Publications related to High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

Spatially Varying Monte Carlo SURE for the Regularization of Biomedical Images

Regularization, filtering, and denoising of biomedical images requires the use of appropriate filters and the adoption of efficient regularization criteria. It has been shown that the Stein’s Unbiased Risk Estimate (SURE) can be used as a proxy for the mea ...

IEEE2019

Regularization via Mass Transportation

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, ...

2019

Robust myelin water imaging from multi-echo T2 data using second-order Tikhonov regularization with control points

Jean-Philippe Thiran, Tobias Kober, Tom Hilbert, Erick Jorge Canales Rodriguez, Marco Pizzolato, Gian Franco Piredda, Alessandro Daducci, Nicolas Kunz

Myelin water imaging is an MRI technique used to quantify myelination in the brain. The state-of-the-art reconstruction method is based on non-negative least squares optimization with zero-order Tikhonov regularization. In this study, a second-order Tikhon ...

2019

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

Martin Jaggi, Chenxin Ma

The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient communication scheme a ...

MICROTOME PUBL2018

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Xin Liu, Hanjie Pan, Feng Xue, Jiaqi Liu

Recently, the type of compound regularizers has become a popular choice for signal reconstruction. The estimation quality is generally sensitive to the values of multiple regularization parameters. In this work, based on BDF algorithm, we develop a data-dr ...

Ieee2017

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

EPFL2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

Some Developments of the Cooray–Rubinstein Formula in the Time Domain

A rigorous formula representing the counterpart of the Cooray-Rubinstein expression in the time domain has recently been derived by the authors. In this paper, the formula is particularized for the cases of a unit step and a linearly rising channel-base cu ...

Institute of Electrical and Electronics Engineers2015

An Equivalence between the Lasso and Support Vector Machines

Martin Jaggi

We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show that the resulting optimization problems are eq ...

Chapman and Hall/CRC2014

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

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Spatially Varying Monte Carlo SURE for the Regularization of Biomedical Images

Regularization via Mass Transportation

Robust myelin water imaging from multi-echo T2 data using second-order Tikhonov regularization with control points

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Some Developments of the Cooray–Rubinstein Formula in the Time Domain

An Equivalence between the Lasso and Support Vector Machines

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Spatially Varying Monte Carlo SURE for the Regularization of Biomedical Images

Regularization via Mass Transportation

CoCoA: A General Framework for Communication-Efficient Distributed Optimization

Optimization Of Compound Regularization Parameters Based On Stein'S Unbiased Risk Estimate

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Robust myelin water imaging from multi-echo T2 data using second-order Tikhonov regularization with control points

Some Developments of the Cooray–Rubinstein Formula in the Time Domain

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

An Equivalence between the Lasso and Support Vector Machines