Related papers: Group Symmetry and Covariance Regularization
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…
Modeling symmetry breaking is essential for understanding the fundamental changes in the behaviors and properties of physical systems, from microscopic particle interactions to macroscopic phenomena like fluid dynamics and cosmic…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…
Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to…
We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer…
We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Quantifying the uncertainty of predictions is a core problem in modern statistics. Methods for predictive inference have been developed under a variety of assumptions, often -- for instance, in standard conformal prediction -- relying on…
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…