Related papers: Stable iterative refinement algorithms for solving…
Information retrieval (IR) methods, like retrieval augmented generation, are fundamental to modern applications but often lack statistical guarantees. Conformal prediction addresses this by retrieving sets guaranteed to include relevant…
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Real-world image super-resolution (RWSR) is a long-standing problem as low-quality (LQ) images often have complex and unidentified degradations. Existing methods such as Generative Adversarial Networks (GANs) or continuous diffusion models…
The Kaczmarz algorithm is an iterative method that solves linear systems of equations. It stands out among iterative algorithms when dealing with large systems for two reasons. First, at each iteration, the Kaczmarz algorithm uses a single…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
Iterative methods have led to better understanding and solving problems such as missing sampling, deconvolution, inverse systems, impulsive and Salt and Pepper noise removal problems. However, the challenges such as the speed of convergence…
Neural operators serve as fast, data-driven surrogates for scientific modeling but typically rely on a monolithic, single-pass inference procedure that struggles to resolve high-frequency details, a limitation known as spectral bias. We…
This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…
Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…