@article{1833,
  abstract     = {Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in the table, and not necessarily containing the overall effect, that is, a common parameter in every cell. Similarly to log-linear models, relational models can be extended to non-negative distributions, but the extension requires more complex methods. An extended relational model is defined as an algebraic variety, and it turns out to be the closure of the original model with respect to the Bregman divergence. In the extended relational model, the MLE of the cell parameters always exists and is unique, but some of its properties may be different from those of the MLE under log-linear models. The MLE can be computed using a generalized iterative scaling procedure based on Bregman projections. },
  author       = {Klimova, Anna and Rudas, Tamás},
  journal      = {Journal of Multivariate Analysis},
  pages        = {440 -- 452},
  publisher    = {Elsevier},
  title        = {{On the closure of relational models}},
  doi          = {10.1016/j.jmva.2015.10.005},
  volume       = {143},
  year         = {2016},
}

@article{2008,
  abstract     = {The paper describes a generalized iterative proportional fitting procedure that can be used for maximum likelihood estimation in a special class of the general log-linear model. The models in this class, called relational, apply to multivariate discrete sample spaces that do not necessarily have a Cartesian product structure and may not contain an overall effect. When applied to the cell probabilities, the models without the overall effect are curved exponential families and the values of the sufficient statistics are reproduced by the MLE only up to a constant of proportionality. The paper shows that Iterative Proportional Fitting, Generalized Iterative Scaling, and Improved Iterative Scaling fail to work for such models. The algorithm proposed here is based on iterated Bregman projections. As a by-product, estimates of the multiplicative parameters are also obtained. An implementation of the algorithm is available as an R-package.},
  author       = {Klimova, Anna and Rudas, Tamás},
  journal      = {Scandinavian Journal of Statistics},
  number       = {3},
  pages        = {832 -- 847},
  publisher    = {Wiley},
  title        = {{Iterative scaling in curved exponential families}},
  doi          = {10.1111/sjos.12139},
  volume       = {42},
  year         = {2015},
}

@article{2014,
  abstract     = {The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-) faithfulness with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association.},
  author       = {Klimova, Anna and Uhler, Caroline and Rudas, Tamás},
  journal      = {Computational Statistics & Data Analysis},
  number       = {7},
  pages        = {57 -- 72},
  publisher    = {Elsevier},
  title        = {{Faithfulness and learning hypergraphs from discrete distributions}},
  doi          = {10.1016/j.csda.2015.01.017},
  volume       = {87},
  year         = {2015},
}

@misc{2007,
  abstract     = {Maximum likelihood estimation under relational models, with or without the overall effect. For more information see the reference manual},
  author       = {Klimova, Anna and Rudas, Tamás},
  publisher    = {The Comprehensive R Archive Network},
  title        = {{gIPFrm: Generalized iterative proportional fitting for relational models}},
  year         = {2014},
}