Related papers: Large deviation inequalities for the nonlinear unb…
We consider the problem of estimating means of two Gaussians in a 2-Gaussian mixture, which is not balanced and is corrupted by noise of an arbitrary distribution. We present a robust algorithm to estimate the parameters, together with…
The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical…
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Many statistical applications require an estimate of a covariance matrix and/or its inverse. When the matrix dimension is large compared to the sample size, which happens frequently, the sample covariance matrix is known to perform poorly…
We introduce a linear-scaling stochastic method to compute real-space maps of any positive local spectral operator in a tight-binding model. By employing positive-definite estimators, the sampling error at each site can be rigorously…
Anomaly detection in medical imaging is a challenging task in contexts where abnormalities are not annotated. This problem can be addressed through unsupervised anomaly detection (UAD) methods, which identify features that do not match with…
We apply the iterative nonlinear programming method, previously proposed in our earlier work, to optimize Schur test functions and thereby provide refined upper bounds for the norms of integral operators. As an illustration, we derive such…
The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…
We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…
We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)=…
Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An urn contains coloured balls, which can be drawn with probabilities proportional to the numbers of balls of…
The four-dimensional nonlinear model is extended to include the inter-channel stimulated Raman scattering, enabling accurate prediction of dual-polarization four-dimensional modulation formats and probabilistically shaped constellations in…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
We conduct a study of graphical models and discuss the quality of model selection approximation by formulating the problem as a detection problem and examining the area under the curve (AUC). We are specifically looking at the model…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more…
As instruction-tuned large language models (LLMs) evolve, aligning pretrained foundation models presents increasing challenges. Existing alignment strategies, which typically leverage diverse and high-quality data sources, often overlook…
Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…