相关论文: Indexability, concentration, and VC theory
Observability of complex systems/networks is the focus of this paper, which is shown to be closely related to the concept of contraction. Indeed, for observable network tracking it is necessary/sufficient to have one node in each…
We propose a new approach for the problem of relative depth estimation from a single image. Instead of directly regressing over depth scores, we formulate the problem as estimation of a probability distribution over depth and aim to learn…
Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…
In this paper, we study the L\'{e}vy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional $\ell^p$-ball with the…
Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this…
We consider contractivity for diffusion semigroups w.r.t. Kantorovich ($L^1$ Wasserstein) distances based on appropriately chosen concave functions. These distances are inbetween total variation and usual Wasserstein distances. It is shown…
High dimensional data often contain multiple facets, and several clustering patterns can co-exist under different variable subspaces, also known as the views. While multi-view clustering algorithms were proposed, the uncertainty…
Pattern comparison represents a fundamental and crucial aspect of scientific modeling, artificial intelligence, and pattern recognition. Three main approaches have typically been applied for pattern comparison: (i) distances; (ii)…
We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Dataset Condensation (DC) aims to reduce deep neural networks training efforts by synthesizing a small dataset such that it will be as effective as the original large dataset. Conventionally, DC relies on a costly bi-level optimization…
The Vapnik-Chervonenkis (VC) dimension of the set of half-spaces of R^d with frontiers parallel to the axes is computed exactly. It is shown that it is much smaller than the intuitive value of d. A good approximation based on the Stirling's…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance, expressed through lower and upper expectations. The results are variants and extensions of De Cooman and Miranda's recent…
Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…
By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…
The disjointness problem - where Alice and Bob are given two subsets of $\{1, \dots, n\}$ and they have to check if their sets intersect - is a central problem in the world of communication complexity. While both deterministic and…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
Deep neural networks often contain far more parameters than training examples, yet they still manage to generalize well in practice. Classical complexity measures such as VC-dimension or PAC-Bayes bounds usually become vacuous in this…
Self-supervised learning enables networks to learn discriminative features from massive data itself. Most state-of-the-art methods maximize the similarity between two augmentations of one image based on contrastive learning. By utilizing…