Related papers: A random matrix perspective of cultural structure:…
We examine the adjacency matrices of three-regular graphs representing one-face maps. Numerical studies reveal that the limiting eigenvalue statistics of these matrices are the same as those of much larger, and more widely studied classes…
Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
We study the distribution of singular values of product of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…
Although creativity is encouraged in the abstract it is often discouraged in educational and workplace settings. Using an agent-based model of cultural evolution, we investigated the idea that tempering the novelty-generating effects of…
We demonstrate the first Recurrent Neural Network architecture for learning Signal Temporal Logic formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Spatial separation is often included in models of ethnic divergence but it has also been realised that urban subcultures can, and frequently do, emerge in sympatry. Previous research tended to attribute this phenomenon to the human tendency…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong, rather than individual qualities. It was recently…
Generative models can be trained to emulate complex empirical data, but are they useful to make predictions in the context of previously unobserved environments? An intuitive idea to promote such extrapolation capabilities is to have the…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance…
Research on the 'cultural alignment' of Large Language Models (LLMs) has emerged in response to growing interest in understanding representation across diverse stakeholders. Current approaches to evaluating cultural alignment through…
Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted…
A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
Cultural values vary significantly around the world. Despite a large heterogeneity, similarities across national cultures are present. This paper studies cross-country culture heterogeneity via the joint inference of country-specific copula…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…