Related papers: Reduced Basis Greedy Selection Using Random Traini…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
Partial differential equation parameter estimation is a mathematical and computational process used to estimate the unknown parameters in a partial differential equation model from observational data. This paper employs a greedy sampling…
Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
Optimal selection of a subset of items from a given set is a hard problem that requires combinatorial optimization. In this paper, we propose a subset selection algorithm that is trainable with gradient-based methods yet achieves…
In this paper, we propose a model reduction method for solving multiscale elliptic PDEs with random coefficients in the multiquery setting using an optimization approach. The optimization approach enables us to construct a set of localized…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical…
Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
Training a good supernet in one-shot NAS methods is difficult since the search space is usually considerably huge (e.g., $13^{21}$). In order to enhance the supernet's evaluation ability, one greedy strategy is to sample good paths, and let…
Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the…
We consider learning a convex combination of basis models, and present some new theoretical and empirical results that demonstrate the effectiveness of a greedy approach. Theoretically, we first consider whether we can use linear, instead…
In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
For constrained, not necessarily monotone submodular maximization, all known approximation algorithms with ratio greater than $1/e$ require continuous ideas, such as queries to the multilinear extension of a submodular function and its…
In the wake of the explosive growth in smartphones and cyberphysical systems, there has been an accelerating shift in how data is generated away from centralised data towards on-device generated data. In response, machine learning…