Related papers: Optimal Rates For Regularization Of Statistical In…
Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is…
In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…
Learning meaningful representations that maintain the content necessary for a particular task while filtering away detrimental variations is a problem of great interest in machine learning. In this paper, we tackle the problem of learning…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
We consider ill-posed inverse problems where the forward operator $T$ is unknown, and instead we have access to training data consisting of functions $f_i$ and their noisy images $Tf_i$. This is a practically relevant and challenging…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. The predominant approach is to alter the supervised learning pipeline by augmenting typical loss functions, letting model…
Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper,…