Related papers: Deep Learning for Subspace Regression

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

A growing number of problems in computational mathematics can be reduced to the solution of many linear systems that are related, often depending smoothly or slowly on a parameter $p$, that is, $A(p)x(p)=b(p)$. We introduce an efficient…

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…

In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…

A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…

spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…

We propose a self-supervised approach for learning physics-based subspaces for real-time simulation. Existing learning-based methods construct subspaces by approximating pre-defined simulation data in a purely geometric way. However, this…

Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…

Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show…

The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…

Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…

In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…

We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…