相关论文: Breaking the curse of dimensionality in structured…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…

We study the $L_p$-discrepancy of random point sets in high dimensions, with emphasis on small values of $p$. Although the classical $L_p$-discrepancy suffers from the curse of dimensionality for all $p \in (1,\infty)$, the gap between…

This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…

The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…

Developments in genome-wide association studies and the increasing availability of summary genetic association data have made the application of two-sample Mendelian Randomization (MR) with summary data increasingly popular. Conventional…

This paper studies inference of preference parameters in semiparametric discrete choice models when these parameters are not point-identified and the identified set is characterized by a class of conditional moment inequalities. Exploring…

In this work we study the validity of the so-called curse of dimensionality for indexing of databases for similarity search. We perform an asymptotic analysis, with a test model based on a sequence of metric spaces $(\Omega_d)$ from which…

Modern vector databases enable efficient retrieval over high-dimensional neural embeddings, powering applications from web search to retrieval-augmented generation. However, classical theory predicts such tasks should suffer from the curse…

Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…

Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large,…

Models with many signals, high-dimensional models, often impose structures on the signal strengths. The common assumption is that only a few signals are strong and most of the signals are zero or close (collectively) to zero. However, such…

We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…

Most approximations for stochastic differential equations with high-dimensional, non-Gaussian inputs suffer from a rapid (e.g., exponential) increase of computational cost, an issue known as the curse of dimensionality. In astrodynamics,…

We suggest that the curse of dimensionality affecting the similarity-based search in large datasets is a manifestation of the phenomenon of concentration of measure on high-dimensional structures. We prove that, under certain geometric…

As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a…

This work investigates the optimization instability of deep neural networks from a less-explored yet insightful perspective: the emergence and amplification of singularities in the parametric space. Our analysis reveals that parametric…

We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…

This work proposes a sampling-based (non-intrusive) approach within the context of low-rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with…