Related papers: A Unifying Framework for Testing Shape Restriction…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…

This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…

We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient…

Communication is one of the key bottlenecks in the distributed training of large-scale machine learning models, and lossy compression of exchanged information, such as stochastic gradients or models, is one of the most effective instruments…

This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between…

In this paper we give a lower bound on the waist of the unit sphere of a uniformly convex normed space by using the localization technique in codimension greater than one and a strong version of the Borsuk-Ulam theorem. The tools used in…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…

Shapley values have emerged as a critical tool for explaining which features impact the decisions made by machine learning models. However, computing exact Shapley values is difficult, generally requiring an exponential (in the feature…

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…

Effect size measures and visualization techniques aimed at maximizing the interpretability and comparability of results from statistical models have long been of great importance and are recently again receiving increased attention in the…

We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…

This paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of inter-agent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to…

The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…

Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…