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Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often…

In supervised batch learning, the predictive normalized maximum likelihood (pNML) has been proposed as the min-max regret solution for the distribution-free setting, where no distributional assumptions are made on the data. However, the…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…

Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. The budding approaches in this space are limited by representational and computational…

Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…

Inspired by the adaptation phenomenon of neuronal firing, we propose the regularity normalization (RN) as an unsupervised attention mechanism (UAM) which computes the statistical regularity in the implicit space of neural networks under the…

Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…

We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space…

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…

The Predictive Normalized Maximum Likelihood (pNML) scheme has been recently suggested for universal learning in the individual setting, where both the training and test samples are individual data. The goal of universal learning is to…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and…

We introduce an information theoretic criterion for Bayesian network structure learning which we call quotient normalized maximum likelihood (qNML). In contrast to the closely related factorized normalized maximum likelihood criterion, qNML…