---
_id: '1833'
abstract:
- lang: eng
  text: '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:
- first_name: Anna
  full_name: Klimova, Anna
  id: 31934120-F248-11E8-B48F-1D18A9856A87
  last_name: Klimova
- first_name: Tamás
  full_name: Rudas, Tamás
  last_name: Rudas
citation:
  ama: Klimova A, Rudas T. On the closure of relational models. <i>Journal of Multivariate
    Analysis</i>. 2016;143:440-452. doi:<a href="https://doi.org/10.1016/j.jmva.2015.10.005">10.1016/j.jmva.2015.10.005</a>
  apa: Klimova, A., &#38; Rudas, T. (2016). On the closure of relational models. <i>Journal
    of Multivariate Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jmva.2015.10.005">https://doi.org/10.1016/j.jmva.2015.10.005</a>
  chicago: Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.”
    <i>Journal of Multivariate Analysis</i>. Elsevier, 2016. <a href="https://doi.org/10.1016/j.jmva.2015.10.005">https://doi.org/10.1016/j.jmva.2015.10.005</a>.
  ieee: A. Klimova and T. Rudas, “On the closure of relational models,” <i>Journal
    of Multivariate Analysis</i>, vol. 143. Elsevier, pp. 440–452, 2016.
  ista: Klimova A, Rudas T. 2016. On the closure of relational models. Journal of
    Multivariate Analysis. 143, 440–452.
  mla: Klimova, Anna, and Tamás Rudas. “On the Closure of Relational Models.” <i>Journal
    of Multivariate Analysis</i>, vol. 143, Elsevier, 2016, pp. 440–52, doi:<a href="https://doi.org/10.1016/j.jmva.2015.10.005">10.1016/j.jmva.2015.10.005</a>.
  short: A. Klimova, T. Rudas, Journal of Multivariate Analysis 143 (2016) 440–452.
date_created: 2018-12-11T11:54:15Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T06:53:30Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.jmva.2015.10.005
intvolume: '       143'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1501.00600
month: '01'
oa: 1
oa_version: Preprint
page: 440 - 452
publication: Journal of Multivariate Analysis
publication_status: published
publisher: Elsevier
publist_id: '5270'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the closure of relational models
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 143
year: '2016'
...
---
_id: '2008'
abstract:
- lang: eng
  text: 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.
acknowledgement: Part of the material presented here was contained in the PhD thesis
  of the first author to which the second author and Thomas Richardson were advisers.
  The authors wish to thank him for several comments and suggestions. We also thank
  the reviewers and the Associate Editor for helpful comments. The proof of Proposition 1
  uses the idea of Olga Klimova, to whom the authors are also indebted. The second
  author was supported in part by Grant K-106154 from the Hungarian National Scientific
  Research Fund (OTKA).
author:
- first_name: Anna
  full_name: Klimova, Anna
  id: 31934120-F248-11E8-B48F-1D18A9856A87
  last_name: Klimova
- first_name: Tamás
  full_name: Rudas, Tamás
  last_name: Rudas
citation:
  ama: Klimova A, Rudas T. Iterative scaling in curved exponential families. <i>Scandinavian
    Journal of Statistics</i>. 2015;42(3):832-847. doi:<a href="https://doi.org/10.1111/sjos.12139">10.1111/sjos.12139</a>
  apa: Klimova, A., &#38; Rudas, T. (2015). Iterative scaling in curved exponential
    families. <i>Scandinavian Journal of Statistics</i>. Wiley. <a href="https://doi.org/10.1111/sjos.12139">https://doi.org/10.1111/sjos.12139</a>
  chicago: Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential
    Families.” <i>Scandinavian Journal of Statistics</i>. Wiley, 2015. <a href="https://doi.org/10.1111/sjos.12139">https://doi.org/10.1111/sjos.12139</a>.
  ieee: A. Klimova and T. Rudas, “Iterative scaling in curved exponential families,”
    <i>Scandinavian Journal of Statistics</i>, vol. 42, no. 3. Wiley, pp. 832–847,
    2015.
  ista: Klimova A, Rudas T. 2015. Iterative scaling in curved exponential families.
    Scandinavian Journal of Statistics. 42(3), 832–847.
  mla: Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential Families.”
    <i>Scandinavian Journal of Statistics</i>, vol. 42, no. 3, Wiley, 2015, pp. 832–47,
    doi:<a href="https://doi.org/10.1111/sjos.12139">10.1111/sjos.12139</a>.
  short: A. Klimova, T. Rudas, Scandinavian Journal of Statistics 42 (2015) 832–847.
date_created: 2018-12-11T11:55:11Z
date_published: 2015-09-01T00:00:00Z
date_updated: 2021-01-12T06:54:41Z
day: '01'
department:
- _id: CaUh
doi: 10.1111/sjos.12139
intvolume: '        42'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1307.3282
month: '09'
oa: 1
oa_version: Preprint
page: 832 - 847
publication: Scandinavian Journal of Statistics
publication_status: published
publisher: Wiley
publist_id: '5068'
quality_controlled: '1'
scopus_import: 1
status: public
title: Iterative scaling in curved exponential families
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2015'
...
---
_id: '2014'
abstract:
- lang: eng
  text: 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:
- first_name: Anna
  full_name: Klimova, Anna
  id: 31934120-F248-11E8-B48F-1D18A9856A87
  last_name: Klimova
- first_name: Caroline
  full_name: Uhler, Caroline
  id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
  last_name: Uhler
  orcid: 0000-0002-7008-0216
- first_name: Tamás
  full_name: Rudas, Tamás
  last_name: Rudas
citation:
  ama: Klimova A, Uhler C, Rudas T. Faithfulness and learning hypergraphs from discrete
    distributions. <i>Computational Statistics &#38; Data Analysis</i>. 2015;87(7):57-72.
    doi:<a href="https://doi.org/10.1016/j.csda.2015.01.017">10.1016/j.csda.2015.01.017</a>
  apa: Klimova, A., Uhler, C., &#38; Rudas, T. (2015). Faithfulness and learning hypergraphs
    from discrete distributions. <i>Computational Statistics &#38; Data Analysis</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.csda.2015.01.017">https://doi.org/10.1016/j.csda.2015.01.017</a>
  chicago: Klimova, Anna, Caroline Uhler, and Tamás Rudas. “Faithfulness and Learning
    Hypergraphs from Discrete Distributions.” <i>Computational Statistics &#38; Data
    Analysis</i>. Elsevier, 2015. <a href="https://doi.org/10.1016/j.csda.2015.01.017">https://doi.org/10.1016/j.csda.2015.01.017</a>.
  ieee: A. Klimova, C. Uhler, and T. Rudas, “Faithfulness and learning hypergraphs
    from discrete distributions,” <i>Computational Statistics &#38; Data Analysis</i>,
    vol. 87, no. 7. Elsevier, pp. 57–72, 2015.
  ista: Klimova A, Uhler C, Rudas T. 2015. Faithfulness and learning hypergraphs from
    discrete distributions. Computational Statistics &#38; Data Analysis. 87(7), 57–72.
  mla: Klimova, Anna, et al. “Faithfulness and Learning Hypergraphs from Discrete
    Distributions.” <i>Computational Statistics &#38; Data Analysis</i>, vol. 87,
    no. 7, Elsevier, 2015, pp. 57–72, doi:<a href="https://doi.org/10.1016/j.csda.2015.01.017">10.1016/j.csda.2015.01.017</a>.
  short: A. Klimova, C. Uhler, T. Rudas, Computational Statistics &#38; Data Analysis
    87 (2015) 57–72.
date_created: 2018-12-11T11:55:13Z
date_published: 2015-07-01T00:00:00Z
date_updated: 2021-01-12T06:54:43Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.csda.2015.01.017
intvolume: '        87'
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1404.6617
month: '07'
oa: 1
oa_version: Preprint
page: 57 - 72
publication: Computational Statistics & Data Analysis
publication_status: published
publisher: Elsevier
publist_id: '5062'
quality_controlled: '1'
scopus_import: 1
status: public
title: Faithfulness and learning hypergraphs from discrete distributions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 87
year: '2015'
...
---
_id: '2007'
abstract:
- lang: eng
  text: Maximum likelihood estimation under relational models, with or without the
    overall effect. For more information see the reference manual
article_processing_charge: No
author:
- first_name: Anna
  full_name: Klimova, Anna
  id: 31934120-F248-11E8-B48F-1D18A9856A87
  last_name: Klimova
- first_name: Tamás
  full_name: Rudas, Tamás
  last_name: Rudas
citation:
  ama: 'Klimova A, Rudas T. gIPFrm: Generalized iterative proportional fitting for
    relational models. 2014.'
  apa: 'Klimova, A., &#38; Rudas, T. (2014). gIPFrm: Generalized iterative proportional
    fitting for relational models. The Comprehensive R Archive Network.'
  chicago: 'Klimova, Anna, and Tamás Rudas. “GIPFrm: Generalized Iterative Proportional
    Fitting for Relational Models.” The Comprehensive R Archive Network, 2014.'
  ieee: 'A. Klimova and T. Rudas, “gIPFrm: Generalized iterative proportional fitting
    for relational models.” The Comprehensive R Archive Network, 2014.'
  ista: 'Klimova A, Rudas T. 2014. gIPFrm: Generalized iterative proportional fitting
    for relational models, The Comprehensive R Archive Network.'
  mla: 'Klimova, Anna, and Tamás Rudas. <i>GIPFrm: Generalized Iterative Proportional
    Fitting for Relational Models</i>. The Comprehensive R Archive Network, 2014.'
  short: A. Klimova, T. Rudas, (2014).
date_created: 2018-12-11T11:55:10Z
date_published: 2014-03-20T00:00:00Z
date_updated: 2022-08-26T08:12:12Z
day: '20'
department:
- _id: CaUh
main_file_link:
- open_access: '1'
  url: 'https://CRAN.R-project.org/package=gIPFrm '
month: '03'
oa: 1
oa_version: Published Version
publisher: The Comprehensive R Archive Network
publist_id: '5069'
status: public
title: 'gIPFrm: Generalized iterative proportional fitting for relational models'
type: research_data_reference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2014'
...