability) and many other useful tools ...
  (read for more description: Amini et al., 2022 <doi:10.1007/s00180-022-01248-x> and its 
  arxiv version: <doi:10.48550/arXiv.2109.12489>).