@inproceedings {27871,
	title = {Data-driven Personalized Cervical Cancer Risk Prediction: A Graph-Perspective},
	journal = {IEEE Statistical Signal Processing Workshop 2021},
	year = {2021},
	pages = {46-50},
	publisher = { IEEE},
	doi = {10.1109/SSP49050.2021.9513824},
	author = {Gogineni, Vinay and Severin R. E. {Langberg} and Naumova, Valeriya and Jan F {Nyg{\r a}rd} and Nyg{\r a}rd, Mari and Grasmair, Markus and Werner, Stefan}
}
@article {25617,
	title = {Adaptive multi-penalty regularization based on a generalized Lasso path},
	journal = {Applied and Computational Harmonic Analysis},
	year = {2018},
	month = {11/2018},
	publisher = {Elsevier},
	doi = {https://doi.org/10.1016/j.acha.2018.11.001},
	url = {https://www.sciencedirect.com/science/article/pii/S1063520318302902},
	author = {Grasmair, Markus and Klock, Timo and Naumova, Valeriya}
}
@article {25613,
	title = {Adaptive multi-penalty regularization based on a generalized Lasso path},
	journal = {arXiv},
	year = {2017},
	publisher = {arXiv},
	abstract = {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.\&nbsp;},
	keywords = {adaptive parameter choice, compressed sensing, exact support recovery, Lasso path, multi-penalty regularization, noise folding},
	author = {Grasmair, Markus and Klock, Timo and Naumova, Valeriya}
}
@article {23927,
	title = {Conditions on optimal support recovery in unmixing problems by means of multi-penalty regularization},
	journal = {Inverse Problems},
	volume = {32},
	year = {2016},
	month = {04/2016},
	publisher = {IOP},
	abstract = {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 \&nbsp;regularization theory and optimization, we study the conditions on optimal support recovery in inverse problems of unmixing type by means of multi-penalty regularization. \&nbsp;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 \&nbsp;the well-established theory for sparse recovery in the single parameter case can be translated to the multi-penalty settings, but \&nbsp;we also demonstrate the enhanced properties of multi-penalty regularization in terms of support identification compared to sole l1-minimization. \&nbsp;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.\&nbsp;Eventually, we confirm a significant improvement in performance compared to standard l1-regularizationfor \&nbsp;compressive sensing problems considered in our experiments.\&nbsp;},
	doi = {https://doi.org/10.1088/0266-5611/32/10/104007},
	url = {http://iopscience.iop.org/article/10.1088/0266-5611/32/10/104007/meta},
	author = {Grasmair, Markus and Naumova, Valeriya}
}
