---
_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. Scandinavian
Journal of Statistics. 2015;42(3):832-847. doi:10.1111/sjos.12139
apa: Klimova, A., & Rudas, T. (2015). Iterative scaling in curved exponential
families. Scandinavian Journal of Statistics. Wiley. https://doi.org/10.1111/sjos.12139
chicago: Klimova, Anna, and Tamás Rudas. “Iterative Scaling in Curved Exponential
Families.” Scandinavian Journal of Statistics. Wiley, 2015. https://doi.org/10.1111/sjos.12139.
ieee: A. Klimova and T. Rudas, “Iterative scaling in curved exponential families,”
Scandinavian Journal of Statistics, 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.”
Scandinavian Journal of Statistics, vol. 42, no. 3, Wiley, 2015, pp. 832–47,
doi:10.1111/sjos.12139.
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: '2006'
abstract:
- lang: eng
text: 'The monotone secant conjecture posits a rich class of polynomial systems,
all of whose solutions are real. These systems come from the Schubert calculus
on flag manifolds, and the monotone secant conjecture is a compelling generalization
of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko).
We present some theoretical evidence for this conjecture, as well as computational
evidence obtained by 1.9 teraHertz-years of computing, and we discuss some of
the phenomena we observed in our data. '
article_processing_charge: No
author:
- first_name: Nicolas
full_name: Hein, Nicolas
last_name: Hein
- first_name: Christopher
full_name: Hillar, Christopher
last_name: Hillar
- first_name: Abraham
full_name: Martin Del Campo Sanchez, Abraham
id: 4CF47F6A-F248-11E8-B48F-1D18A9856A87
last_name: Martin Del Campo Sanchez
- first_name: Frank
full_name: Sottile, Frank
last_name: Sottile
- first_name: Zach
full_name: Teitler, Zach
last_name: Teitler
citation:
ama: Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. The monotone
secant conjecture in the real Schubert calculus. Experimental Mathematics.
2015;24(3):261-269. doi:10.1080/10586458.2014.980044
apa: Hein, N., Hillar, C., Martin del Campo Sanchez, A., Sottile, F., & Teitler,
Z. (2015). The monotone secant conjecture in the real Schubert calculus. Experimental
Mathematics. Taylor & Francis. https://doi.org/10.1080/10586458.2014.980044
chicago: Hein, Nicolas, Christopher Hillar, Abraham Martin del Campo Sanchez, Frank
Sottile, and Zach Teitler. “The Monotone Secant Conjecture in the Real Schubert
Calculus.” Experimental Mathematics. Taylor & Francis, 2015. https://doi.org/10.1080/10586458.2014.980044.
ieee: N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, and Z. Teitler,
“The monotone secant conjecture in the real Schubert calculus,” Experimental
Mathematics, vol. 24, no. 3. Taylor & Francis, pp. 261–269, 2015.
ista: Hein N, Hillar C, Martin del Campo Sanchez A, Sottile F, Teitler Z. 2015.
The monotone secant conjecture in the real Schubert calculus. Experimental Mathematics.
24(3), 261–269.
mla: Hein, Nicolas, et al. “The Monotone Secant Conjecture in the Real Schubert
Calculus.” Experimental Mathematics, vol. 24, no. 3, Taylor & Francis,
2015, pp. 261–69, doi:10.1080/10586458.2014.980044.
short: N. Hein, C. Hillar, A. Martin del Campo Sanchez, F. Sottile, Z. Teitler,
Experimental Mathematics 24 (2015) 261–269.
date_created: 2018-12-11T11:55:10Z
date_published: 2015-06-23T00:00:00Z
date_updated: 2021-01-12T06:54:40Z
day: '23'
department:
- _id: CaUh
doi: 10.1080/10586458.2014.980044
intvolume: ' 24'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1109.3436
month: '06'
oa: 1
oa_version: Preprint
page: 261 - 269
publication: Experimental Mathematics
publication_status: published
publisher: Taylor & Francis
publist_id: '5070'
quality_controlled: '1'
scopus_import: 1
status: public
title: The monotone secant conjecture in the real Schubert calculus
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
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. Computational Statistics & Data Analysis. 2015;87(7):57-72.
doi:10.1016/j.csda.2015.01.017
apa: Klimova, A., Uhler, C., & Rudas, T. (2015). Faithfulness and learning hypergraphs
from discrete distributions. Computational Statistics & Data Analysis.
Elsevier. https://doi.org/10.1016/j.csda.2015.01.017
chicago: Klimova, Anna, Caroline Uhler, and Tamás Rudas. “Faithfulness and Learning
Hypergraphs from Discrete Distributions.” Computational Statistics & Data
Analysis. Elsevier, 2015. https://doi.org/10.1016/j.csda.2015.01.017.
ieee: A. Klimova, C. Uhler, and T. Rudas, “Faithfulness and learning hypergraphs
from discrete distributions,” Computational Statistics & Data Analysis,
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 & Data Analysis. 87(7), 57–72.
mla: Klimova, Anna, et al. “Faithfulness and Learning Hypergraphs from Discrete
Distributions.” Computational Statistics & Data Analysis, vol. 87,
no. 7, Elsevier, 2015, pp. 57–72, doi:10.1016/j.csda.2015.01.017.
short: A. Klimova, C. Uhler, T. Rudas, Computational Statistics & 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: '1911'
abstract:
- lang: eng
text: The topological Tverberg theorem has been generalized in several directions
by setting extra restrictions on the Tverberg partitions. Restricted Tverberg
partitions, defined by the idea that certain points cannot be in the same part,
are encoded with graphs. When two points are adjacent in the graph, they are not
in the same part. If the restrictions are too harsh, then the topological Tverberg
theorem fails. The colored Tverberg theorem corresponds to graphs constructed
as disjoint unions of small complete graphs. Hell studied the case of paths and
cycles. In graph theory these partitions are usually viewed as graph colorings.
As explored by Aharoni, Haxell, Meshulam and others there are fundamental connections
between several notions of graph colorings and topological combinatorics. For
ordinary graph colorings it is enough to require that the number of colors q satisfy
q>Δ, where Δ is the maximal degree of the graph. It was proven by the first
author using equivariant topology that if q>Δ 2 then the topological Tverberg
theorem still works. It is conjectured that q>KΔ is also enough for some constant
K, and in this paper we prove a fixed-parameter version of that conjecture. The
required topological connectivity results are proven with shellability, which
also strengthens some previous partial results where the topological connectivity
was proven with the nerve lemma.
acknowledgement: Patrik Norén gratefully acknowledges support from the Wallenberg
foundation
author:
- first_name: Alexander
full_name: Engström, Alexander
last_name: Engström
- first_name: Patrik
full_name: Noren, Patrik
id: 46870C74-F248-11E8-B48F-1D18A9856A87
last_name: Noren
citation:
ama: Engström A, Noren P. Tverberg’s Theorem and Graph Coloring. Discrete &
Computational Geometry. 2014;51(1):207-220. doi:10.1007/s00454-013-9556-3
apa: Engström, A., & Noren, P. (2014). Tverberg’s Theorem and Graph Coloring.
Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-013-9556-3
chicago: Engström, Alexander, and Patrik Noren. “Tverberg’s Theorem and Graph Coloring.”
Discrete & Computational Geometry. Springer, 2014. https://doi.org/10.1007/s00454-013-9556-3.
ieee: A. Engström and P. Noren, “Tverberg’s Theorem and Graph Coloring,” Discrete
& Computational Geometry, vol. 51, no. 1. Springer, pp. 207–220, 2014.
ista: Engström A, Noren P. 2014. Tverberg’s Theorem and Graph Coloring. Discrete
& Computational Geometry. 51(1), 207–220.
mla: Engström, Alexander, and Patrik Noren. “Tverberg’s Theorem and Graph Coloring.”
Discrete & Computational Geometry, vol. 51, no. 1, Springer, 2014,
pp. 207–20, doi:10.1007/s00454-013-9556-3.
short: A. Engström, P. Noren, Discrete & Computational Geometry 51 (2014) 207–220.
date_created: 2018-12-11T11:54:40Z
date_published: 2014-01-01T00:00:00Z
date_updated: 2021-01-12T06:54:01Z
day: '01'
department:
- _id: CaUh
doi: 10.1007/s00454-013-9556-3
intvolume: ' 51'
issue: '1'
language:
- iso: eng
month: '01'
oa_version: None
page: 207 - 220
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '5183'
scopus_import: 1
status: public
title: Tverberg's Theorem and Graph Coloring
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 51
year: '2014'
...
---
_id: '2011'
abstract:
- lang: eng
text: The protection of privacy of individual-level information in genome-wide association
study (GWAS) databases has been a major concern of researchers following the publication
of “an attack” on GWAS data by Homer et al. (2008). Traditional statistical methods
for confidentiality and privacy protection of statistical databases do not scale
well to deal with GWAS data, especially in terms of guarantees regarding protection
from linkage to external information. The more recent concept of differential
privacy, introduced by the cryptographic community, is an approach that provides
a rigorous definition of privacy with meaningful privacy guarantees in the presence
of arbitrary external information, although the guarantees may come at a serious
price in terms of data utility. Building on such notions, Uhler et al. (2013)
proposed new methods to release aggregate GWAS data without compromising an individual’s
privacy. We extend the methods developed in Uhler et al. (2013) for releasing
differentially-private χ2χ2-statistics by allowing for arbitrary number of cases
and controls, and for releasing differentially-private allelic test statistics.
We also provide a new interpretation by assuming the controls’ data are known,
which is a realistic assumption because some GWAS use publicly available data
as controls. We assess the performance of the proposed methods through a risk-utility
analysis on a real data set consisting of DNA samples collected by the Wellcome
Trust Case Control Consortium and compare the methods with the differentially-private
release mechanism proposed by Johnson and Shmatikov (2013).
acknowledgement: This research was partially supported by NSF Awards EMSW21-RTG and
BCS-0941518 to the Department of Statistics at Carnegie Mellon University, and by
NSF Grant BCS-0941553 to the Department of Statistics at Pennsylvania State University.
This work was also supported in part by the National Center for Research Resources,
Grant UL1 RR033184, and is now at the National Center for Advancing Translational
Sciences, Grant UL1 TR000127 to Pennsylvania State University. The content is solely
the responsibility of the authors and does not necessarily represent the official
views of the NSF and NIH.
author:
- first_name: Fei
full_name: Yu, Fei
last_name: Yu
- first_name: Stephen
full_name: Fienberg, Stephen
last_name: Fienberg
- first_name: Alexandra
full_name: Slaković, Alexandra
last_name: Slaković
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: Yu F, Fienberg S, Slaković A, Uhler C. Scalable privacy-preserving data sharing
methodology for genome-wide association studies. Journal of Biomedical Informatics.
2014;50:133-141. doi:10.1016/j.jbi.2014.01.008
apa: Yu, F., Fienberg, S., Slaković, A., & Uhler, C. (2014). Scalable privacy-preserving
data sharing methodology for genome-wide association studies. Journal of Biomedical
Informatics. Elsevier. https://doi.org/10.1016/j.jbi.2014.01.008
chicago: Yu, Fei, Stephen Fienberg, Alexandra Slaković, and Caroline Uhler. “Scalable
Privacy-Preserving Data Sharing Methodology for Genome-Wide Association Studies.”
Journal of Biomedical Informatics. Elsevier, 2014. https://doi.org/10.1016/j.jbi.2014.01.008.
ieee: F. Yu, S. Fienberg, A. Slaković, and C. Uhler, “Scalable privacy-preserving
data sharing methodology for genome-wide association studies,” Journal of Biomedical
Informatics, vol. 50. Elsevier, pp. 133–141, 2014.
ista: Yu F, Fienberg S, Slaković A, Uhler C. 2014. Scalable privacy-preserving data
sharing methodology for genome-wide association studies. Journal of Biomedical
Informatics. 50, 133–141.
mla: Yu, Fei, et al. “Scalable Privacy-Preserving Data Sharing Methodology for Genome-Wide
Association Studies.” Journal of Biomedical Informatics, vol. 50, Elsevier,
2014, pp. 133–41, doi:10.1016/j.jbi.2014.01.008.
short: F. Yu, S. Fienberg, A. Slaković, C. Uhler, Journal of Biomedical Informatics
50 (2014) 133–141.
date_created: 2018-12-11T11:55:12Z
date_published: 2014-08-01T00:00:00Z
date_updated: 2021-01-12T06:54:42Z
day: '01'
department:
- _id: CaUh
doi: 10.1016/j.jbi.2014.01.008
intvolume: ' 50'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1401.5193
month: '08'
oa: 1
oa_version: Submitted Version
page: 133 - 141
publication: Journal of Biomedical Informatics
publication_status: published
publisher: Elsevier
publist_id: '5065'
quality_controlled: '1'
scopus_import: 1
status: public
title: Scalable privacy-preserving data sharing methodology for genome-wide association
studies
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2014'
...