相关论文: Complexities of convex combinations and bounding t…

This paper describes a new approach for learning structures of large Bayesian networks based on blocks resulting from feature space clustering. This clustering is obtained using normalized mutual information. And the subsequent aggregation…

This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a…

We derive generic information-theoretic and PAC-Bayesian generalization bounds involving an arbitrary convex comparator function, which measures the discrepancy between the training and population loss. The bounds hold under the assumption…

Class imbalance remains a major challenge in machine learning, especially in multi-class problems with long-tailed distributions. Existing methods, such as data resampling, cost-sensitive techniques, and logistic loss modifications, though…

We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…

In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…

The Weak Gravity Conjecture imposes stringent constraints on effective field theories to allow for an ultraviolet completion within quantum gravity. While substantial evidence supports the conjecture across broad classes of string…

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel…

We prove polynomial-time solvability of a large class of clustering problems where a weighted set of items has to be partitioned into clusters with respect to some balancing constraints. The data points are weighted with respect to…

In this paper we investigate the question of how much combined measurements can increase the accuracy of additive quantities. Therefore, we consider a set of measurements from a selection of all possible combinations of the $n$ labeled…

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…

Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…

This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a…

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…

This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…

Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…

The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also…

In this paper, we study the strength of convex relaxations obtained by convexification of aggregation of constraints for a set $S$ described by two bilinear bipartite equalities. Aggregation is the process of rescaling the original…