Related papers: Measure-Valued Variational Models with Application…
We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where…
Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for…
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…
In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused…
Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the…
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
This paper deals with collisionless transport equations in bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonally invariant velocity measure $\bm{m}(\d v)$ with support…
Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To…
This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and…
Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…
We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…
We give formulas for the spectral radius of weighted endomorphisms $a\alpha: C(X,D)\to C(X,D)$, $a\in C(X,D)$, where $X$ is a compact Hausdorff space and $D$ is a unital Banach algebra. Under the assumption that $\alpha$ generates a partial…
We resume the results from \cite{Vershik FA} on the classification of measurable functions in several variables, with some minor corrections of purely technical nature, and give a partial solution to the characterization problem of…
Ultrasound imaging, despite its widespread use in medicine, often suffers from various sources of noise and artifacts that impact the signal-to-noise ratio and overall image quality. Enhancing ultrasound images requires a delicate balance…