Related papers: Cardinality Sparsity: Applications in Matrix-Matri…
Matrix scaling problems with sparse cost matrices arise frequently in various domains, such as optimal transport, image processing, and machine learning. The Sinkhorn-Knopp algorithm is a popular iterative method for solving these problems,…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
We explore a new type of sparsity for the generalized moment problem (GMP) that we call ideal-sparsity. This sparsity exploits the presence of equality constraints requiring the measure to be supported on the variety of an ideal generated…
Known sparsity thresholds for basis pursuit to deliver the maximally sparse solution of the compressed sensing recovery problem typically depend on the dictionary's coherence. While the coherence is easy to compute, it can lead to rather…
Hyperparameter optimization is an essential component in many data science pipelines and typically entails exhaustive time and resource-consuming computations in order to explore the combinatorial search space. Similar to this problem,…
The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest…
Many machine learning problems require the prediction of multi-dimensional labels. Such structured prediction models can benefit from modeling dependencies between labels. Recently, several deep learning approaches to structured prediction…
Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
Deep neural networks employ specialized architectures for vision, sequential and language tasks, yet this proliferation obscures their underlying commonalities. We introduce a unified matrix-order framework that casts convolutional,…
In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…
In recent years, machine learning-based cardinality estimation methods are replacing traditional methods. This change is expected to contribute to one of the most important applications of cardinality estimation, the query optimizer, to…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Solutions to the linear complementarity problem (LCP) are naturally sparse in many applications such as bimatrix games and portfolio section problems. Despite that it gives rise to the hardness, sparsity makes optimization faster and…
Dimensionality reduction techniques play an essential role in data analytics, signal processing and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis,…
Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant challenge for efficiently computing gradients through…
Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…