---
_id: '1089'
abstract:
- lang: eng
text: We discuss properties of distributions that are multivariate totally positive
of order two (MTP2) related to conditional independence. In particular, we show
that any independence model generated by an MTP2 distribution is a compositional
semigraphoid which is upward-stable and singleton-transitive. In addition, we
prove that any MTP2 distribution satisfying an appropriate support condition is
faithful to its concentration graph. Finally, we analyze factorization properties
of MTP2 distributions and discuss ways of constructing MTP2 distributions; in
particular we give conditions on the log-linear parameters of a discrete distribution
which ensure MTP2 and characterize conditional Gaussian distributions which satisfy
MTP2.
article_processing_charge: No
author:
- first_name: Shaun
full_name: Fallat, Shaun
last_name: Fallat
- first_name: Steffen
full_name: Lauritzen, Steffen
last_name: Lauritzen
- first_name: Kayvan
full_name: Sadeghi, Kayvan
last_name: Sadeghi
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Nanny
full_name: Wermuth, Nanny
last_name: Wermuth
- first_name: Piotr
full_name: Zwiernik, Piotr
last_name: Zwiernik
citation:
ama: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. Total positivity
in Markov structures. Annals of Statistics. 2017;45(3):1152-1184. doi:10.1214/16-AOS1478
apa: Fallat, S., Lauritzen, S., Sadeghi, K., Uhler, C., Wermuth, N., & Zwiernik,
P. (2017). Total positivity in Markov structures. Annals of Statistics.
Institute of Mathematical Statistics. https://doi.org/10.1214/16-AOS1478
chicago: Fallat, Shaun, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny
Wermuth, and Piotr Zwiernik. “Total Positivity in Markov Structures.” Annals
of Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AOS1478.
ieee: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, and P. Zwiernik,
“Total positivity in Markov structures,” Annals of Statistics, vol. 45,
no. 3. Institute of Mathematical Statistics, pp. 1152–1184, 2017.
ista: Fallat S, Lauritzen S, Sadeghi K, Uhler C, Wermuth N, Zwiernik P. 2017. Total
positivity in Markov structures. Annals of Statistics. 45(3), 1152–1184.
mla: Fallat, Shaun, et al. “Total Positivity in Markov Structures.” Annals of
Statistics, vol. 45, no. 3, Institute of Mathematical Statistics, 2017, pp.
1152–84, doi:10.1214/16-AOS1478.
short: S. Fallat, S. Lauritzen, K. Sadeghi, C. Uhler, N. Wermuth, P. Zwiernik, Annals
of Statistics 45 (2017) 1152–1184.
date_created: 2018-12-11T11:50:05Z
date_published: 2017-06-01T00:00:00Z
date_updated: 2023-09-20T11:46:53Z
day: '01'
department:
- _id: CaUh
doi: 10.1214/16-AOS1478
external_id:
isi:
- '000404395900008'
intvolume: ' 45'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1510.01290
month: '06'
oa: 1
oa_version: Submitted Version
page: 1152 - 1184
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: Annals of Statistics
publication_identifier:
issn:
- '00905364'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '6288'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Total positivity in Markov structures
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 45
year: '2017'
...
---
_id: '698'
abstract:
- lang: eng
text: 'Extracellular matrix signals from the microenvironment regulate gene expression
patterns and cell behavior. Using a combination of experiments and geometric models,
we demonstrate correlations between cell geometry, three-dimensional (3D) organization
of chromosome territories, and gene expression. Fluorescence in situ hybridization
experiments showed that micropatterned fibroblasts cultured on anisotropic versus
isotropic substrates resulted in repositioning of specific chromosomes, which
contained genes that were differentially regulated by cell geometries. Experiments
combined with ellipsoid packing models revealed that the mechanosensitivity of
chromosomes was correlated with their orientation in the nucleus. Transcription
inhibition experiments suggested that the intermingling degree was more sensitive
to global changes in transcription than to chromosome radial positioning and its
orientations. These results suggested that cell geometry modulated 3D chromosome
arrangement, and their neighborhoods correlated with gene expression patterns
in a predictable manner. This is central to understanding geometric control of
genetic programs involved in cellular homeostasis and the associated diseases. '
author:
- first_name: Yejun
full_name: Wang, Yejun
last_name: Wang
- first_name: Mallika
full_name: Nagarajan, Mallika
last_name: Nagarajan
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Gv
full_name: Shivashankar, Gv
last_name: Shivashankar
citation:
ama: Wang Y, Nagarajan M, Uhler C, Shivashankar G. Orientation and repositioning
of chromosomes correlate with cell geometry dependent gene expression. Molecular
Biology of the Cell. 2017;28(14):1997-2009. doi:10.1091/mbc.E16-12-0825
apa: Wang, Y., Nagarajan, M., Uhler, C., & Shivashankar, G. (2017). Orientation
and repositioning of chromosomes correlate with cell geometry dependent gene expression.
Molecular Biology of the Cell. American Society for Cell Biology. https://doi.org/10.1091/mbc.E16-12-0825
chicago: Wang, Yejun, Mallika Nagarajan, Caroline Uhler, and Gv Shivashankar. “Orientation
and Repositioning of Chromosomes Correlate with Cell Geometry Dependent Gene Expression.”
Molecular Biology of the Cell. American Society for Cell Biology, 2017.
https://doi.org/10.1091/mbc.E16-12-0825.
ieee: Y. Wang, M. Nagarajan, C. Uhler, and G. Shivashankar, “Orientation and repositioning
of chromosomes correlate with cell geometry dependent gene expression,” Molecular
Biology of the Cell, vol. 28, no. 14. American Society for Cell Biology, pp.
1997–2009, 2017.
ista: Wang Y, Nagarajan M, Uhler C, Shivashankar G. 2017. Orientation and repositioning
of chromosomes correlate with cell geometry dependent gene expression. Molecular
Biology of the Cell. 28(14), 1997–2009.
mla: Wang, Yejun, et al. “Orientation and Repositioning of Chromosomes Correlate
with Cell Geometry Dependent Gene Expression.” Molecular Biology of the Cell,
vol. 28, no. 14, American Society for Cell Biology, 2017, pp. 1997–2009, doi:10.1091/mbc.E16-12-0825.
short: Y. Wang, M. Nagarajan, C. Uhler, G. Shivashankar, Molecular Biology of the
Cell 28 (2017) 1997–2009.
date_created: 2018-12-11T11:47:59Z
date_published: 2017-07-07T00:00:00Z
date_updated: 2021-01-12T08:11:17Z
day: '07'
ddc:
- '519'
department:
- _id: CaUh
doi: 10.1091/mbc.E16-12-0825
file:
- access_level: open_access
checksum: de01dac9e30970cfa6ae902480a4e04d
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:10:53Z
date_updated: 2020-07-14T12:47:46Z
file_id: '4844'
file_name: IST-2017-892-v1+1_Mol._Biol._Cell-2017-Wang-1997-2009.pdf
file_size: 1086097
relation: main_file
file_date_updated: 2020-07-14T12:47:46Z
has_accepted_license: '1'
intvolume: ' 28'
issue: '14'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: 1997 - 2009
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: Molecular Biology of the Cell
publication_identifier:
issn:
- '10591524'
publication_status: published
publisher: American Society for Cell Biology
publist_id: '7001'
pubrep_id: '892'
quality_controlled: '1'
scopus_import: 1
status: public
title: Orientation and repositioning of chromosomes correlate with cell geometry dependent
gene expression
tmp:
image: /images/cc_by_nc_sa.png
legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC
BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2017'
...
---
_id: '1208'
abstract:
- lang: eng
text: We study parameter estimation in linear Gaussian covariance models, which
are p-dimensional Gaussian models with linear constraints on the covariance matrix.
Maximum likelihood estimation for this class of models leads to a non-convex optimization
problem which typically has many local maxima. Using recent results on the asymptotic
distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient
conditions for any hill climbing method to converge to the global maximum. Although
we are primarily interested in the case in which n≫p, the proofs of our results
utilize large sample asymptotic theory under the scheme n/p→γ>1. Remarkably,
our numerical simulations indicate that our results remain valid for p as small
as 2. An important consequence of this analysis is that, for sample sizes n≃14p,
maximum likelihood estimation for linear Gaussian covariance models behaves as
if it were a convex optimization problem. © 2016 The Royal Statistical Society
and Blackwell Publishing Ltd.
article_processing_charge: No
author:
- first_name: Piotr
full_name: Zwiernik, Piotr
last_name: Zwiernik
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Donald
full_name: Richards, Donald
last_name: Richards
citation:
ama: 'Zwiernik P, Uhler C, Richards D. Maximum likelihood estimation for linear
Gaussian covariance models. Journal of the Royal Statistical Society Series
B: Statistical Methodology. 2017;79(4):1269-1292. doi:10.1111/rssb.12217'
apa: 'Zwiernik, P., Uhler, C., & Richards, D. (2017). Maximum likelihood estimation
for linear Gaussian covariance models. Journal of the Royal Statistical Society.
Series B: Statistical Methodology. Wiley-Blackwell. https://doi.org/10.1111/rssb.12217'
chicago: 'Zwiernik, Piotr, Caroline Uhler, and Donald Richards. “Maximum Likelihood
Estimation for Linear Gaussian Covariance Models.” Journal of the Royal Statistical
Society. Series B: Statistical Methodology. Wiley-Blackwell, 2017. https://doi.org/10.1111/rssb.12217.'
ieee: 'P. Zwiernik, C. Uhler, and D. Richards, “Maximum likelihood estimation for
linear Gaussian covariance models,” Journal of the Royal Statistical Society.
Series B: Statistical Methodology, vol. 79, no. 4. Wiley-Blackwell, pp. 1269–1292,
2017.'
ista: 'Zwiernik P, Uhler C, Richards D. 2017. Maximum likelihood estimation for
linear Gaussian covariance models. Journal of the Royal Statistical Society. Series
B: Statistical Methodology. 79(4), 1269–1292.'
mla: 'Zwiernik, Piotr, et al. “Maximum Likelihood Estimation for Linear Gaussian
Covariance Models.” Journal of the Royal Statistical Society. Series B: Statistical
Methodology, vol. 79, no. 4, Wiley-Blackwell, 2017, pp. 1269–92, doi:10.1111/rssb.12217.'
short: 'P. Zwiernik, C. Uhler, D. Richards, Journal of the Royal Statistical Society.
Series B: Statistical Methodology 79 (2017) 1269–1292.'
date_created: 2018-12-11T11:50:43Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2023-09-20T11:17:21Z
day: '01'
department:
- _id: CaUh
doi: 10.1111/rssb.12217
external_id:
isi:
- '000411712300012'
intvolume: ' 79'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1408.5604
month: '09'
oa: 1
oa_version: Submitted Version
page: 1269 - 1292
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: 'Journal of the Royal Statistical Society. Series B: Statistical Methodology'
publication_identifier:
issn:
- '13697412'
publication_status: published
publisher: Wiley-Blackwell
publist_id: '6142'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximum likelihood estimation for linear Gaussian covariance models
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 79
year: '2017'
...
---
_id: '1293'
abstract:
- lang: eng
text: For a graph G with p vertices the closed convex cone S⪰0(G) consists of all
real positive semidefinite p×p matrices whose sparsity pattern is given by G,
that is, those matrices with zeros in the off-diagonal entries corresponding to
nonedges of G. The extremal rays of this cone and their associated ranks have
applications to matrix completion problems, maximum likelihood estimation in Gaussian
graphical models in statistics, and Gauss elimination for sparse matrices. While
the maximum rank of an extremal ray in S⪰0(G), known as the sparsity order of
G, has been characterized for different classes of graphs, we here study all possible
extremal ranks of S⪰0(G). We investigate when the geometry of the (±1)-cut polytope
of G yields a polyhedral characterization of the set of extremal ranks of S⪰0(G).
For a graph G without K5 minors, we show that appropriately chosen normal vectors
to the facets of the (±1)-cut polytope of G specify the off-diagonal entries of
extremal matrices in S⪰0(G). We also prove that for appropriately chosen scalars
the constant term of the linear equation of each facet-supporting hyperplane is
the rank of its corresponding extremal matrix in S⪰0(G). Furthermore, we show
that if G is series-parallel then this gives a complete characterization of all
possible extremal ranks of S⪰0(G). Consequently, the sparsity order problem for
series-parallel graphs can be solved in terms of polyhedral geometry.
acknowledgement: We wish to thank Alexander Engström and Bernd Sturmfels for various
valuable discussions and insights. We also thank the two anonymous referees for
their thoughtful feedback on the paper. CU was partially supported by the Austrian
Science Fund (FWF) Y 903-N35.
author:
- first_name: Liam T
full_name: Solus, Liam T
id: 2AADA620-F248-11E8-B48F-1D18A9856A87
last_name: Solus
- first_name: Caroline
full_name: Uhler, Caroline
id: 49ADD78E-F248-11E8-B48F-1D18A9856A87
last_name: Uhler
orcid: 0000-0002-7008-0216
- first_name: Ruriko
full_name: Yoshida, Ruriko
last_name: Yoshida
citation:
ama: Solus LT, Uhler C, Yoshida R. Extremal positive semidefinite matrices whose
sparsity pattern is given by graphs without K5 minors. Linear Algebra and Its
Applications. 2016;509:247-275. doi:10.1016/j.laa.2016.07.026
apa: Solus, L. T., Uhler, C., & Yoshida, R. (2016). Extremal positive semidefinite
matrices whose sparsity pattern is given by graphs without K5 minors. Linear
Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2016.07.026
chicago: Solus, Liam T, Caroline Uhler, and Ruriko Yoshida. “Extremal Positive Semidefinite
Matrices Whose Sparsity Pattern Is given by Graphs without K5 Minors.” Linear
Algebra and Its Applications. Elsevier, 2016. https://doi.org/10.1016/j.laa.2016.07.026.
ieee: L. T. Solus, C. Uhler, and R. Yoshida, “Extremal positive semidefinite matrices
whose sparsity pattern is given by graphs without K5 minors,” Linear Algebra
and Its Applications, vol. 509. Elsevier, pp. 247–275, 2016.
ista: Solus LT, Uhler C, Yoshida R. 2016. Extremal positive semidefinite matrices
whose sparsity pattern is given by graphs without K5 minors. Linear Algebra and
Its Applications. 509, 247–275.
mla: Solus, Liam T., et al. “Extremal Positive Semidefinite Matrices Whose Sparsity
Pattern Is given by Graphs without K5 Minors.” Linear Algebra and Its Applications,
vol. 509, Elsevier, 2016, pp. 247–75, doi:10.1016/j.laa.2016.07.026.
short: L.T. Solus, C. Uhler, R. Yoshida, Linear Algebra and Its Applications 509
(2016) 247–275.
date_created: 2018-12-11T11:51:11Z
date_published: 2016-11-15T00:00:00Z
date_updated: 2021-01-12T06:49:40Z
day: '15'
department:
- _id: CaUh
doi: 10.1016/j.laa.2016.07.026
intvolume: ' 509'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1506.06702.pdf
month: '11'
oa: 1
oa_version: Preprint
page: 247 - 275
project:
- _id: 2530CA10-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Y 903-N35
name: 'Gaussian Graphical Models: Theory and Applications'
publication: Linear Algebra and Its Applications
publication_status: published
publisher: Elsevier
publist_id: '6024'
quality_controlled: '1'
scopus_import: 1
status: public
title: Extremal positive semidefinite matrices whose sparsity pattern is given by
graphs without K5 minors
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 509
year: '2016'
...