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Sep 18, 2013
09/13

by
Magnus Rattray

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Previous analytical studies of on-line Independent Component Analysis (ICA) learning rules have focussed on asymptotic stability and efficiency. In practice the transient stages of learning will often be more significant in determining the success of an algorithm. This is demonstrated here with an analysis of a Hebbian ICA algorithm which can find a small number of non-Gaussian components given data composed of a linear mixture of independent source signals. An idealised data model is...

Source: http://arxiv.org/abs/cond-mat/0105057v1

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3.0

Jun 30, 2018
06/18

by
Panagiotis Papastamoulis; Magnus Rattray

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Next generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally...

Topics: Genomics, Computation, Quantitative Biology, Applications, Statistics

Source: http://arxiv.org/abs/1701.03095

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9.0

Aug 11, 2020
08/20

by
Gleb Basalyga; Magnus Rattray

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Source: http://academictorrents.com/details/3b1322671d42bb6e951a700fad288137dcaefece

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78

Sep 21, 2013
09/13

by
Magnus Rattray; Jonathan Shapiro

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A formalism for describing the dynamics of Genetic Algorithms (GAs) using methods from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best...

Source: http://arxiv.org/abs/cond-mat/9609109v1

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8.0

Jun 30, 2018
06/18

by
Panagiotis Papastamoulis; Magnus Rattray

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Recent advances in molecular biology allow the quantification of the transcriptome and scoring transcripts as differentially or equally expressed between two biological conditions. Although these two tasks are closely linked, the available inference methods treat them separately: a primary model is used to estimate expression and its output is post-processed using a differential expression model. In this paper, both issues are simultaneously addressed by proposing the joint estimation of...

Topics: Quantitative Methods, Quantitative Biology, Statistics, Methodology

Source: http://arxiv.org/abs/1412.3050

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44

Sep 22, 2013
09/13

by
Gleb Basalyga; Magnus Rattray

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The learning dynamics of on-line independent component analysis is analysed in the limit of large data dimension. We study a simple Hebbian learning algorithm that can be used to separate out a small number of non-Gaussian components from a high-dimensional data set. The de-mixing matrix parameters are confined to a Stiefel manifold of tall, orthogonal matrices and we introduce a natural gradient variant of the algorithm which is appropriate to learning on this manifold. For large input...

Source: http://arxiv.org/abs/cond-mat/0309554v1

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63

Sep 18, 2013
09/13

by
Magnus Rattray; David Saad

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Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods of statistical physics which accurately characterize both transient and asymptotic behavior. A solution of the learning dynamics is obtained for the case of multilayer neural network training in the limit of large input dimension. We find that natural gradient...

Source: http://arxiv.org/abs/cond-mat/9901212v1

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40

Sep 21, 2013
09/13

by
Magnus Rattray; Jonathan L. Shapiro

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We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection. Equations of motion are derived for the cumulants of the trait distribution in the diffusion limit and under the assumption of linkage equilibrium. Because of the additive nature of cumulants, this reduces to the problem of determining equations of motion for...

Source: http://arxiv.org/abs/adap-org/9907009v3

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51

Sep 23, 2013
09/13

by
Peter Glaus; Antti Honkela; Magnus Rattray

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Motivation: High-throughput sequencing enables expression analysis at the level of individual transcripts. The analysis of transcriptome expression levels and differential expression estimation requires a probabilistic approach to properly account for ambiguity caused by shared exons and finite read sampling as well as the intrinsic biological variance of transcript expression. Results: We present BitSeq (Bayesian Inference of Transcripts from Sequencing data), a Bayesian approach for...

Source: http://arxiv.org/abs/1109.0863v2

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6.0

Jun 30, 2018
06/18

by
James Hensman; Magnus Rattray; Neil D. Lawrence

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In this publication, we combine two Bayesian non-parametric models: the Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP model is to introduce a variation on the GP prior which enables us to model structured time-series data, i.e. data containing groups where we wish to model inter- and intra-group variability. Our innovation in the DP model is an implementation of a new fast collapsed variational inference procedure which enables us to optimize our variationala...

Topics: Machine Learning, Computing Research Repository, Computer Vision and Pattern Recognition, Learning,...

Source: http://arxiv.org/abs/1401.1605

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158

Sep 23, 2013
09/13

by
Nicolas Durrande; James Hensman; Magnus Rattray; Neil D. Lawrence

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We consider the problem of detecting the periodic part of a function given the observations of some input/output tuples (xi,yi). As they are known for being powerful tools for dealing with such data, our approach is based on Gaussian process regression models which are closely related to reproducing kernel Hilbert spaces (RKHS). The latter offer a powerful framework for decomposing covariance functions as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of...

Source: http://arxiv.org/abs/1303.7090v1

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5.0

Jun 29, 2018
06/18

by
Jing Yang; Christopher A. Penfold; Murray R. Grant; Magnus Rattray

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Time course data are often used to study the changes to a biological process after perturbation. Statistical methods have been developed to determine whether such a perturbation induces changes over time, e.g. comparing a perturbed and unperturbed time course dataset to uncover differences. However, existing methods do not provide a principled statistical approach to identify the specific time when the two time course datasets first begin to diverge after a perturbation; we call this the...

Topics: Quantitative Biology, Quantitative Methods

Source: http://arxiv.org/abs/1602.01743

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7.0

Jun 30, 2018
06/18

by
James Hensman; Panagiotis Papastamoulis; Peter Glaus; Antti Honkela; Magnus Rattray

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Motivation: Assigning RNA-seq reads to their transcript of origin is a fundamental task in transcript expression estimation. Where ambiguities in assignments exist due to transcripts sharing sequence, e.g. alternative isoforms or alleles, the problem can be solved through probabilistic inference. Bayesian methods have been shown to provide accurate transcript abundance estimates compared to competing methods. However, exact Bayesian inference is intractable and approximate methods such as...

Topics: Quantitative Methods, Quantitative Biology, Genomics

Source: http://arxiv.org/abs/1412.5995

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100

Sep 23, 2013
09/13

by
Ciira wa Maina; Filomena Matarese; Korbinian Grote; Hendrik G. Stunnenberg; George Reid; Antti Honkela; Neil D. Lawrence; Magnus Rattray

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Gene transcription mediated by RNA polymerase II (pol-II) is a key step in gene expression. The dynamics of pol-II moving along the transcribed region influences the rate and timing of gene expression. In this work we present a probabilistic model of transcription dynamics which is fitted to pol-II occupancy time course data measured using ChIP-Seq. The model can be used to estimate transcription speed and to infer the temporal pol-II activity profile at the gene promoter. Model parameters are...

Source: http://arxiv.org/abs/1303.4926v1

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13

Jun 27, 2018
06/18

by
Antti Honkela; Jaakko Peltonen; Hande Topa; Iryna Charapitsa; Filomena Matarese; Korbinian Grote; Hendrik G. Stunnenberg; George Reid; Neil D. Lawrence; Magnus Rattray

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Genes with similar transcriptional activation kinetics can display very different temporal mRNA profiles due to differences in transcription time, degradation rate and RNA processing kinetics. Recent studies have shown that a splicing-associated RNA production delay can be significant. We introduce a joint model of transcriptional activation and mRNA accumulation which can be used for inference of transcription rate, RNA production delay and degradation rate given genome-wide data from...

Topics: Quantitative Methods, Applications, Genomics, Statistics, Quantitative Biology

Source: http://arxiv.org/abs/1503.01081