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@ARTICLE{Perrakis:276090,
      author       = {Perrakis, Konstantinos and Lartigue, Thomas-Alan-Jean and
                      Dondelinger, Frank and Mukherjee, Sach},
      title        = {{R}egularized {J}oint {M}ixture {M}odels},
      journal      = {Journal of machine learning research},
      volume       = {24},
      number       = {19},
      issn         = {1532-4435},
      address      = {Brookline, MA},
      publisher    = {Microtome Publishing},
      reportid     = {DZNE-2025-00171},
      pages        = {1 - 47},
      year         = {2023},
      abstract     = {Regularized regression models are well studied and, under
                      appropriate conditions, offerfast and statistically
                      interpretable results. However, large data in many
                      applications areheterogeneous in the sense of harboring
                      distributional differences between latent groups.Then, the
                      assumption that the conditional distribution of response Y
                      given features X is thesame for all samples may not hold.
                      Furthermore, in scientific applications, the
                      covariancestructure of the features may contain important
                      signals and its learning is also affected bylatent group
                      structure. We propose a class of mixture models for paired
                      data pX, Y q thatcouples together the distribution of X
                      (using sparse graphical models) and the conditionalY | X
                      (using sparse regression models). The regression and
                      graphical models are specificto the latent groups and model
                      parameters are estimated jointly. This allows signals
                      ineither or both of the feature distribution and regression
                      model to inform learning of latentstructure and provides
                      automatic control of confounding by such structure.
                      Estimationis handled via an expectation-maximization
                      algorithm, whose convergence is establishedtheoretically. We
                      illustrate the key ideas via empirical examples. An R
                      package is availableat
                      https://github.com/k-perrakis/regjmix.},
      cin          = {AG Mukherjee},
      ddc          = {004},
      cid          = {I:(DE-2719)1013030},
      pnm          = {354 - Disease Prevention and Healthy Aging (POF4-354)},
      pid          = {G:(DE-HGF)POF4-354},
      typ          = {PUB:(DE-HGF)16},
      url          = {https://pub.dzne.de/record/276090},
}