198 research outputs found
Theoretical Perspectives on Deep Learning Methods in Inverse Problems
In recent years, there have been significant advances
in the use of deep learning methods in inverse problems such as
denoising, compressive sensing, inpainting, and super-resolution.
While this line of works has predominantly been driven by
practical algorithms and experiments, it has also given rise to
a variety of intriguing theoretical problems. In this paper, we
survey some of the prominent theoretical developments in this line
of works, focusing in particular on generative priors, untrained
neural network priors, and unfolding algorithms. In addition to
summarizing existing results in these topics, we highlight several
ongoing challenges and open problems
A Bayesian Framework for Multivariate Differential Analysis accounting for Missing Data
Current statistical methods in differential proteomics analysis generally
leave aside several challenges, such as missing values, correlations between
peptide intensities and uncertainty quantification. Moreover, they provide
point estimates, such as the mean intensity for a given peptide or protein in a
given condition. The decision of whether an analyte should be considered as
differential is then based on comparing the p-value to a significance
threshold, usually 5%. In the state-of-the-art limma approach, a hierarchical
model is used to deduce the posterior distribution of the variance estimator
for each analyte. The expectation of this distribution is then used as a
moderated estimation of variance and is injected directly into the expression
of the t-statistic. However, instead of merely relying on the moderated
estimates, we could provide more powerful and intuitive results by leveraging a
fully Bayesian approach and hence allow the quantification of uncertainty. The
present work introduces this idea by taking advantage of standard results from
Bayesian inference with conjugate priors in hierarchical models to derive a
methodology tailored to handle multiple imputation contexts. Furthermore, we
aim to tackle a more general problem of multivariate differential analysis, to
account for possible inter-peptide correlations. By defining a hierarchical
model with prior distributions on both mean and variance parameters, we achieve
a global quantification of uncertainty for differential analysis. The inference
is thus performed by computing the posterior distribution for the difference in
mean peptide intensities between two experimental conditions. In contrast to
more flexible models that can be achieved with hierarchical structures, our
choice of conjugate priors maintains analytical expressions for direct sampling
from posterior distributions without requiring expensive MCMC methods.Comment: 21 pages, 5 figure
Metamotifs--a generative model for building families of nucleotide position weight matrices.
BACKGROUND: Development of high-throughput methods for measuring DNA interactions of transcription factors together with computational advances in short motif inference algorithms is expanding our understanding of transcription factor binding site motifs. The consequential growth of sequence motif data sets makes it important to systematically group and categorise regulatory motifs. It has been shown that there are familial tendencies in DNA sequence motifs that are predictive of the family of factors that binds them. Further development of methods that detect and describe familial motif trends has the potential to help in measuring the similarity of novel computational motif predictions to previously known data and sensitively detecting regulatory motifs similar to previously known ones from novel sequence. RESULTS: We propose a probabilistic model for position weight matrix (PWM) sequence motif families. The model, which we call the 'metamotif' describes recurring familial patterns in a set of motifs. The metamotif framework models variation within a family of sequence motifs. It allows for simultaneous estimation of a series of independent metamotifs from input position weight matrix (PWM) motif data and does not assume that all input motif columns contribute to a familial pattern. We describe an algorithm for inferring metamotifs from weight matrix data. We then demonstrate the use of the model in two practical tasks: in the Bayesian NestedMICA model inference algorithm as a PWM prior to enhance motif inference sensitivity, and in a motif classification task where motifs are labelled according to their interacting DNA binding domain. CONCLUSIONS: We show that metamotifs can be used as PWM priors in the NestedMICA motif inference algorithm to dramatically increase the sensitivity to infer motifs. Metamotifs were also successfully applied to a motif classification problem where sequence motif features were used to predict the family of protein DNA binding domains that would interact with it. The metamotif based classifier is shown to compare favourably to previous related methods. The metamotif has great potential for further use in machine learning tasks related to especially de novo computational sequence motif inference. The metamotif methods presented have been incorporated into the NestedMICA suite.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are
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