@article{22228,
  abstract     = {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 𝑛 needed to guarantee recovery is superlinear in the signal dimension 𝑑. In this paper, we develop exact asymptotics on spectral methods in the challenging proportional regime in which 𝑛,𝑑 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.},
  author       = {Zhang, Yihan and Mondelli, Marco and Venkataramanan, Ramji},
  issn         = {2577-0187},
  journal      = {SIAM Journal on Mathematics of Data Science},
  keywords     = {spectral estimator, generalized linear models, mixed regression, high-dimensional asymptotics, random matrix theory, approximate message passing (AMP)},
  number       = {2},
  pages        = {411--439},
  publisher    = {SIAM},
  title        = {{Precise asymptotics for spectral methods in mixed generalized linear models}},
  doi          = {10.1137/24m1702854},
  volume       = {8},
  year         = {2026},
}

@phdthesis{17368,
  abstract     = {Recent advancements in molecular diagnostic techniques have enabled the collection of
multiple types of omics data from patients, including genomics, epigenomics, proteomics,
and transcriptomics. However, we lack effective methods for integrating all these different
data types and combining them with clinical outcomes to study the molecular mechanisms
that govern pathological phenotypes. We present multi-omics BayesW, a penalized Bayesian
regression method that can handle general omics data for survival analysis of time-to-event
phenotypes. Our method can: (1) accommodate incomplete data by allowing censored
individuals, (2) use continuous time-to-event data to test associations of markers with a
phenotype and (3) estimate effects jointly while allowing for independent groups of biological
markers. Extensive simulations using planted signals on real data demonstrate that our model
accurately retrieves the true parameters of the model while controlling for false discoveries
and maintaining the expected prediction accuracy. We address data correlations by estimating
the effects jointly, even between omic groups, while also estimating the individual variance
explained by each group. We apply our model to two datasets. Using 18,000 individuals from
the Generation Scotland study we model the association of time at onset of Type 2 Diabetes,
Stroke, Ischemic Disease, and Osteoarthritis from baseline study entry, with 831,724 CpG
methylation probes. We find that large proportions of variation in disease onset times can
be attributed to methylation as measured in whole blood at baseline in individuals without
disease symptoms. We then apply our model to The Cancer Genome Atlas (TCGA) pan-cancer
dataset, in which we use 5 types of omics: copy number variation, epigenetics, somatic
mutations, miRNA, and gene expression. For cancer survival age-at-onset we find that, when
fitting the 5 groups together, almost all variation attributable to "omics" data is explained by
DNA methylation. When considering progression times, both methylation and gene expression
explain a large part of the variance. We found 2 genes that are significantly associated (95%
posterior inclusion probability) with cancer survival time, conditional on all other genome-wide
omics data variation. Owing to the vast variability of mechanisms characterizing different
cancers, there are likely few specific genes with a strong signal in a pan-cancer setting. Taken
together, we showed the applicability of our multi-omics BayesW model to a wide-range of
biological questions in multi-omics data.
},
  author       = {Villanueva Marijuan, Ariadna},
  issn         = {2791-4585},
  keywords     = {Epigenetics, Multi-omics, Bayesian regression},
  pages        = {60},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Bayesian linear regression for analyzing general omics data with time-to-event phenotypes}},
  doi          = {10.15479/at:ista:17368},
  year         = {2024},
}

@misc{5584,
  abstract     = {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). 

The data consists of
(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.
(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.
(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. },
  author       = {Deny, Stephane and Marre, Olivier and Botella-Soler, Vicente and Martius, Georg S and Tkacik, Gasper},
  keywords     = {retina, decoding, regression, neural networks, complex stimulus},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Nonlinear decoding of a complex movie from the mammalian retina}},
  doi          = {10.15479/AT:ISTA:98},
  year         = {2018},
}