Related papers: Intrinsic dimension and its application to associa…
Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…
The characteristics of data like distribution and heterogeneity, become more complex and counterintuitive as dimensionality increases. This phenomenon is known as curse of dimensionality, where common patterns and relationships (e.g.,…
High-dimensional computational challenges are frequently explained via the curse of dimensionality, i.e., increasing the number of dimensions leads to exponentially growing computational complexity. In this commentary, we argue that…
Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a…
We study the integration and approximation problems for monotone and convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function…
The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from…
Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…
During the last decade, the deluge of multimedia data has impacted a wide range of research areas, including multimedia retrieval, 3D tracking, database management, data mining, machine learning, social media analysis, medical imaging, and…
High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states:…
We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality.…
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…
We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper (arXiv:cs/0703125). The main features of our approach are that a high intrinsic dimension of a…
In this dissertation we study the tractability of the information-based complexity $n(\varepsilon,d)$ for $d$-variate function approximation problems. In the deterministic setting for many unweighted problems the curse of dimensionality…
Although learning in high dimensions is commonly believed to suffer from the curse of dimensionality, modern machine learning methods often exhibit an astonishing power to tackle a wide range of challenging real-world learning problems…
Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…
We prove the curse of dimensionality in the worst case setting for numerical integration for a number of classes of smooth $d$-variate functions. Roughly speaking, we consider different bounds for the derivatives of $f \in C^k(D_d)$ and ask…
Difficulties in replication and reproducibility of empirical evidences in machine learning research have become a prominent topic in recent years. Ensuring that machine learning research results are sound and reliable requires…
Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that…
This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be…
There is an increasing body of evidence suggesting that exact nearest neighbour search in high-dimensional spaces is affected by the curse of dimensionality at a fundamental level. Does it necessarily mean that the same is true for k…