Related papers: Complexity Measures on the Symmetric Group and Bey…
We explore the role of group symmetries in binary classification tasks, presenting a novel framework that leverages the principles of Neyman-Pearson optimality. Contrary to the common intuition that larger symmetry groups lead to improved…
We consider the problem of characterizing the class of those permutation groups that are the symmetry groups of Boolean functions. These are exactly the automorphism groups of hypergraphs. They are also called the relation groups. In this…
The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model…
When uncertainty meets costly information gathering, a fundamental question emerges: which data points should we probe to unlock near-optimal solutions? Sparsification of stochastic packing problems addresses this trade-off. The existing…
Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
While intuitive for humans, the concept of visual complexity is hard to define and quantify formally. We suggest adopting the multi-scale structural complexity (MSSC) measure, an approach that defines structural complexity of an object as…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Symmetry is conventionally described in a contrariety manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry…
Exploiting the explicit bijection between the density of singular values and the density of eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size, we aim at finding the induced probability measure on…
This work builds on a rich discourse surrounding the social brain hypothesis as well as the definition and quantification of social complexity. We believe this manuscript provides a new perspective on the topic by pairing a conceptual…
: In studies of discrete structures, functions are frequently used that express proximity, but are not metrics. We consider a class of such functions that is characterized by a normalization condition and an inequality that plays the same…
This paper presents a method to detect and recognize symmetries in Boolean functions. The idea is to use information theoretic measures of Boolean functions to detect sub-space of possible symmetric variables. Coupled with the new…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
Representational similarity metrics are fundamental tools in neuroscience and AI, yet we lack systematic comparisons of their discriminative power across model families. We introduce a quantitative framework to evaluate representational…
We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…