Martin Slawski

Non-negative least squares for high-dimensional linear models: Consistency and sparse recovery without regularization

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a necessity in such setting. Deviating from this paradigm, we show that non-negativity constraints on the regression coefficients may be similarly effective as explicit regularization if the design matrix has additional properties, which are met in several applications of non-negative least squares (NNLS). We show that for these designs, the performance of NNLS with regard to prediction and estimation is comparable to that of the lasso. We argue further that in specific cases, NNLS may have a better

MeDeCom: discovery and quantification of latent components of heterogeneous methylomes

\ell_{\infty}

Isotope pattern deconvolution for peptide mass spectrometry by non-negative least squares/least absolute deviation template matching

-rate in estimation and hence also advantages with respect to support recovery when combined with thresholding. From a practical point of view, NNLS does not depend on a regularization parameter and is hence easier to use.

Sparse recovery by thresholded non-negative least squares

It is important for large-scale epigenomic studies to determine and explore the nature of hidden confounding variation, most importantly cell composition. We developed MeDeCom as a novel reference-free computational framework that allows the decomposition of complex DNA methylomes into latent methylation components and their proportions in each sample. MeDeCom is based on constrained non-negative matrix factorization with a new biologically motivated regularization function. It accurately recovers cell-type-specific latent methylation components and their proportions. MeDeCom is a new unsupervised tool for the exploratory study of the major sources of methylation variation, which should lead to a deeper understanding and better biological interpretation.

Estimation of positive definite M-matrices and structure learning for attractive Gaussian Markov random fields

BackgroundThe robust identification of isotope patterns originating from peptides being analyzed through mass spectrometry (MS) is often significantly hampered by noise artifacts and the interference of overlapping patterns arising e.g. from post-translational modifications. As the classification of the recorded data points into either ‘noise’ or ‘signal’ lies at the very root of essentially every proteomic application, the quality of the automated processing of mass spectra can significantly influence the way the data might be interpreted within a given biological context.ResultsWe propose non-negative least squares/non-negative least absolute deviation regression to fit a raw spectrum by templates imitating isotope patterns. In a carefully designed validation scheme, we show that the method exhibits excellent performance in pattern picking. It is demonstrated that the method is able to disentangle complicated overlaps of patterns.ConclusionsWe find that regularization is not necessary to prevent overfitting and that thresholding is an effective and user-friendly way to perform feature selection. The proposed method avoids problems inherent in regularization-based approaches, comes with a set of well-interpretable parameters whose default configuration is shown to generalize well without the need for fine-tuning, and is applicable to spectra of different platforms. The R package IPPD implements the method and is available from the Bioconductor platform (http://bioconductor.fhcrc.org/help/bioc-views/devel/bioc/html/IPPD.html).