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We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…
Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space $\mathbf{R}^s$, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general $\mathbf{R}^s$-valued functionals…
We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to…
Matrix-valued covariance functions are crucial to geostatistical modeling of multivariate spatial data. The classical assumption of symmetry of a multivariate covariance function is overlay restrictive and has been considered as unrealistic…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
The spatial sign correlation (D\"urre, Vogel and Fried, 2015) is a highly robust and easy-to-compute, bivariate correlation estimator based on the spatial sign covariance matrix. Since the estimator is inefficient when the marginal scales…
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to…
Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness…
Cointegration analysis was developed for non-stationary linear processes that exhibit stationary relationships between coordinates. Estimation of the cointegration relationships in a multi-dimensional cointegrated process typically proceeds…
We study the problem of learning an unknown function using random feature models. Our main contribution is an exact asymptotic analysis of such learning problems with Gaussian data. Under mild regularity conditions for the feature matrix,…
As network data has become ubiquitous in the sciences, there has been growing interest in network models whose structure is driven by latent node-level variables in a (typically low-dimensional) latent geometric space. These "latent…
An overarching objective in contemporary statistical network analysis is extracting salient information from datasets consisting of multiple networks. To date, considerable attention has been devoted to node and network clustering, while…
Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
Variational inference provides approximations to the computationally intractable posterior distribution in Bayesian networks. A prominent medical application of noisy-or Bayesian network is to infer potential diseases given observed…
Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including…