---
_id: '2010'
abstract:
- lang: eng
text: Many algorithms for inferring causality rely heavily on the faithfulness assumption.
The main justification for imposing this assumption is that the set of unfaithful
distributions has Lebesgue measure zero, since it can be seen as a collection
of hypersurfaces in a hypercube. However, due to sampling error the faithfulness
condition alone is not sufficient for statistical estimation, and strong-faithfulness
has been proposed and assumed to achieve uniform or high-dimensional consistency.
In contrast to the plain faithfulness assumption, the set of distributions that
is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly
large as we show in this paper. We study the strong-faithfulness condition from
a geometric and combinatorial point of view and give upper and lower bounds on
the Lebesgue measure of strong-faithful distributions for various classes of directed
acyclic graphs. Our results imply fundamental limitations for the PC-algorithm
and potentially also for other algorithms based on partial correlation testing
in the Gaussian case.
author:
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Garvesh
full_name: Raskutti, Garvesh
last_name: Raskutti
- first_name: Peter
full_name: Bühlmann, Peter
last_name: Bühlmann
- first_name: Bin
full_name: Yu, Bin
last_name: Yu
citation:
ama: Uhler C, Raskutti G, Bühlmann P, Yu B. Geometry of the faithfulness assumption
in causal inference. The Annals of Statistics. 2013;41(2):436-463. doi:10.1214/12-AOS1080
apa: Uhler, C., Raskutti, G., Bühlmann, P., & Yu, B. (2013). Geometry of the
faithfulness assumption in causal inference. The Annals of Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/12-AOS1080
chicago: Uhler, Caroline, Garvesh Raskutti, Peter Bühlmann, and Bin Yu. “Geometry
of the Faithfulness Assumption in Causal Inference.” The Annals of Statistics.
Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/12-AOS1080.
ieee: C. Uhler, G. Raskutti, P. Bühlmann, and B. Yu, “Geometry of the faithfulness
assumption in causal inference,” The Annals of Statistics, vol. 41, no.
2. Institute of Mathematical Statistics, pp. 436–463, 2013.
ista: Uhler C, Raskutti G, Bühlmann P, Yu B. 2013. Geometry of the faithfulness
assumption in causal inference. The Annals of Statistics. 41(2), 436–463.
mla: Uhler, Caroline, et al. “Geometry of the Faithfulness Assumption in Causal
Inference.” The Annals of Statistics, vol. 41, no. 2, Institute of Mathematical
Statistics, 2013, pp. 436–63, doi:10.1214/12-AOS1080.
short: C. Uhler, G. Raskutti, P. Bühlmann, B. Yu, The Annals of Statistics 41 (2013)
436–463.
date_created: 2018-12-11T11:55:11Z
date_published: 2013-04-01T00:00:00Z
date_updated: 2021-01-12T06:54:42Z
day: '01'
department:
- _id: CaUh
doi: 10.1214/12-AOS1080
external_id:
arxiv:
- '1207.0547'
intvolume: ' 41'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: www.doi.org/10.1214/12-AOS1080
month: '04'
oa: 1
oa_version: Published Version
page: 436 - 463
publication: The Annals of Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '5066'
quality_controlled: '1'
scopus_import: 1
status: public
title: Geometry of the faithfulness assumption in causal inference
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 41
year: '2013'
...
---
_id: '2009'
abstract:
- lang: eng
text: Traditional statistical methods for confidentiality protection of statistical
databases do not scale well to deal with GWAS databases 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 which 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, we propose new methods to release aggregate GWAS data without
compromising an individual’s privacy. We present methods for releasing differentially
private minor allele frequencies, chi-square statistics and p-values. We compare
these approaches on simulated data and on a GWAS study of canine hair length involving
685 dogs. We also propose a privacy-preserving method for finding genome-wide
associations based on a differentially-private approach to penalized logistic
regression.
article_processing_charge: No
author:
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Aleksandra
full_name: Slavkovic, Aleksandra
last_name: Slavkovic
- first_name: Stephen
full_name: Fienberg, Stephen
last_name: Fienberg
citation:
ama: Uhler C, Slavkovic A, Fienberg S. Privacy-preserving data sharing for genome-wide
association studies. Journal of Privacy and Confidentiality . 2013;5(1):137-166.
doi:10.29012/jpc.v5i1.629
apa: Uhler, C., Slavkovic, A., & Fienberg, S. (2013). Privacy-preserving data
sharing for genome-wide association studies. Journal of Privacy and Confidentiality
. Carnegie Mellon University. https://doi.org/10.29012/jpc.v5i1.629
chicago: Uhler, Caroline, Aleksandra Slavkovic, and Stephen Fienberg. “Privacy-Preserving
Data Sharing for Genome-Wide Association Studies.” Journal of Privacy and Confidentiality
. Carnegie Mellon University, 2013. https://doi.org/10.29012/jpc.v5i1.629.
ieee: C. Uhler, A. Slavkovic, and S. Fienberg, “Privacy-preserving data sharing
for genome-wide association studies,” Journal of Privacy and Confidentiality
, vol. 5, no. 1. Carnegie Mellon University, pp. 137–166, 2013.
ista: Uhler C, Slavkovic A, Fienberg S. 2013. Privacy-preserving data sharing for
genome-wide association studies. Journal of Privacy and Confidentiality . 5(1),
137–166.
mla: Uhler, Caroline, et al. “Privacy-Preserving Data Sharing for Genome-Wide Association
Studies.” Journal of Privacy and Confidentiality , vol. 5, no. 1, Carnegie
Mellon University, 2013, pp. 137–66, doi:10.29012/jpc.v5i1.629.
short: C. Uhler, A. Slavkovic, S. Fienberg, Journal of Privacy and Confidentiality 5
(2013) 137–166.
date_created: 2018-12-11T11:55:11Z
date_published: 2013-08-01T00:00:00Z
date_updated: 2021-01-12T06:54:41Z
day: '01'
department:
- _id: CaUh
doi: 10.29012/jpc.v5i1.629
intvolume: ' 5'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://repository.cmu.edu/jpc/vol5/iss1/6
month: '08'
oa: 1
oa_version: Published Version
page: 137 - 166
publication: 'Journal of Privacy and Confidentiality '
publication_status: published
publisher: Carnegie Mellon University
publist_id: '5067'
quality_controlled: '1'
status: public
title: Privacy-preserving data sharing for genome-wide association studies
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 5
year: '2013'
...
---
_id: '2280'
abstract:
- lang: eng
text: The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal
container so as to minimize a measure of overlap between ellipsoids is considered.
A bilevel optimization formulation is given, together with an algorithm for the
general case and a simpler algorithm for the special case in which all ellipsoids
are in fact spheres. Convergence results are proved and computational experience
is described and illustrated. The motivating application-chromosome organization
in the human cell nucleus-is discussed briefly, and some illustrative results
are presented.
author:
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Stephen
full_name: Wright, Stephen
last_name: Wright
citation:
ama: Uhler C, Wright S. Packing ellipsoids with overlap. SIAM Review. 2013;55(4):671-706.
doi:10.1137/120872309
apa: Uhler, C., & Wright, S. (2013). Packing ellipsoids with overlap. SIAM
Review. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/120872309
chicago: Uhler, Caroline, and Stephen Wright. “Packing Ellipsoids with Overlap.”
SIAM Review. Society for Industrial and Applied Mathematics , 2013. https://doi.org/10.1137/120872309.
ieee: C. Uhler and S. Wright, “Packing ellipsoids with overlap,” SIAM Review,
vol. 55, no. 4. Society for Industrial and Applied Mathematics , pp. 671–706,
2013.
ista: Uhler C, Wright S. 2013. Packing ellipsoids with overlap. SIAM Review. 55(4),
671–706.
mla: Uhler, Caroline, and Stephen Wright. “Packing Ellipsoids with Overlap.” SIAM
Review, vol. 55, no. 4, Society for Industrial and Applied Mathematics , 2013,
pp. 671–706, doi:10.1137/120872309.
short: C. Uhler, S. Wright, SIAM Review 55 (2013) 671–706.
date_created: 2018-12-11T11:56:44Z
date_published: 2013-11-07T00:00:00Z
date_updated: 2021-01-12T06:56:30Z
day: '07'
department:
- _id: CaUh
doi: 10.1137/120872309
external_id:
arxiv:
- '1204.0235'
intvolume: ' 55'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1204.0235
month: '11'
oa: 1
oa_version: Preprint
page: 671 - 706
publication: SIAM Review
publication_status: published
publisher: 'Society for Industrial and Applied Mathematics '
publist_id: '4655'
quality_controlled: '1'
scopus_import: 1
status: public
title: Packing ellipsoids with overlap
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 55
year: '2013'
...
---
_id: '2959'
abstract:
- lang: eng
text: We study maximum likelihood estimation in Gaussian graphical models from a
geometric point of view. An algebraic elimination criterion allows us to find
exact lower bounds on the number of observations needed to ensure that the maximum
likelihood estimator (MLE) exists with probability one. This is applied to bipartite
graphs, grids and colored graphs. We also study the ML degree, and we present
the first instance of a graph for which the MLE exists with probability one, even
when the number of observations equals the treewidth.
acknowledgement: "I wish to thank Bernd Sturmfels for many helpful discus- sions and
Steffen Lauritzen for introducing me to the problem of the existence of the MLE
in Gaussian graphical models. I would also like to thank two referees who provided
helpful comments on the original version of this paper.\r\n"
author:
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
citation:
ama: Uhler C. Geometry of maximum likelihood estimation in Gaussian graphical models.
Annals of Statistics. 2012;40(1):238-261. doi:10.1214/11-AOS957
apa: Uhler, C. (2012). Geometry of maximum likelihood estimation in Gaussian graphical
models. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/11-AOS957
chicago: Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian
Graphical Models.” Annals of Statistics. Institute of Mathematical Statistics,
2012. https://doi.org/10.1214/11-AOS957.
ieee: C. Uhler, “Geometry of maximum likelihood estimation in Gaussian graphical
models,” Annals of Statistics, vol. 40, no. 1. Institute of Mathematical
Statistics, pp. 238–261, 2012.
ista: Uhler C. 2012. Geometry of maximum likelihood estimation in Gaussian graphical
models. Annals of Statistics. 40(1), 238–261.
mla: Uhler, Caroline. “Geometry of Maximum Likelihood Estimation in Gaussian Graphical
Models.” Annals of Statistics, vol. 40, no. 1, Institute of Mathematical
Statistics, 2012, pp. 238–61, doi:10.1214/11-AOS957.
short: C. Uhler, Annals of Statistics 40 (2012) 238–261.
date_created: 2018-12-11T12:00:33Z
date_published: 2012-02-01T00:00:00Z
date_updated: 2021-01-12T07:40:04Z
day: '01'
department:
- _id: CaUh
doi: 10.1214/11-AOS957
intvolume: ' 40'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1012.2643
month: '02'
oa: 1
oa_version: Preprint
page: 238 - 261
publication: Annals of Statistics
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '3767'
quality_controlled: '1'
scopus_import: 1
status: public
title: Geometry of maximum likelihood estimation in Gaussian graphical models
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 40
year: '2012'
...