Related papers: Numerical Identification of Nonlocal Potential in …
Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub- diffusions driven by fractional…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
This work presents a parallel variant of the algorithm introduced in [Acceleration of block coordinate descent methods with identification strategies Comput. Optim. Appl. 72(3):609--640, 2019] to minimize the sum of a partially separable…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
As with many other problems, real-world regression is plagued by the presence of noisy labels, an inevitable issue that demands our attention. Fortunately, much real-world data often exhibits an intrinsic property of continuously ordered…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
Collective graphical models exploit inter-instance associative dependence to output more accurate labelings. However existing models support very limited kind of associativity which restricts accuracy gains. This paper makes two major…
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…
We propose an outlier robust multivariate time series model which can be used for detecting previously unseen anomalous sounds based on noisy training data. The presented approach doesn't assume the presence of labeled anomalies in the…
Sparse training reduces the memory and computational costs of deep neural networks. However, sparse optimization methods, e.g., those adding an $\ell_1$ penalty, often control sparsity only indirectly through a regularization parameter…
The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…
Sparse solution problems play an important role in both signal processing and image restoration. In this paper, we propose a stochastic column-block nonlinear Bregman method for efficiently computing sparse solutions to nonlinear systems.…
Numerical homogenization, i.e. the finite-dimensional approximation of solution spaces of PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements. These basis elements are oftentimes found after a…
Subspace segmentation assumes that data comes from the union of different subspaces and the purpose of segmentation is to partition the data into the corresponding subspace. Low-rank representation (LRR) is a classic spectral-type method…
Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key…
In this paper we propose a data augmentation method for time series with irregular sampling, Time-Conditional Generative Adversarial Network (T-CGAN). Our approach is based on Conditional Generative Adversarial Networks (CGAN), where the…