@inbook {24104,
	title = {Multi-penalty regularization for detecting relevant variables},
	booktitle = {Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science},
	volume = {2},
	year = {2017},
	pages = {889-916},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	edition = {Novel Methods in Harmonic Analysis,},
	abstract = {In this paper we propose a new method for detecting relevant variablesfrom a priori given high-dimensional data under the assumption that input-output dependence is described by a nonlinear function depending on a fewvariables. The method is based on the inspection of the behavior of discrepan-cies of a multi-penalty regularization with a component-wise penalization forsmall 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 syntheticdata and in the reconstruction of gene regulatory networks. In the latter ex-ample, the obtained results provide a clear evidence of the competitiveness ofthe proposed method.},
	keywords = {causality networks, gene regulatory networks., multi-penalty regularization, variables detection},
	url = {http://www.springer.com/de/book/9783319555553},
	author = {Hlavackova-Schindler, Katerina and Naumova, Valeriya and Sergei V {Pereverzyev}},
	editor = {Pesenson, Isaac}
}
@inbook {Simula.simula.3100,
	title = {Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App},
	booktitle = {Prediction Methods for Blood Glucose Concentration. Lecture Notes in Bioengineering. },
	year = {2016},
	month = {12/2015},
	pages = {93-105},
	publisher = {Springer International Publishing},
	organization = {Springer International Publishing},
	address = {Aachen (Germany)},
	abstract = {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 {\textquoteleft}{\textquoteleft}DIAdvisor: personal glucose predictive diabetes advisor{\textquoteright}{\textquoteright} (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 {\textquoteleft}{\textquoteleft}gold standard{\textquoteright}{\textquoteright} metric, Clarke Error Grid Analysis, and the recently introduced metric, Prediction-Error Grid Analysis.},
	author = {Naumova, Valeriya and Nita, Lucian and Poulsen, Jens and Sergei V {Pereverzyev}}
}
@inbook {Simula.simula.3070,
	title = {Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences},
	booktitle = {Statistics and Causality: Methods for Applied Empirical Research},
	year = {2015},
	pages = {1-41},
	publisher = {John Wiley \& Sons Limited Wiley},
	organization = {John Wiley \& Sons Limited Wiley},
	chapter = {1},
	address = {West Sussex, United Kingdom},
	abstract = {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.},
	author = {Naumova, Valeriya and Hlavackova-Schindler, Katerina and Sergei V {Pereverzyev}},
	editor = {Wiedermann, Wolfgang and von Eye, Alexander}
}
@misc {Simula.simula.2842,
	title = {Meta-Learning Based Blood Glucose Predictor for Diabetic Smartphone App},
	year = {2014},
	month = {June},
	author = {Naumova, Valeriya and Sergei V {Pereverzyev} and Nita, Lucian and Poulsen, Jens}
}
@misc {24107,
	title = {Multi-Parameter Regularization and High-Dimensional Learning},
	year = {2014},
	note = {Co-organizer of the minisymposium},
	publisher = {SIAM Uncertainty Quantification},
	address = {Savannah, USA},
	abstract = {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, andextracting predictive model from them is an impossible task unless one relies on some a-priori knowledg of properties of expected model. Toovercome these fundamental challenges, we incorporate additional information through optimization by means of multiparameterregularization. The main goals of the proposed minisymposium are to set up a new agenda and give a new impulse to the cooperation betweenapproximation and regularization theories within the intrinsic uncertainty of learning process for real-life data.},
	url = {https://www.siam.org/meetings/uq14/uq14_program.pdf},
	author = {Fornasier, Massimo and Naumova, Valeriya and Sergei V {Pereverzyev}}
}
@article {Simula.simula.3098,
	title = {Multi-Penalty Regularization for Detecting Relevant Variables},
	journal = {Computational Statistics and Data Analysis},
	year = {2014},
	publisher = {unknown},
	address = {unknown},
	abstract = {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.},
	author = {Hlavackova-Schindler, Katerina and Naumova, Valeriya and Sergei V {Pereverzyev}}
}
@article {Simula.simula.2840,
	title = {Parameter Choice Strategies for Multi-Penalty Regularization},
	journal = {SIAM Journal on Numerical Analysis},
	volume = {52},
	number = {4},
	year = {2014},
	pages = {1770-1794},
	publisher = {Society for Industrial and Applied Mathematics},
	address = {Philadelphia, USA},
	abstract = {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 {\textquotedblleft}classical{\textquotedblright} regularization methods.},
	doi = {10.1137/130930248},
	author = {Naumova, Valeriya and Fornasier, Massimo and Sergei V {Pereverzyev}}
}
@article {24103,
	title = {Regularized collocation for spherical harmonics gravitational field modeling},
	journal = {GEM - International Journal on Geomathematics},
	volume = {5},
	year = {2014},
	month = {04/2014},
	pages = {81-98},
	publisher = {Springer},
	address = {Berlin Heidelberg},
	abstract = {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.},
	keywords = {Collocation method, Discrepancy principle, Ill-posed problem, Regularization, Satellite gravity modeling, Spherical harmonics},
	author = {Naumova, Valeriya and Sergei V {Pereverzyev} and Tkachenko, Pavlo}
}
@article {24114,
	title = {Multi-penalty regularization with a component-wise penalization},
	journal = {Inverse Problems},
	volume = {29},
	year = {2013},
	pages = {15},
	publisher = {IOP Publishing},
	abstract = {We discuss a new regularization scheme for reconstructing the solution of alinear ill-posed operator equation from given noisy data in the Hilbert spacesetting. In this new scheme, the regularized approximation is decomposedinto several components, which are defined by minimizing a multi-penaltyfunctional. We show theoretically and numerically that under a proper choiceof the regularization parameters, the regularized approximation exhibits theso-called compensatory property, in the sense that it performs similar to thebest of the single-penalty regularization with the same penalizing operator.},
	keywords = {inverse problems, parameter choice, Regularization},
	author = {Naumova, Valeriya and Sergei V {Pereverzyev}}
}
@article {24110,
	title = {A meta-learning approach to the regularized learning{\textemdash}Case study: Blood glucose prediction},
	journal = {Neural Networks},
	volume = {33},
	year = {2012},
	pages = {181{\textendash}193},
	publisher = {Elsevier},
	abstract = {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.},
	keywords = {Learning theory; Meta-learning; Adaptive parameter choice; Kernel choice; Regularization; Blood glucose prediction},
	author = {Naumova, Valeriya and Sergei V {Pereverzyev} and Sampath, Sivananthan}
}
@article {24111,
	title = {Assessment of Blood Glucose Predictors: The Prediction-Error Grid Analysis},
	journal = {Diabetes Technology \& Therapeutics},
	volume = {13},
	year = {2011},
	pages = {787-796},
	publisher = {Mary Ann Liebert Inc},
	abstract = {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 \&ldquo;DIAdvisor.\&rdquo; 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\&thinsp;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.},
	keywords = {diabetes, predictor assessment},
	author = {Sivananthan, Sampath and Naumova, Valeriya and Chiara Dalla {Man} and Facchinetti, Andrea and Renard, Eric and Cobelli, Claudio and Sergei V {Pereverzyev}}
}
@article {24112,
	title = {Extrapolation in variable RKHSs with application to the blood glucose reading},
	journal = {Inverse Problems},
	volume = {27},
	year = {2011},
	pages = {075010},
	publisher = {IOP Publishing},
	abstract = {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.},
	keywords = {deiabetes management, inverse problems, Regularization, RKHS},
	author = {Naumova, Valeriya and Sergei V {Pereverzyev} and Sampath, Sivananthan}
}
@inproceedings {24115,
	title = {Reading blood glucose from subcutaneous electric current by means of a regularization in variable Reproducing Kernel Hilbert Spaces},
	journal = {IEEE Conference on Decision and Control and European Control Conference},
	year = {2011},
	pages = {5158-5163},
	publisher = {IEEE},
	abstract = {In this paper we propose an adaptive kernelregularization algorithm for blood glucose reading from subcutaneouselectric current. We illustrate the proposed algorithmwith clinical data and quantify its clinical accuracy by meansof the Clarke error grid analysis (EGA) and by the numberof detected hypoglycemic events. We show that the proposedalgorithm provides more accurate blood glucose reading thana commercially available system.},
	author = {Naumova, Valeriya and Sergei V {Pereverzyev} and Sampath, Sivananthan}
}
