---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22228'
abstract:
- lang: eng
text: "In a mixed generalized linear model, the goal is to learn multiple signals
from unlabeled observations: each sample comes from exactly one signal, but it
is not known which one. We consider the prototypical problem of estimating two
statistically independent signals in a mixed generalized linear model with Gaussian
covariates. Spectral methods are a popular class of estimators which output the
top two eigenvectors of a suitable data-dependent matrix. However, despite the
wide applicability, their design is still obtained via heuristic considerations,
and the number of samples \U0001D45B needed to guarantee recovery is superlinear
in the signal dimension \U0001D451. In this paper, we develop exact asymptotics
on spectral methods in the challenging proportional regime in which \U0001D45B,\U0001D451
grow large and their ratio converges to a finite constant. This allows us optimize
the design of the spectral method, and combine it with a simple linear estimator,
to minimize the estimation error. Our characterization exploits a mix of tools
from random matrices, free probability, and the theory of approximate message
passing algorithms. Numerical simulations for mixed linear regression and phase
retrieval demonstrate the advantage enabled by our analysis over existing designs
of spectral methods."
acknowledgement: The first and second authors were partially supported by the 2019
Lopez-Loreta prize.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Yihan
full_name: Zhang, Yihan
last_name: Zhang
- first_name: Marco
full_name: Mondelli, Marco
id: 27EB676C-8706-11E9-9510-7717E6697425
last_name: Mondelli
orcid: 0000-0002-3242-7020
- first_name: Ramji
full_name: Venkataramanan, Ramji
last_name: Venkataramanan
citation:
ama: Zhang Y, Mondelli M, Venkataramanan R. Precise asymptotics for spectral methods
in mixed generalized linear models. SIAM Journal on Mathematics of Data Science.
2026;8(2):411-439. doi:10.1137/24m1702854
apa: Zhang, Y., Mondelli, M., & Venkataramanan, R. (2026). Precise asymptotics
for spectral methods in mixed generalized linear models. SIAM Journal on Mathematics
of Data Science. SIAM. https://doi.org/10.1137/24m1702854
chicago: Zhang, Yihan, Marco Mondelli, and Ramji Venkataramanan. “Precise Asymptotics
for Spectral Methods in Mixed Generalized Linear Models.” SIAM Journal on Mathematics
of Data Science. SIAM, 2026. https://doi.org/10.1137/24m1702854.
ieee: Y. Zhang, M. Mondelli, and R. Venkataramanan, “Precise asymptotics for spectral
methods in mixed generalized linear models,” SIAM Journal on Mathematics of
Data Science, vol. 8, no. 2. SIAM, pp. 411–439, 2026.
ista: Zhang Y, Mondelli M, Venkataramanan R. 2026. Precise asymptotics for spectral
methods in mixed generalized linear models. SIAM Journal on Mathematics of Data
Science. 8(2), 411–439.
mla: Zhang, Yihan, et al. “Precise Asymptotics for Spectral Methods in Mixed Generalized
Linear Models.” SIAM Journal on Mathematics of Data Science, vol. 8, no.
2, SIAM, 2026, pp. 411–39, doi:10.1137/24m1702854.
short: Y. Zhang, M. Mondelli, R. Venkataramanan, SIAM Journal on Mathematics of
Data Science 8 (2026) 411–439.
corr_author: '1'
das_tickbox: '0'
date_created: 2026-06-30T13:03:41Z
date_published: 2026-06-01T00:00:00Z
date_updated: 2026-08-12T06:23:07Z
day: '01'
ddc:
- '000'
department:
- _id: MaMo
doi: 10.1137/24m1702854
external_id:
arxiv:
- '2211.11368'
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fulldoi: https://doi.org/10.1137/24m1702854
has_accepted_license: '1'
intvolume: ' 8'
issue: '2'
keyword:
- spectral estimator
- generalized linear models
- mixed regression
- high-dimensional asymptotics
- random matrix theory
- approximate message passing (AMP)
language:
- iso: eng
mathsc:
- '62E20'
- 62J05
- 62J12
month: '06'
oa: 1
oa_version: Published Version
page: 411-439
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: SIAM Journal on Mathematics of Data Science
publication_identifier:
eissn:
- 2577-0187
publication_status: published
publisher: SIAM
quality_controlled: '1'
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status: public
supplementarymaterial: no
title: Precise asymptotics for spectral methods in mixed generalized linear models
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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year: '2026'
...
---
OA_place: publisher
_id: '17368'
abstract:
- lang: eng
text: "Recent advancements in molecular diagnostic techniques have enabled the collection
of\r\nmultiple types of omics data from patients, including genomics, epigenomics,
proteomics,\r\nand transcriptomics. However, we lack effective methods for integrating
all these different\r\ndata types and combining them with clinical outcomes to
study the molecular mechanisms\r\nthat govern pathological phenotypes. We present
multi-omics BayesW, a penalized Bayesian\r\nregression method that can handle
general omics data for survival analysis of time-to-event\r\nphenotypes. Our method
can: (1) accommodate incomplete data by allowing censored\r\nindividuals, (2)
use continuous time-to-event data to test associations of markers with a\r\nphenotype
and (3) estimate effects jointly while allowing for independent groups of biological\r\nmarkers.
Extensive simulations using planted signals on real data demonstrate that our
model\r\naccurately retrieves the true parameters of the model while controlling
for false discoveries\r\nand maintaining the expected prediction accuracy. We
address data correlations by estimating\r\nthe effects jointly, even between omic
groups, while also estimating the individual variance\r\nexplained by each group.
We apply our model to two datasets. Using 18,000 individuals from\r\nthe Generation
Scotland study we model the association of time at onset of Type 2 Diabetes,\r\nStroke,
Ischemic Disease, and Osteoarthritis from baseline study entry, with 831,724 CpG\r\nmethylation
probes. We find that large proportions of variation in disease onset times can\r\nbe
attributed to methylation as measured in whole blood at baseline in individuals
without\r\ndisease symptoms. We then apply our model to The Cancer Genome Atlas
(TCGA) pan-cancer\r\ndataset, in which we use 5 types of omics: copy number variation,
epigenetics, somatic\r\nmutations, miRNA, and gene expression. For cancer survival
age-at-onset we find that, when\r\nfitting the 5 groups together, almost all variation
attributable to \"omics\" data is explained by\r\nDNA methylation. When considering
progression times, both methylation and gene expression\r\nexplain a large part
of the variance. We found 2 genes that are significantly associated (95%\r\nposterior
inclusion probability) with cancer survival time, conditional on all other genome-wide\r\nomics
data variation. Owing to the vast variability of mechanisms characterizing different\r\ncancers,
there are likely few specific genes with a strong signal in a pan-cancer setting.
Taken\r\ntogether, we showed the applicability of our multi-omics BayesW model
to a wide-range of\r\nbiological questions in multi-omics data.\r\n"
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Ariadna
full_name: Villanueva Marijuan, Ariadna
id: e0ae4864-133f-11ed-8f02-adaa8dd27540
last_name: Villanueva Marijuan
citation:
ama: Villanueva Marijuan A. Bayesian linear regression for analyzing general omics
data with time-to-event phenotypes. 2024. doi:10.15479/at:ista:17368
apa: Villanueva Marijuan, A. (2024). Bayesian linear regression for analyzing
general omics data with time-to-event phenotypes. Institute of Science and
Technology Austria. https://doi.org/10.15479/at:ista:17368
chicago: Villanueva Marijuan, Ariadna. “Bayesian Linear Regression for Analyzing
General Omics Data with Time-to-Event Phenotypes.” Institute of Science and Technology
Austria, 2024. https://doi.org/10.15479/at:ista:17368.
ieee: A. Villanueva Marijuan, “Bayesian linear regression for analyzing general
omics data with time-to-event phenotypes,” Institute of Science and Technology
Austria, 2024.
ista: Villanueva Marijuan A. 2024. Bayesian linear regression for analyzing general
omics data with time-to-event phenotypes. Institute of Science and Technology
Austria.
mla: Villanueva Marijuan, Ariadna. Bayesian Linear Regression for Analyzing General
Omics Data with Time-to-Event Phenotypes. Institute of Science and Technology
Austria, 2024, doi:10.15479/at:ista:17368.
short: A. Villanueva Marijuan, Bayesian Linear Regression for Analyzing General
Omics Data with Time-to-Event Phenotypes, Institute of Science and Technology
Austria, 2024.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-08-02T10:52:40Z
date_published: 2024-08-13T00:00:00Z
date_updated: 2026-10-02T11:35:19Z
day: '13'
ddc:
- '610'
degree_awarded: MS
department:
- _id: GradSch
- _id: MaRo
doi: 10.15479/at:ista:17368
doi_confirm: '1'
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creator: avillanu
date_created: 2024-08-14T11:51:24Z
date_updated: 2025-02-14T23:30:03Z
embargo: 2025-02-14
file_id: '17433'
file_name: Masters_thesis_AriadnaVillanueva.pdf
file_size: 13052436
relation: main_file
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date_created: 2024-08-14T11:51:57Z
date_updated: 2025-02-14T23:30:03Z
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file_size: 45642547
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file_date_updated: 2025-02-14T23:30:03Z
fulldoi: https://doi.org/10.15479/at:ista:17368
has_accepted_license: '1'
keyword:
- Epigenetics
- Multi-omics
- Bayesian regression
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-sa/4.0/
month: '08'
oa: 1
oa_version: Published Version
page: '60'
publication_identifier:
issn:
- 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
researchdata_availability: no
status: public
supervisor:
- first_name: Matthew Richard
full_name: Robinson, Matthew Richard
id: E5D42276-F5DA-11E9-8E24-6303E6697425
last_name: Robinson
orcid: 0000-0001-8982-8813
supplementarymaterial: no
title: Bayesian linear regression for analyzing general omics data with time-to-event
phenotypes
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BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...
---
_id: '5584'
abstract:
- lang: eng
text: "This package contains data for the publication \"Nonlinear decoding of a
complex movie from the mammalian retina\" by Deny S. et al, PLOS Comput Biol (2018).
\r\n\r\nThe data consists of\r\n(i) 91 spike sorted, isolated rat retinal ganglion
cells that pass stability and quality criteria, recorded on the multi-electrode
array, in response to the presentation of the complex movie with many randomly
moving dark discs. The responses are represented as 648000 x 91 binary matrix,
where the first index indicates the timebin of duration 12.5 ms, and the second
index the neural identity. The matrix entry is 0/1 if the neuron didn't/did spike
in the particular time bin.\r\n(ii) README file and a graphical illustration of
the structure of the experiment, specifying how the 648000 timebins are split
into epochs where 1, 2, 4, or 10 discs were displayed, and which stimulus segments
are exact repeats or unique ball trajectories.\r\n(iii) a 648000 x 400 matrix
of luminance traces for each of the 20 x 20 positions (\"sites\") in the movie
frame, with time that is locked to the recorded raster. The luminance traces are
produced as described in the manuscript by filtering the raw disc movie with a
small gaussian spatial kernel. "
article_processing_charge: No
author:
- first_name: Stephane
full_name: Deny, Stephane
last_name: Deny
- first_name: Olivier
full_name: Marre, Olivier
last_name: Marre
- first_name: Vicente
full_name: Botella-Soler, Vicente
last_name: Botella-Soler
- first_name: Georg S
full_name: Martius, Georg S
id: 3A276B68-F248-11E8-B48F-1D18A9856A87
last_name: Martius
- first_name: Gasper
full_name: Tkacik, Gasper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkacik
orcid: 0000-0002-6699-1455
citation:
ama: Deny S, Marre O, Botella-Soler V, Martius GS, Tkačik G. Nonlinear decoding
of a complex movie from the mammalian retina. 2018. doi:10.15479/AT:ISTA:98
apa: Deny, S., Marre, O., Botella-Soler, V., Martius, G. S., & Tkačik, G. (2018).
Nonlinear decoding of a complex movie from the mammalian retina. Institute of
Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:98
chicago: Deny, Stephane, Olivier Marre, Vicente Botella-Soler, Georg S Martius,
and Gašper Tkačik. “Nonlinear Decoding of a Complex Movie from the Mammalian Retina.”
Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:98.
ieee: S. Deny, O. Marre, V. Botella-Soler, G. S. Martius, and G. Tkačik, “Nonlinear
decoding of a complex movie from the mammalian retina.” Institute of Science and
Technology Austria, 2018.
ista: Deny S, Marre O, Botella-Soler V, Martius GS, Tkačik G. 2018. Nonlinear decoding
of a complex movie from the mammalian retina, Institute of Science and Technology
Austria, 10.15479/AT:ISTA:98.
mla: Deny, Stephane, et al. Nonlinear Decoding of a Complex Movie from the Mammalian
Retina. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:98.
short: S. Deny, O. Marre, V. Botella-Soler, G.S. Martius, G. Tkačik, (2018).
datarep_id: '98'
date_created: 2018-12-12T12:31:39Z
date_published: 2018-03-29T00:00:00Z
date_updated: 2025-04-15T08:18:24Z
day: '29'
ddc:
- '570'
department:
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- _id: GaTk
doi: 10.15479/AT:ISTA:98
file:
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creator: system
date_created: 2018-12-12T13:02:24Z
date_updated: 2020-07-14T12:47:07Z
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date_updated: 2020-07-14T12:47:07Z
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fulldoi: https://doi.org/10.15479/AT:ISTA:98
has_accepted_license: '1'
keyword:
- retina
- decoding
- regression
- neural networks
- complex stimulus
month: '03'
oa: 1
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...