Related papers: Why summation by parts is not enough

We propose an sparse Bayesian learning (SBL)-based method that leverages group sparsity and multiple parameterized dictionaries to detect the relevant dictionary entries and estimate their continuous parameters by combining data from…

The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…

Efficiency of intrinsic operator techniques (using only products and ranks of tensor operators) is first evidenced by condensed proofs of already known $\bigtriangledown$-triangle sum rules of su(2)/su$_q$(2). {\em A new compact}…

This paper presents a more stable implementation and a highly accurate numerical tool for predicting flooding in urban areas. We started with the (linearised) well-posedness analysis by [1], where far-field boundary conditions were proposed…

Motivated by recent progress on stochastic matching with few queries, we embark on a systematic study of the sparsification of stochastic packing problems (SPP) more generally. Specifically, we consider SPPs where elements are independently…

Accurate 3D shape representation is essential in engineering applications such as design, optimization, and simulation. In practice, engineering workflows require structured, part-based representations, as objects are inherently designed as…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

Sparse Subspace Clustering (SSC) is a popular unsupervised machine learning method for clustering data lying close to an unknown union of low-dimensional linear subspaces; a problem with numerous applications in pattern recognition and…

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…

In the research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series [6], the…

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning…

The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distributed storage, and space-time coding. A central problem is to…

We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…

Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and physical sciences. In various settings, the polynomials depend on external parameters that may…

Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…

Distributed sparse learning with a cluster of multiple machines has attracted much attention in machine learning, especially for large-scale applications with high-dimensional data. One popular way to implement sparse learning is to use…

Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to…

This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…