Martin Slawski
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Martin Slawski has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Ping Li
The Hong Kong Polytechnic University
2 shared publications - Gilles Gasparoni
Department of Genetics/Epigenetics Universität Des Saarlandes Saarbrücken Germany
1 shared publication - Jörn Walter
Department of Genetics/Epigenetics Universität Des Saarlandes Saarbrücken Germany
1 shared publication - Matthias Hein
Department of Mathematics and Computer Science Saarland University 66123 Saarbrücken Germany
1 shared publication - Nikita Vedeneev
Machine Learning Group, Saarland University, Campus E1.1, Saarbrücken66123, Germany
1 shared publication - Pavlo Lutsik
Department of EpiGenetics, Saarland University, Campus A2.4, Saarbrücken, 66123, Germany
1 shared publication
Latest Publications
- Open Access
- 24 March 2017
- Published by Springer Nature in Genome Biology
- Vol. 18 (1) , 1-20
MeDeCom: discovery and quantification of latent components of heterogeneous methylomes
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.
- 24 March 2017
- Published by Springer Nature in Genome Biology
- Vol. 18 (1) , 1-20
Open AccessMeDeCom: discovery and quantification of latent components of heterogeneous methylomes
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.
- Open Access
Linear signal recovery from $b$-bit-quantized linear measurements: precise analysis of the trade-off between bit depth and number of measurements
We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. Our interest is in linear approaches to signal recovery, where "linear" means that non-linearity resulting from quantization is ignored and the observations are treated as if they arose from a linear measurement model. Specifically, the focus is on a generalization of a method for one-bit observations due to Plan and Vershynin [\emph{IEEE~Trans. Inform. Theory, \textbf{59} (2013), 482--494}]. At the heart of the present paper is a precise characterization of the optimal trade-off between the number of measurements $m$ and the bit depth per measurement $b$ given a total budget of $B = m \cdot b$ bits when the goal is to minimize the $\ell_2$-error in estimating the signal. It turns out that the choice $b = 1$ is optimal for estimating the unit vector (direction) corresponding to the signal for any level of additive Gaussian noise before quantization as well as for a specific model of adversarial noise, while the choice $b = 2$ is optimal for estimating the direction and the norm (scale) of the signal. Moreover, Lloyd-Max quantization is shown to be an optimal quantization scheme w.r.t. $\ell_2$-estimation error. Our analysis is corroborated by numerical experiments showing nearly perfect agreement with our theoretical predictions. The paper is complemented by an empirical comparison to alternative methods of signal recovery taking the non-linearity resulting from quantization into account. The results of that comparison point to a regime change depending on the noise level: in a low-noise setting, linear signal recovery falls short of more sophisticated competitors while being competitive in moderate- and high-noise settings.Open AccessLinear signal recovery from $b$-bit-quantized linear measurements: precise analysis of the trade-off between bit depth and number of measurements
We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. Our interest is in linear approaches to signal recovery, where "linear" means that non-linearity resulting from quantization is ignored and the observations are treated as if they arose from a linear measurement model. Specifically, the focus is on a generalization of a method for one-bit observations due to Plan and Vershynin [\emph{IEEE~Trans. Inform. Theory, \textbf{59} (2013), 482--494}]. At the heart of the present paper is a precise characterization of the optimal trade-off between the number of measurements $m$ and the bit depth per measurement $b$ given a total budget of $B = m \cdot b$ bits when the goal is to minimize the $\ell_2$-error in estimating the signal. It turns out that the choice $b = 1$ is optimal for estimating the unit vector (direction) corresponding to the signal for any level of additive Gaussian noise before quantization as well as for a specific model of adversarial noise, while the choice $b = 2$ is optimal for estimating the direction and the norm (scale) of the signal. Moreover, Lloyd-Max quantization is shown to be an optimal quantization scheme w.r.t. $\ell_2$-estimation error. Our analysis is corroborated by numerical experiments showing nearly perfect agreement with our theoretical predictions. The paper is complemented by an empirical comparison to alternative methods of signal recovery taking the non-linearity resulting from quantization into account. The results of that comparison point to a regime change depending on the noise level: in a low-noise setting, linear signal recovery falls short of more sophisticated competitors while being competitive in moderate- and high-noise settings. - Open Access
Methods for Sparse and Low-Rank Recovery under Simplex Constraints
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The situation is analogous for the use of nuclear norm regularization for low-rank recovery of Hermitian positive semidefinite matrices with given trace. In the present paper, we discuss several strategies to deal with this situation, from simple to more complex. As a starting point, we consider empirical risk minimization (ERM). It follows from existing theory that ERM enjoys better theoretical properties w.r.t.~prediction and $\ell_2$-estimation error than $\ell_1$-regularization. In light of this, we argue that ERM combined with a subsequent sparsification step like thresholding is superior to the heuristic of using $\ell_1$-regularization after dropping the sum constraint and subsequent normalization. At the next level, we show that any sparsity-promoting regularizer under simplex constraints cannot be convex. A novel sparsity-promoting regularization scheme based on the inverse or negative of the squared $\ell_2$-norm is proposed, which avoids shortcomings of various alternative methods from the literature. Our approach naturally extends to Hermitian positive semidefinite matrices with given trace. Numerical studies concerning compressed sensing, sparse mixture density estimation, portfolio optimization and quantum state tomography are used to illustrate the key points of the paper.
Open AccessMethods for Sparse and Low-Rank Recovery under Simplex Constraints
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The situation is analogous for the use of nuclear norm regularization for low-rank recovery of Hermitian positive semidefinite matrices with given trace. In the present paper, we discuss several strategies to deal with this situation, from simple to more complex. As a starting point, we consider empirical risk minimization (ERM). It follows from existing theory that ERM enjoys better theoretical properties w.r.t.~prediction and $\ell_2$-estimation error than $\ell_1$-regularization. In light of this, we argue that ERM combined with a subsequent sparsification step like thresholding is superior to the heuristic of using $\ell_1$-regularization after dropping the sum constraint and subsequent normalization. At the next level, we show that any sparsity-promoting regularizer under simplex constraints cannot be convex. A novel sparsity-promoting regularization scheme based on the inverse or negative of the squared $\ell_2$-norm is proposed, which avoids shortcomings of various alternative methods from the literature. Our approach naturally extends to Hermitian positive semidefinite matrices with given trace. Numerical studies concerning compressed sensing, sparse mixture density estimation, portfolio optimization and quantum state tomography are used to illustrate the key points of the paper.