Related papers: Using Supervised Learning to Construct the Best Re…

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…

In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…

In this paper we investigate the connection between supervised learning and linear inverse problems. We first show that a linear inverse problem can be view as a function approximation problem in a reproducing kernel Hilbert space (RKHS)…

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…

The exponential growth of volume, variety and velocity of data is raising the need for investigations of automated or semi-automated ways to extract useful patterns from the data. It requires deep expert knowledge and extensive…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…

Recently, with the significant developments in deep learning techniques, solving underdetermined inverse problems has become one of the major concerns in the medical imaging domain. Typical examples include undersampled magnetic resonance…

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…

Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…

This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are…

Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…

Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely…

Many real-world phenomena are observed at multiple resolutions. Predictive models designed to predict these phenomena typically consider different resolutions separately. This approach might be limiting in applications where predictions are…

In this work, we propose a simple yet effective meta-learning algorithm in semi-supervised learning. We notice that most existing consistency-based approaches suffer from overfitting and limited model generalization ability, especially when…