Related papers: Interpretable Discovery of One-parameter Subgroups…
A new ensemble framework for interpretable model called Linear Iterative Feature Embedding (LIFE) has been developed to achieve high prediction accuracy, easy interpretation and efficient computation simultaneously. The LIFE algorithm is…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…
Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting…
We analyze the structure of one-parameter subgroups of SO(3,2). We find two new types of subgroups in comparison with the structure of the one-parameter subgroups of SO(2,2), and we construct explicit examples for these subgroups. We also…
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…
Model calibration and debiasing are fundamental yet operationally expensive challenges in large-scale recommendation systems. Existing approaches treat them as separate problems requiring distinct infrastructure: post-hoc calibration…
Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choice of the uncertainty set. While large sets ensure reliability, they often lead to overly…
The study of parameter-dependent partial differential equations (parametric PDEs) with countably many parameters has been actively studied for the last few decades. In particular, it has been well known that a certain type of parametric…
Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…
Decision-making in complex systems often relies on machine learning models, yet highly accurate models such as XGBoost and neural networks can obscure the reasoning behind their predictions. In operations research applications,…
We build quasi--isometry invariants of relatively hyperbolic groups which detect the hyperbolic parts of the group; these are variations of the stable dimension constructions previously introduced by the authors. We prove that, given any…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…
We identify the images of the comparision maps from ordinary homology and Sobolev homology, respectively, to the $l^1$-homology of a word-hyperbolic group with coefficients in complete normed modules. The underlying idea is that there is a…
We introduce a path-theoretic framework for understanding the representation theory of (quantum) symmetric and general linear groups and their higher level generalisations over fields of arbitrary characteristic. Our first main result is a…
Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…