Publications
Journal Article
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization
Inverse Problems 37, no. 5 (2021): 055008.Status: Published
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2021 |
Journal | Inverse Problems |
Volume | 37 |
Issue | 5 |
Pagination | 055008 |
Publisher | IOP Publishing Ltd |
Nationwide rollout reveals efficacy of epidemic control through digital contact tracing
Nature Communications 12 (2021).Status: Published
Nationwide rollout reveals efficacy of epidemic control through digital contact tracing
Afilliation | Communication Systems, Scientific Computing, Machine Learning |
Project(s) | The Center for Resilient Networks and Applications, Department of Data Science and Knowledge Discovery , Department of Computational Physiology |
Publication Type | Journal Article |
Year of Publication | 2021 |
Journal | Nature Communications |
Volume | 12 |
Number | 5918 |
Publisher | Springer Nature |
DOI | 10.1038/s41467-021-26144-8 |
Robust recovery of low-rank matrices with non-orthogonal sparse decomposition from incomplete measurements
Applied Mathematics and Computation 392 (2021): 125702.Status: Published
Robust recovery of low-rank matrices with non-orthogonal sparse decomposition from incomplete measurements
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2021 |
Journal | Applied Mathematics and Computation |
Volume | 392 |
Pagination | 125702 |
Publisher | Elsevier |
Proceedings, refereed
Data-driven Personalized Cervical Cancer Risk Prediction: A Graph-Perspective
In IEEE Statistical Signal Processing Workshop 2021. IEEE, 2021.Status: Published
Data-driven Personalized Cervical Cancer Risk Prediction: A Graph-Perspective
Afilliation | Machine Learning |
Project(s) | Department of Data Science and Knowledge Discovery |
Publication Type | Proceedings, refereed |
Year of Publication | 2021 |
Conference Name | IEEE Statistical Signal Processing Workshop 2021 |
Pagination | 46-50 |
Publisher | IEEE |
DOI | 10.1109/SSP49050.2021.9513824 |
Journal Article
A machine learning approach to optimal Tikhonov regularization I: Affine manifolds
Analysis and Applications (2020).Status: Accepted
A machine learning approach to optimal Tikhonov regularization I: Affine manifolds
Inspired by several real-life applications in audio processing and medical image analysis, where the quantity of interest is generated by several sources to be accurately modeled and separated, as well as by recent advances in regularization theory and optimization, we study the conditions on optimal support recovery in inverse problems of unmixing type by means of multi-penalty regularization.
We consider and analyze a regularization functional composed of a data-fidelity term, where signal and noise are additively mixed, a non-smooth, convex, sparsity promoting term, and a quadratic penalty term to model the noise. We prove not only that the well-established theory for sparse recovery in the single parameter case can be translated to the multi-penalty settings, but we also demonstrate the enhanced properties of multi-penalty regularization in terms of support identification compared to sole $\ell^1$-minimization. We additionally confirm and support the theoretical results by extensive numerical simulations, which give a statistics of robustness of the multi-penalty regularization scheme with respect to the single-parameter counterpart.
Eventually, we confirm a significant improvement in performance compared to standard $\ell^1$-regularization for compressive sensing problems considered in our experiments.
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2020 |
Journal | Analysis and Applications |
Publisher | MIT Press |
URL | http://arxiv.org/abs/1610.01952 |
Talks, contributed
A Combined In-Silico and Machine Learning Approach towards Predicting Arrhythmic Risk in Post-Infarction Patients
In Computing in Cardiology, Singapore, 2019.Status: Published
A Combined In-Silico and Machine Learning Approach towards Predicting Arrhythmic Risk in Post-Infarction Patients
Afilliation | Scientific Computing |
Project(s) | MI-RISK: Risk factors for sudden cardiac death during acute myocardial infarction , Department of Computational Physiology |
Publication Type | Talks, contributed |
Year of Publication | 2019 |
Location of Talk | Computing in Cardiology, Singapore |
Proceedings, refereed
Automated and objective segmentation of medical image using machine learning techniques: all models are wrong, but some are useful
In Computational and Mathematical Biomedical Engineering. Sendai, Japan: CMBE, 2019.Status: Published
Automated and objective segmentation of medical image using machine learning techniques: all models are wrong, but some are useful
Medical images are the basis of ”patient-specific” simulations but come with severe limitations, most notably through operator dependencies like image segmentation. The aim was to develop an open- source pipeline for automated and objective segmentation. Combining latest advances from machine learning and signal processing, we demonstrate that the pipeline preserve all major characteristic features of a test image and identify minor branches, which can be further modified by the user. In conclusion, the default pipeline will in the majority of cases offer labor free automated and objective segmentation, or at worst provide an optimal starting point for manual segmentation.
Afilliation | Scientific Computing, Machine Learning |
Project(s) | Simula Metropolitan Center for Digital Engineering, Department of Computational Physiology |
Publication Type | Proceedings, refereed |
Year of Publication | 2019 |
Conference Name | Computational and Mathematical Biomedical Engineering |
Publisher | CMBE |
Place Published | Sendai, Japan |
Monte Carlo wavelets: a randomized approach to frame discretization
In Sampling Theory and Applications. IEEE, 2019.Status: Published
Monte Carlo wavelets: a randomized approach to frame discretization
Afilliation | Scientific Computing, Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Proceedings, refereed |
Year of Publication | 2019 |
Conference Name | Sampling Theory and Applications |
Publisher | IEEE |
Talks, invited
Automated parameter estimation for selected inverse problems
In Grenoble, France, 2019.Status: Published
Automated parameter estimation for selected inverse problems
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2019 |
Location of Talk | Grenoble, France |
Covariance and precision matrix estimation, and dimension reduction in regression problems
In Oslo, Norway, 2019.Status: Published
Covariance and precision matrix estimation, and dimension reduction in regression problems
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2019 |
Location of Talk | Oslo, Norway |
Towards nonlinear sufficient dimension reduction
In AIP conference, Grenoble, France, 2019.Status: Published
Towards nonlinear sufficient dimension reduction
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2019 |
Location of Talk | AIP conference, Grenoble, France |
Type of Talk | Conference talk |
Poster
Linear convergence and support recovery for non-convex multi-penalty regularization
SPARS 2019, Toulouse, France, 2019.Status: Published
Linear convergence and support recovery for non-convex multi-penalty regularization
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Poster |
Year of Publication | 2019 |
Place Published | SPARS 2019, Toulouse, France |
Unsupervised Parameter Selection in Variational Regularization
SPARS 2019, Toulouse, France, 2019.Status: Published
Unsupervised Parameter Selection in Variational Regularization
Afilliation | Scientific Computing, Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Poster |
Year of Publication | 2019 |
Place Published | SPARS 2019, Toulouse, France |
Journal Article
Nonlinear generalization of the monotone single index model
Information and Inference (2019).Status: Published
Nonlinear generalization of the monotone single index model
Afilliation | Scientific Computing, Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2019 |
Journal | Information and Inference |
Publisher | IMA |
Unsupervised parameter selection for denoising with the elastic net
Machine Learning (2019).Status: Submitted
Unsupervised parameter selection for denoising with the elastic net
Afilliation | Scientific Computing, Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2019 |
Journal | Machine Learning |
Publisher | Springer |
Poster
A geometrical approach for nonlinear single-index model estimation
ICML Workshop Stockholm, 2018.Status: Published
A geometrical approach for nonlinear single-index model estimation
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Poster |
Year of Publication | 2018 |
Place Published | ICML Workshop Stockholm |
High-dimensional function learning on curves
Cambridge, UK, 2018.Status: Published
High-dimensional function learning on curves
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Poster |
Year of Publication | 2018 |
Place Published | Cambridge, UK |
Inference and estimation for nonlinear single index models
Machine Learning Summer School Spain, 2018.Status: Published
Inference and estimation for nonlinear single index models
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Poster |
Year of Publication | 2018 |
Place Published | Machine Learning Summer School Spain |
Journal Article
A Learning Theory Approach to a Computationally Efficient Parameter Selection for the Elastic Net
arXiv (2018).Status: Submitted
A Learning Theory Approach to a Computationally Efficient Parameter Selection for the Elastic Net
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2018 |
Journal | arXiv |
Date Published | 09/2018 |
Publisher | arXiv |
Adaptive multi-penalty regularization based on a generalized Lasso path
Applied and Computational Harmonic Analysis (2018).Status: Published
Adaptive multi-penalty regularization based on a generalized Lasso path
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2018 |
Journal | Applied and Computational Harmonic Analysis |
Date Published | 11/2018 |
Publisher | Elsevier |
URL | https://www.sciencedirect.com/science/article/pii/S1063520318302902 |
DOI | 10.1016/j.acha.2018.11.001 |
Fast Dictionary Learning from Incomplete Data
EURASIP Journal on Advances in Signal Processing 2018, no. 1 (2018): 12.Status: Published
Fast Dictionary Learning from Incomplete Data
This paper extends the recently proposed and theoretically justified iterative thresholding and K residual means algorithm ITKrM to learning dicionaries from incomplete/masked training data (ITKrMM). It further adapts the algorithm to the presence of a low rank component in the data and provides a strategy for recovering this low rank component again from incomplete data. Several synthetic experiments show the advantages of incorporating information about the corruption into the algorithm. Finally, image inpainting is considered as application example, which demonstrates the superior performance of ITKrMM in terms of speed and/or reconstruction quality compared to its closest dictionary learning counterpart.
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2018 |
Journal | EURASIP Journal on Advances in Signal Processing |
Volume | 2018 |
Issue | 1 |
Pagination | 12 |
Date Published | 02/2018 |
Publisher | Springer |
URL | http://rdcu.be/HD8p |
DOI |
Talks, invited
A machine learning approach for adaptive parameter selection
In University of Oslo, Norway, 2018.Status: Published
A machine learning approach for adaptive parameter selection
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2018 |
Location of Talk | University of Oslo, Norway |
A machine learning approach to optimal regularization
In European Women in Mathematics, Graz, Austria, 2018.Status: Published
A machine learning approach to optimal regularization
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2018 |
Location of Talk | European Women in Mathematics, Graz, Austria |
A machine learning approach to optimal regularization: Affine Manifolds
In NTNU, Norway, 2018.Status: Published
A machine learning approach to optimal regularization: Affine Manifolds
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2018 |
Location of Talk | NTNU, Norway |
Multi-parameter regularization for solving inverse problems of unmixing type
In University of Cambridge, UK, 2018.Status: Published
Multi-parameter regularization for solving inverse problems of unmixing type
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2018 |
Location of Talk | University of Cambridge, UK |
Talks, contributed
Nonlinear estimation of single index models
In Nonlinear Data: Theory and Algorithms Oberwolfach, 2018.Status: Published
Nonlinear estimation of single index models
Afilliation | Machine Learning |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, contributed |
Year of Publication | 2018 |
Location of Talk | Nonlinear Data: Theory and Algorithms Oberwolfach |
Type of Talk | Workshop talk |
Talks, invited
A machine learning approach to optimal regularization: affine manifolds
In International Workshop Dictionary Learning on Manifolds, Nice, France, 2017.Status: Published
A machine learning approach to optimal regularization: affine manifolds
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2017 |
Location of Talk | International Workshop Dictionary Learning on Manifolds, Nice, France |
Type of Talk | keynote talk |
URL | http://dlm.cosmostat.org/programme/ |
A novel approach for prediction of the future blood glucose evolution in a diabetes patient
In AFib-TrainNet Status Seminar, Hamburg, Germany, 2017.Status: Submitted
A novel approach for prediction of the future blood glucose evolution in a diabetes patient
Afilliation | Scientific Computing |
Project(s) | AFib-TrainNet: EU Training Network on Novel Targets and Methods in Atrial Fibrillation, Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2017 |
Location of Talk | AFib-TrainNet Status Seminar, Hamburg, Germany |
Advanced statistics and data analysis for blood glucose prediction and diabetes
In Universitäres Herzzentrum Hamburg, Germany, 2017.Status: Accepted
Advanced statistics and data analysis for blood glucose prediction and diabetes
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2017 |
Location of Talk | Universitäres Herzzentrum Hamburg, Germany |
Type of Talk | Invited talk |
Dictionary Learning from Incomplete Data for Efficient Image Restoration
In 2017 European Signal Processing Conference, Kos Island, Greece. EURASIP, 2017.Status: Published
Dictionary Learning from Incomplete Data for Efficient Image Restoration
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, invited |
Year of Publication | 2017 |
Location of Talk | 2017 European Signal Processing Conference, Kos Island, Greece |
Publisher | EURASIP |
Type of Talk | Invited talk |
URL | http://www.eusipco2017.org |
Image separation using multi-penalty regularization
In CEA Saclay, France, 2017.Status: Published
Image separation using multi-penalty regularization
Afilliation | Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2017 |
Location of Talk | CEA Saclay, France |
Innovative solution of unmixing problems by means of multi-penalty regularization
In Applied Inverse Problems, Hangzhou, China, 2017.Status: Published
Innovative solution of unmixing problems by means of multi-penalty regularization
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2017 |
Location of Talk | Applied Inverse Problems, Hangzhou, China |
Journal Article
Adaptive multi-penalty regularization based on a generalized Lasso path
arXiv (2017).Status: Submitted
Adaptive multi-penalty regularization based on a generalized Lasso path
For many algorithms, parameter tuning remains a challenging task, which be- comes tedious in a multi-parameter setting. Multi-penalty regularization, suc- cessfully used for solving undetermined sparse regression problems of unmixing type, is one of such examples. We propose a novel algorithmic framework for an adaptive parameter choice in multi-penalty regularization with focus on correct support recovery. By extending ideas on regularization paths, we provide an efficient procedure for the construction of regions containing structurally sim- ilar solutions, i.e., solutions with the same sparsity and sign pattern, over the range of parameters. Combined with a model selection criterion, regularization parameters are chosen in a data-adaptive manner. Another advantage of our algorithm is that it provides an overview on the solution stability over the pa- rameter range. We provide a numerical analysis of our method and compare it to the state-of-the-art algorithms for compressed sensing problems to demonstrate the robustness and power of the proposed algorithm.
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Journal Article |
Year of Publication | 2017 |
Journal | arXiv |
Publisher | arXiv |
Keywords | adaptive parameter choice, compressed sensing, exact support recovery, Lasso path, multi-penalty regularization, noise folding |
Proceedings, refereed
Dictionary Learning from Incomplete Data for Efficient Image Restoration
In 2017 25th European Signal Processing Conference (EUSIPCO). IEEE, 2017.Status: Published
Dictionary Learning from Incomplete Data for Efficient Image Restoration
In real-world image processing applications, the data is high dimensional but the amount of high-quality data needed to train the model is very limited. In this paper, we extend a recently presented method for dictionary learning from incomplete data, the so-called Iterative Thresholding and $K$ residual Means for Masked data, to deal with high-dimensional data in an efficient way. In particular, the proposed algorithm incorporates a corruption model directly at the dictionary learning stage, also enabling reconstruction of the low-rank component again from corrupted signals. These modifications circumvent some difficulties associated with the efficient dictionary learning procedure in the presence of limited or incomplete data.
We choose an image inpainting problem as a guiding example, and further propose a procedure for automatic detection and reconstruction of the low-rank component from incomplete data and adaptive parameter selection for the sparse image reconstruction. We benchmark the efficacy and efficiency of our algorithm in terms of computing time and accuracy on colour and 3D medical images by comparing it to its dictionary learning counterparts.
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Proceedings, refereed |
Year of Publication | 2017 |
Conference Name | 2017 25th European Signal Processing Conference (EUSIPCO) |
Publisher | IEEE |
ISBN Number | 978-0-9928626-7-1 |
ISSN Number | 2076-1465 |
DOI | 10.23919/EUSIPCO.2017.8081444 |
Talk, keynote
Multi-parameter regularisation for solving unmixing problems in signal processing: theoretical and practical aspects
In Mathematical Signal Processing and Data Analysis, Bremen, Germany, 2017.Status: Published
Multi-parameter regularisation for solving unmixing problems in signal processing: theoretical and practical aspects
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talk, keynote |
Year of Publication | 2017 |
Location of Talk | Mathematical Signal Processing and Data Analysis, Bremen, Germany |
Date Published | 09/2017 |
Type of Talk | Plenary talk |
URL | http://www.math.uni-bremen.de/cda/GAMM-MSIP2017/#place |
Book Chapter
Multi-penalty regularization for detecting relevant variables
In Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science, 889-916. Novel Methods in Harmonic Analysis, ed. Vol. 2. Springer International Publishing, 2017.Status: Published
Multi-penalty regularization for detecting relevant variables
In this paper we propose a new method for detecting relevant variables
from a priori given high-dimensional data under the assumption that input-
output dependence is described by a nonlinear function depending on a few
variables. The method is based on the inspection of the behavior of discrepan-
cies of a multi-penalty regularization with a component-wise penalization for
small and large values of regularization parameters. We provide the justifica-
tion of the proposed method under a certain condition on sampling operators.
The effectiveness of the method is demonstrated in the example with synthetic
data and in the reconstruction of gene regulatory networks. In the latter ex-
ample, the obtained results provide a clear evidence of the competitiveness of
the proposed method.
Afilliation | Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Book Chapter |
Year of Publication | 2017 |
Book Title | Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science |
Volume | 2 |
Edition | Novel Methods in Harmonic Analysis, |
Pagination | 889-916 |
Publisher | Springer International Publishing |
Keywords | causality networks, gene regulatory networks., multi-penalty regularization, variables detection |
URL | http://www.springer.com/de/book/9783319555553 |
Talks, contributed
Nearly Optimal Parameter selection for the Elastic Net
In Hangzhou, China, 2017.Status: Published
Nearly Optimal Parameter selection for the Elastic Net
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Talks, contributed |
Year of Publication | 2017 |
Location of Talk | Hangzhou, China |
Proceedings, non-refereed
Robust Recovery of Low-Rank Matrices using Multi-Penalty Regularization
In NIPS Workshop Optimisation for Machine Learning. Long Beach, USA, 2017.Status: Published
Robust Recovery of Low-Rank Matrices using Multi-Penalty Regularization
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension |
Publication Type | Proceedings, non-refereed |
Year of Publication | 2017 |
Conference Name | NIPS Workshop Optimisation for Machine Learning |
Place Published | Long Beach, USA |
URL | http://opt-ml.org |
Journal Article
Combination of Neural Inverse Optimal Control with a Kernel-Based Regularization Learning Algorithm to Prevent Hypoglycemia in Type 1 Diabetes Patients
IEEE Transactions on Neural Networks and Learning Systems (2016).Status: Submitted
Combination of Neural Inverse Optimal Control with a Kernel-Based Regularization Learning Algorithm to Prevent Hypoglycemia in Type 1 Diabetes Patients
Hypoglycemia periods in Type 1 Diabetes mellitus (T1DM) patients are a dangerous condition leading to serious acute complications, such as diabetic coma or death.
Despite recent technological and scientific advances in T1DM therapy management, prevention of severe hypoglycemic periods still remains a challenge.
In this paper, we present a novel combination of a neural inverse optimal control via control Lyapunov function (CLF) combined with a kernel-based regularization learning
predictive algorithm (KAR) for optimal control of the blood glucose levels with a strong focus on timely detection and prevention of acute debilitating and harmful hypoglycemic
events. We describe how the proposed scheme can be used for aforementioned problem and report the results of the tests
on University of Virginia (UVA)/Padova Simulator as well as comparing them with existing literature. The performance assessment of the algorithms has been made with the use of control variability grid analysis (CVGA).
Afilliation | Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2016 |
Journal | IEEE Transactions on Neural Networks and Learning Systems |
Publisher | IEEE |
Conditions on optimal support recovery in unmixing problems by means of multi-penalty regularization
Inverse Problems 32, no. 10 (2016).Status: Published
Conditions on optimal support recovery in unmixing problems by means of multi-penalty regularization
Inspired by several real-life applications in audio processing and medical image analysis, where the quantity of interest is generated by several sources to be accurately modeled and separated, as well as by recent advances in regularization theory and optimization, we study the conditions on optimal support recovery in inverse problems of unmixing type by means of multi-penalty regularization.
We consider and analyze a regularization functional composed of a data-fidelity term, where signal and noise are additively mixed, a non-smooth, convex, sparsity promoting term, and a quadratic penalty term to model the noise. We prove not only that the well-established theory for sparse recovery in the single parameter case can be translated to the multi-penalty settings, but we also demonstrate the enhanced properties of multi-penalty regularization in terms of support identification compared to sole l1-minimization. We additionally confirm and support the theoretical results by extensive numerical simulations, which give a statistics of robustness of the multi-penalty regularization scheme with respect to the single-parameter counterpart.
Eventually, we confirm a significant improvement in performance compared to standard l1-regularization
for compressive sensing problems considered in our experiments.
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2016 |
Journal | Inverse Problems |
Volume | 32 |
Issue | 10 |
Date Published | 04/2016 |
Publisher | IOP |
URL | http://iopscience.iop.org/article/10.1088/0266-5611/32/10/104007/meta |
DOI | 10.1088/0266-5611/32/10/104007 |
Talks, invited
Dictionary Learning from Incomplete Data
In 2016 SIAM Conference on Imaging Science, 2016.Status: Published
Dictionary Learning from Incomplete Data
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2016 |
Location of Talk | 2016 SIAM Conference on Imaging Science |
From Big Data to Big Insights
In EUMLS Final Conference, 2016.Status: Published
From Big Data to Big Insights
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2016 |
Location of Talk | EUMLS Final Conference |
Innovative solution of unmixing problems by means of multi-penalty regularization: theoretical and algorithmical aspects
In University of Graz, 2016.Status: Published
Innovative solution of unmixing problems by means of multi-penalty regularization: theoretical and algorithmical aspects
Afilliation | Scientific Computing |
Project(s) | FunDaHD: Function-driven Data Learning in High Dimension, Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2016 |
Location of Talk | University of Graz |
Book Chapter
Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App
In Prediction Methods for Blood Glucose Concentration. Lecture Notes in Bioengineering. , 93-105. Aachen (Germany): Springer International Publishing, 2016.Status: Published
Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App
The obvious and highly accepted convenience of smartphone apps will, already in the nearest future, bring new opportunities for diabetes therapy management. In particular, it is expected that smartphones will be able to read, store, and display the blood glucose concentration from the continuous glucose monitoring systems. Using our knowledge and experience gained in the framework of the large-scale European Union FP7 funded project ``DIAdvisor: personal glucose predictive diabetes advisor'' (2008-2012), we explore a possibility to develop a novel smartphone app for diabetes patients that provides estimations of the future blood glucose concentration from current and past blood glucose readings. In addition to reliable clinical accuracy, a prediction algorithm implemented in such an app should satisfy multiple requirements, such as easily and quickly implementable on any mobile operating system, portability from individual to individual without readjustment or retraining procedure, and a low battery usage feature. In this study, we present a description of the prediction algorithm, developed in the course of the DIAdvisor project, and its version on Android OS that meets the above-mentioned requirements. Additionally, we compare the clinical accuracy of the algorithm with the state-of-the-art in terms of the ``gold standard'' metric, Clarke Error Grid Analysis, and the recently introduced metric, Prediction-Error Grid Analysis.
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Book Chapter |
Year of Publication | 2016 |
Book Title | Prediction Methods for Blood Glucose Concentration. Lecture Notes in Bioengineering. |
Pagination | 93-105 |
Date Published | 12/2015 |
Publisher | Springer International Publishing |
Place Published | Aachen (Germany) |
Book Chapter
Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences
In Statistics and Causality: Methods for Applied Empirical Research, 1-41. West Sussex, United Kingdom: John Wiley & Sons Limited Wiley, 2015.Status: Published
Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences
Granger causality, based on a vector autoregressive model, is one of the most popular methods for uncovering the temporal dependencies between time series. The application of Granger causality to detect inference among a big number of variables (genes) requires a variable selection procedure. To fight with lack of informative data, the so called regularization procedures are applied. In this chapter, we review current literature applying Granger causality with Lasso regularization technique for ill-posed problems. We discuss regularization procedures for inverse and ill-posed problems and present our recent approaches that are evaluated in a case study of gene regulatory networks reconstruction.
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Book Chapter |
Year of Publication | 2015 |
Book Title | Statistics and Causality: Methods for Applied Empirical Research |
Chapter | 1 |
Pagination | 1-41 |
Publisher | John Wiley & Sons Limited Wiley |
Place Published | West Sussex, United Kingdom |
Talk, keynote
Autumn School on Mathematical Imaging and Statistical Learning
In University of Verona, 2014.Status: Published
Autumn School on Mathematical Imaging and Statistical Learning
Making accurate predictions is a crucial factor in many systems (such as in medical treatments and prevention, geomathematics, social dynamics, financial computations) for cost savings, efficiency, health, safety, and organizational purposes. Learning theory and Machine learning provide a suitable framework and effective algorithms for a broad spectrum of real-life applications. The set of techniques based on these research areas already became a key technology to extract information from a vast amount of unstructured data around us and make sense of it.
Approaches developed in the framework of learning theory are very much dependent on the quality of measured data. However, the situation mostly encountered in real-life applications is to have only at disposal incomplete or rough high-dimensional data, and extracting a predictive model from them is an impossible task unless one can rely on some a-priori knowledge of properties of the expected model. The impossibility of making a reliable prediction is the result of the combination of different factors, the most relevant being the incompleteness of the data, the roughness/noisiness of the data, and their intrinsic high-dimensional nature.
In order to break simultaneously all of these negative factors playing against us in a predictive attempt, we shall use regularization methods in learning theory.
The main goals of the proposed course are to discuss the connections between regularization theory and learning theory by reviewing the state of the art machine learning algorithms and discussing strategies of further development.
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talk, keynote |
Year of Publication | 2014 |
Location of Talk | University of Verona |
Type of Talk | Invited Course within the Autumn School |
URL | http://profs.sci.univr.it/sip14/naumova_abstract.html |
Talks, invited
Meta-Learning Approach to the Image Denoising Problem
In SIAM Conference on Imaging Science, 2014.Status: Published
Meta-Learning Approach to the Image Denoising Problem
Afilliation | , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2014 |
Location of Talk | SIAM Conference on Imaging Science |
Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App
In Workshop on Design, use and evaluation of prediction methods for blood glucose concentration, 2014.Status: Published
Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App
Afilliation | Scientific Computing, , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2014 |
Location of Talk | Workshop on Design, use and evaluation of prediction methods for blood glucose concentration |
Minimization of Multi-Penalty Functionals by Alternating Iterative Thresholding and Optimal Parameter Choices
In SIAM Conference on Uncertainty Quantification, 2014.Status: Published
Minimization of Multi-Penalty Functionals by Alternating Iterative Thresholding and Optimal Parameter Choices
Afilliation | , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2014 |
Location of Talk | SIAM Conference on Uncertainty Quantification |
Multi-penalty Regularization for High-Dimensional Data Learning
In UCSD, 2014.Status: Published
Multi-penalty Regularization for High-Dimensional Data Learning
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2014 |
Location of Talk | UCSD |
Type of Talk | Invited Talk at Multimodal Imaging Lab Department of Cognitive Science |
Numerical Methods for Diabetes Technology
In UCSD, 2014.Status: Published
Numerical Methods for Diabetes Technology
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Talks, invited |
Year of Publication | 2014 |
Location of Talk | UCSD |
Type of Talk | Talk at the Cardiac Mechanics Lab Department of Bioengineering |
Poster
Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App
2014.Status: Published
Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App
Afilliation | , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Poster |
Year of Publication | 2014 |
Date Published | June |
Journal Article
Minimization of Multi-Penalty Functionals by Alternating Iterative Thresholding and Optimal Parameter Choices
Inverse Problems 30 (2014): 1-35.Status: Published
Minimization of Multi-Penalty Functionals by Alternating Iterative Thresholding and Optimal Parameter Choices
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity prior is motivated by the largely expected geometrical/structured features of high-dimensional data, which may not be well-represented in the framework of typically more isotropic Hilbert spaces. In this paper, we are particularly interested in regularizers which are able to correctly model and separate the multiple components of additively mixed signals. This situation is rather common as pure signals may be corrupted by additive noise. To this end, we consider a regularization functional composed by a data-fidelity term, where signal and noise are additively mixed, a non-smooth and non-convex sparsity promoting term, and a penalty term to model the noise. We propose and analyze the convergence of an iterative alternating algorithm based on simple iterative thresholding steps to perform the minimization of the functional. By means of this algorithm, we explore the effect of choosing different regularization parameters and penalization norms in terms of the quality of recovering the pure signal and separating it from additive noise. For a given fixed noise level numerical experiments confirm a significant improvement in performance compared to standard one-parameter regularization methods. By using high-dimensional data analysis methods such as principal component analysis, we are able to show the correct geometrical clustering of regularized solutions around the expected solution. Eventually, for the compressive sensing problems considered in our experiments we provide a guideline for a choice of regularization norms and parameters.
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2014 |
Journal | Inverse Problems |
Volume | 30 |
Number | 12 |
Pagination | 1-35 |
Date Published | October |
Publisher | IOP Publishing |
Place Published | Bristol, UK |
DOI | 10.1088/0266-5611/30/12/125003 |
Multi-Penalty Regularization for Detecting Relevant Variables
Computational Statistics and Data Analysis (2014).Status: Submitted
Multi-Penalty Regularization for Detecting Relevant Variables
In this paper we propose a new method for detecting relevant variables from a priori given high-dimensional data under the assumption that input-output dependence is described by a nonlinear function depending on a few variables. The method is based on the inspection of the behavior of discrepancies of a multi-penalty regularization with a component-wise penalization for small and large values of regularization parameters. We provide the justification of the proposed method under a certain condition on sampling operators. The effectiveness of the method is demonstrated in the example with synthetic data and in the reconstruction of gene regulatory networks. In the latter example, the obtained results provide a clear evidence of the competitiveness of the proposed method.
Afilliation | , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2014 |
Journal | Computational Statistics and Data Analysis |
Publisher | unknown |
Place Published | unknown |
Parameter Choice Strategies for Multi-Penalty Regularization
SIAM Journal on Numerical Analysis 52 (2014): 1770-1794.Status: Published
Parameter Choice Strategies for Multi-Penalty Regularization
The widespread applicability of the multipenalty regularization is limited by the fact that theoretically optimal rate of reconstruction for a given problem can be realized by a one-parameter counterpart, provided that relevant information on the problem is available and taken into account in the regularization. In this paper, we explore the situation where no such information is given, but still accuracy of optimal order can be guaranteed by employing multipenalty regularization. Our focus is on the analysis and the justification of an a posteriori parameter choice rule for such a regularization scheme. First we present a modified version of the discrepancy principle within the multipenalty regularization framework. As a consequence we provide a theoretical justification to the multipenalty regularization scheme equipped with the a posteriori parameter choice rule. We then establish a fast numerical realization of the proposed discrepancy principle based on a model function approximation. Finally, we provide extensive numerical results which confirm and support the theoretical estimates and illustrate the robustness and the superiority of the proposed scheme compared to the “classical” regularization methods.
Afilliation | , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2014 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 52 |
Number | 4 |
Pagination | 1770-1794 |
Publisher | Society for Industrial and Applied Mathematics |
Place Published | Philadelphia, USA |
DOI | 10.1137/130930248 |
Regularized collocation for spherical harmonics gravitational field modeling
GEM - International Journal on Geomathematics 5, no. 1 (2014): 81-98.Status: Published
Regularized collocation for spherical harmonics gravitational field modeling
Motivated by the problem of satellite gravity gradiometry, which is the reconstruction of the Earth gravity potential from the satellite data provided in the form of the second-order partial derivatives of the gravity potential at a satellite altitude, we discuss a special regularization technique for solving this severely ill-posed problem in a spherical framework. We are especially interested in the regularized collocation method. As a core ingredient we present an a posteriori parameter choice rule, namely the weighted discrepancy principle, and prove its order optimality. Finally, we illustrate our theoretical findings by numerical results for the computation of the Fourier coefficients of the gravitational potential directly from the noisy synthetic data.
Afilliation | Scientific Computing, |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2014 |
Journal | GEM - International Journal on Geomathematics |
Volume | 5 |
Issue | 1 |
Pagination | 81-98 |
Date Published | 04/2014 |
Publisher | Springer |
Place Published | Berlin Heidelberg |
Keywords | Collocation method, Discrepancy principle, Ill-posed problem, Regularization, Satellite gravity modeling, Spherical harmonics |
Miscellaneous
Multi-Parameter Regularization and High-Dimensional Learning
Savannah, USA: SIAM Uncertainty Quantification, 2014.Status: Published
Multi-Parameter Regularization and High-Dimensional Learning
Making accurate predictions is a crucial factor in many systems. The situation encountered in real-life applications is to have only at disposal incomplete/ rough high-dimensional data, and
extracting predictive model from them is an impossible task unless one relies on some a-priori knowledg of properties of expected model. To
overcome these fundamental challenges, we incorporate additional information through optimization by means of multiparameter
regularization. The main goals of the proposed minisymposium are to set up a new agenda and give a new impulse to the cooperation between
approximation and regularization theories within the intrinsic uncertainty of learning process for real-life data.
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Publication Type | Miscellaneous |
Year of Publication | 2014 |
Publisher | SIAM Uncertainty Quantification |
Place Published | Savannah, USA |
Notes | Co-organizer of the minisymposium |
URL | https://www.siam.org/meetings/uq14/uq14_program.pdf |
Journal Article
Multi-penalty regularization with a component-wise penalization
Inverse Problems 29 (2013): 15.Status: Published
Multi-penalty regularization with a component-wise penalization
We discuss a new regularization scheme for reconstructing the solution of a
linear ill-posed operator equation from given noisy data in the Hilbert space
setting. In this new scheme, the regularized approximation is decomposed
into several components, which are defined by minimizing a multi-penalty
functional. We show theoretically and numerically that under a proper choice
of the regularization parameters, the regularized approximation exhibits the
so-called compensatory property, in the sense that it performs similar to the
best of the single-penalty regularization with the same penalizing operator.
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Publication Type | Journal Article |
Year of Publication | 2013 |
Journal | Inverse Problems |
Volume | 29 |
Pagination | 15 |
Publisher | IOP Publishing |
Keywords | inverse problems, parameter choice, Regularization |
Journal Article
A meta-learning approach to the regularized learning—Case study: Blood glucose prediction
Neural Networks 33 (2012): 181-193.Status: Published
A meta-learning approach to the regularized learning—Case study: Blood glucose prediction
In this paper we present a new scheme of a kernel-based regularization learning algorithm, in which the kernel and the regularization parameter are adaptively chosen on the base of previous experience with similar learning tasks. The construction of such a scheme is motivated by the problem of prediction of the blood glucose levels of diabetic patients. We describe how the proposed scheme can be used for this problem and report the results of the tests with real clinical data as well as comparing them with existing literature.
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Publication Type | Journal Article |
Year of Publication | 2012 |
Journal | Neural Networks |
Volume | 33 |
Pagination | 181–193 |
Publisher | Elsevier |
Keywords | Learning theory; Meta-learning; Adaptive parameter choice; Kernel choice; Regularization; Blood glucose prediction |
Book
Numerical Methods for Diabetes Technology
In Mathematical Algorithms for a Better Management of Type 1 Diabetes. Germany: LAP LAMBERT Academic Publishing, 2012.Status: Published
Numerical Methods for Diabetes Technology
In this work, we develop new mathematical tools for diabetes therapy management, where the key problem is to predict the future blood glucose levels of a diabetic patient from available current and past information about therapeutically valuable factors. We provide a theoretical analysis of the developed techniques and demonstrate them in real-life applications. To show the efficiency of the developed mathematical tools, we provide an extensive collection of the results of numerical experiments with simulated and real clinical data, as well as comparing them with existing literature. This research has been performed in the course of the project 'DIAdvisor' (DIAdvisor: personal glucose predictive diabetes advisor) funded by the European Commission within 7-th Framework Programme. The author gratefully acknowledges the support of the 'DIAdvisor' consortium.
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Publication Type | Book |
Year of Publication | 2012 |
Secondary Title | Mathematical Algorithms for a Better Management of Type 1 Diabetes |
Number of Pages | 176 |
Publisher | LAP LAMBERT Academic Publishing |
Place Published | Germany |
Keywords | adaptive parameter choice, diabetes technology, DIAdvisor, inverse problems, learning theory, Meta-Learning, numerical analysis, numerical differentiation, prediction of the blood glucose concentration, Regularization methods |
Journal Article
Assessment of Blood Glucose Predictors: The Prediction-Error Grid Analysis
Diabetes Technology & Therapeutics 13, no. 8 (2011): 787-796.Status: Published
Assessment of Blood Glucose Predictors: The Prediction-Error Grid Analysis
Background: Prediction of the future blood glucose (BG) evolution from continuous glucose monitoring (CGM) data is a promising direction in diabetes therapy management, and several glucose predictors have recently been proposed. This raises the problem of their assessment. There were attempts to use for such assessment the continuous glucose-error grid analysis (CG-EGA), originally developed for CGM devices. However, in the CG-EGA the BG rate of change is estimated from past BG readings, whereas predictors provide BG estimation ahead of time. Therefore, the original CG-EGA should be modified to assess predictors. Here we propose a new version of the CG-EGA, the Prediction-Error Grid Analysis (PRED-EGA).
Methods: The analysis is based both on simulated data and on data from clinical trials, performed in the European FP7-project “DIAdvisor.” Simulated data are used to test the ability of the analyzed CG-EGA modifications to capture erroneous predictions in controlled situation. Real data are used to show the impact of the different CG-EGA versions in the evaluation of a predictor.
Results: Using the data of 10 virtual and 10 real subjects and analyzing two different predictors, we demonstrate that the straightforward application of the CG-EGA does not adequately classify the prediction performance. For example, we observed that up to 70% of 20 min ahead predictions in the hyperglycemia region that are classified by this application as erroneous are, in fact, accurate. Moreover, for predictions during hypoglycemia the assessments produced by the straightforward application of the CG-EGA are not only too pessimistic (in up to 60% of cases), but this version is not able to detect real erroneous predictions. In contrast, the proposed modification of the CG-EGA, where the rate of change is estimated on the predicted BG profile, is an adequate metric for the assessment of predictions.
Conclusions: We propose a new CG-EGA, the PRED-EGA, for the assessment of glucose predictors. The presented analysis shows that, compared with the straightforward application of the CG-EGA, the PRED-EGA gives a significant reduction of the misclassification cases. A reduction by a factor of at least 4 was observed in the study. Moreover, the PRED-EGA is much more robust against uncertainty in the input and references.
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Publication Type | Journal Article |
Year of Publication | 2011 |
Journal | Diabetes Technology & Therapeutics |
Volume | 13 |
Issue | 8 |
Pagination | 787-796 |
Publisher | Mary Ann Liebert Inc |
Keywords | diabetes, predictor assessment |
Extrapolation in variable RKHSs with application to the blood glucose reading
Inverse Problems 27, no. 7 (2011): 075010.Status: Published
Extrapolation in variable RKHSs with application to the blood glucose reading
In this paper we present a new scheme of a kernel adaptive regularization algorithm, where the kernel and the regularization parameter are adaptively chosen within the regularization procedure. The construction of such a fully adaptive regularization algorithm is motivated by the problem of reading the blood glucose concentration of diabetic patients. We describe how the proposed scheme can be used for this purpose and report the results of numerical experiments with real clinical data.
Afilliation | Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Publication Type | Journal Article |
Year of Publication | 2011 |
Journal | Inverse Problems |
Volume | 27 |
Issue | 7 |
Pagination | 075010 |
Publisher | IOP Publishing |
Keywords | deiabetes management, inverse problems, Regularization, RKHS |
Proceedings, refereed
Reading blood glucose from subcutaneous electric current by means of a regularization in variable Reproducing Kernel Hilbert Spaces
In IEEE Conference on Decision and Control and European Control Conference. IEEE, 2011.Status: Published
Reading blood glucose from subcutaneous electric current by means of a regularization in variable Reproducing Kernel Hilbert Spaces
In this paper we propose an adaptive kernel
regularization algorithm for blood glucose reading from subcutaneous
electric current. We illustrate the proposed algorithm
with clinical data and quantify its clinical accuracy by means
of the Clarke error grid analysis (EGA) and by the number
of detected hypoglycemic events. We show that the proposed
algorithm provides more accurate blood glucose reading than
a commercially available system.
Afilliation | Scientific Computing |
Project(s) | No Simula project |
Publication Type | Proceedings, refereed |
Year of Publication | 2011 |
Conference Name | IEEE Conference on Decision and Control and European Control Conference |
Pagination | 5158-5163 |
Publisher | IEEE |