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In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…
Probabilistic Circuits (PCs) are tractable representations of probability distributions allowing for exact and efficient computation of likelihoods and marginals. Recent advancements have improved the scalability of PCs either by leveraging…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy and reliability of the resulting PCE-based response…
The great success of deep neural networks is built upon their over-parameterization, which smooths the optimization landscape without degrading the generalization ability. Despite the benefits of over-parameterization, a huge amount of…
We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum $A=D+\varepsilon B$ of a sparse and efficiently exponentiable matrix $D$ with sparse exponential $e^D$ and a dense…
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $\varphi$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computational grids. To overcome this barrier, we extend the…
Motion planning is an essential aspect of autonomous systems and robotics and is an active area of research. A recently-proposed sampling-based motion planning algorithm, termed 'Generalized Shape Expansion' (GSE), has been shown to possess…
The inversion of structured sparse matrices is a key but computationally and memory-intensive operation in many scientific applications. There are cases, however, where only particular entries of the full inverse are required. This has…
In this paper, we enhance a recent algorithm for approximate spectral factorization of matrix functions, extending its capabilities to precisely factorize rational matrices when an exact lower-upper triangular factorization is available.…