相关论文: On the novel geometric and negative binomial INAR(…

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Consistent improvement of image priors over the years has led to the development of better inverse problem solvers. Diffusion models are the newcomers to this arena, posing the strongest known prior to date. Recently, such models operating…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inverses are used. Most…

The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for…

In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…

Group Relative Policy Optimization (GRPO) has emerged as a promising critic-free reinforcement learning paradigm for reasoning tasks. However, standard GRPO employs a coarse-grained credit assignment mechanism that propagates group-level…

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive…

Recently, impressive denoising results have been achieved by Bayesian approaches which assume Gaussian models for the image patches. This improvement in performance can be attributed to the use of per-patch models. Unfortunately such an…

Motivated by the general robustness properties of the 01 loss we propose a single hidden layer 01 loss neural network trained with stochastic coordinate descent as a defense against adversarial attacks in machine learning. One measure of a…

Transformation Synchronization is the problem of recovering absolute transformations from a given set of pairwise relative motions. Despite its usefulness, the problem remains challenging due to the influences from noisy and outlier…

The recent explosive interest in the reasoning capabilities of large language models, such as DeepSeek-R1, has demonstrated remarkable success through reinforcement learning-based fine-tuning frameworks, exemplified by methods like Group…

Binary neural networks (BNNs), where both weights and activations are binarized into 1 bit, have been widely studied in recent years due to its great benefit of highly accelerated computation and substantially reduced memory footprint that…

We develop a novel reference prior for Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) random effects. This is particularly important in the context of objective Bayes variable selection with sample size $n$…

The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…

A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…

Recently, machine learning has been introduced in the inverse design of physical devices, i.e., the automatic generation of device geometries for a desired physical response. In particular, generative adversarial networks have been proposed…

In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications such complex systems can be associated with some underlying…

Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving…