Multiscale blind source separation

Tree structures, showing hierarchical relationships and the latent structures between samples, are ubiquitous in genomic and biomedical sciences. A common question in many studies is whether there is an association between a response variable measured on each sample and the latent group structure represented by some given tree. Currently, this is addressed on an ad hoc basis, usually requiring the user to decide on an appropriate number of clusters to prune out of the tree to be tested against the response variable. Here, we present a statistical method with statistical guarantees that tests for association between the response variable and a fixed tree structure across all levels of the tree hierarchy with high power while accounting for the overall false positive error rate. This enhances the robustness and reproducibility of such findings.

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“…For an arbitrary given test vectorp (which may depend on Y), we define the multiscale statistic (11,(17)(18)(19) Tn(p, Y) = max…”

Section: )mentioning

confidence: 99%

Testing for dependence on tree structures

Behr

Ansari

Munk

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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“…Therefore, recent years have witnessed a renaissance in change-point inference motivated by several applications which require computationally fast and statistically efficient finding of potentially many change-points in large data sets, see e.g. Olshen et al (2004), Siegmund (2013) and Behr et al (2018) for its relevance to cancer genetics, Chen and Zhang (2015) for network analysis, Aue et al (2014) for econometrics, and Hotz et al (2013) for electrophysiology, to name a few. This challenges statistical methodology due to the multiscale nature of these problems (i.e.…”

Section: Introductionmentioning

confidence: 99%

Multiscale change-point segmentation: beyond step functions

Li¹,

Guo²,

Munk³

2019

Electron. J. Statist.

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Modern multiscale type segmentation methods are known to detect multiple changepoints with high statistical accuracy, while allowing for fast computation. Underpinning theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper this will be extended to certain function classes beyond such step functions in a nonparametric regression setting, revealing certain multiscale segmentation methods as robust to deviation from such piecewise constant functions. Our main finding is the adaptation over such function classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Hölder functions of smoothness order 0 < α ≤ 1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a logfactor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations.MSC 2010 subject classifications: 62G08, 62G20, 62G35.

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“…Ignoring any sequencing error, we have E(Y |F ) = F. Our aim is to reconstruct both the matrices S and W from the measurement matrix Y . This amounts to a specific type of a finite alphabet blind separation problem [Behr andMunk, 2017, Behr et al, 2018].…”

Section: Methodsmentioning

confidence: 99%

Multiple Haplotype Reconstruction from Allele Frequency Data

Pelizzola

Behr

et al. 2020

Preprint

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1AbstractWe propose a new method that is able to accurately infer major haplotypes and their frequencies just from multiple samples of allele frequency data. Our approach seems to be the first that is able to estimate more than one haplotype given such data. Even the accuracy of experimentally obtained allele frequencies can be improved by re-estimating them from our reconstructed haplotypes.Reconstructing haplotypes from sequencing data is of interest to several areas of biological and medical research. In evolutionary genetics, for instance, haplotypes help to better understand the genetic architecture of adaptation. Here we consider genomic time series data from three evolve and re-sequence experiments as an application. However, the approach can in principle be used in a wider context, as only data from multiple samples are needed, not necessarily collected over time.

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Multiscale blind source separation

Cited by 14 publications

References 69 publications

Testing for dependence on tree structures

Testing for dependence on tree structures

Multiscale change-point segmentation: beyond step functions

Multiple Haplotype Reconstruction from Allele Frequency Data

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