Related papers: Intrinsic dimension and its application to associa…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical,…
We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded $F_{1}$-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Cutting and Packing problems are occurring in different industries with a direct impact on the revenue of businesses. Generally, the goal in Cutting and Packing is to assign a set of smaller objects to a set of larger objects. To solve…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
Deep clustering, a method for partitioning complex, high-dimensional data using deep neural networks, presents unique evaluation challenges. Traditional clustering validation measures, designed for low-dimensional spaces, are problematic…
Advances in computational power and hardware efficiency have enabled tackling increasingly complex, high-dimensional problems. While artificial intelligence (AI) achieves remarkable results, the interpretability of high-dimensional…
In recent work it has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality in terms of the number of samples needed. As a consequence,…
Two pressing topics in the theory of deep learning are the interpretation of feature learning (FL) mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich FL often appear in the form of…
We present deterministic algorithms for the uniform recovery of $d$-variate rank one tensors from function values. These tensors are given as product of $d$ univariate functions whose $r$th weak derivative is bounded by $M$. The recovery…
Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Recently, it has been shown that the trajectories of iterative…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…
Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…
The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…
Particle filters are a popular and flexible class of numerical algorithms to solve a large class of nonlinear filtering problems. However, standard particle filters with importance weights have been shown to require a sample size that…
Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…