Related papers: Categorical and geometric methods in statistical, …

Logic-Geometric Programming (LGP) is a powerful motion and manipulation planning framework, which represents hierarchical structure using logic rules that describe discrete aspects of problems, e.g., touch, grasp, hit, or push, and solves…

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…

Following Thurston's geometrisation picture in dimension three, we study geometric manifolds in a more general setting in arbitrary dimensions, with respect to the following problems: (i) The existence of maps of non-zero degree (domination…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…

This article presents a new way to understand the descriptive ability of tree shape statistics. Where before tree shape statistics were chosen by their ability to distinguish between macroevolutionary models, the ``resolution'' presented in…

Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more…

Mechanistic learning, the synergistic combination of knowledge-driven and data-driven modeling, is an emerging field. In particular, in mathematical oncology, the application of mathematical modeling to cancer biology and oncology, the use…

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

I survey methods from differential geometry, algebraic geometry and representation theory relevant for the permanent v. determinant problem from computer science, an algebraic analog of the P v. NP problem.

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…

This paper presents an extension and an elaboration of the theory of differential similarity, which was originally proposed in arXiv:1401.2411 [cs.LG]. The goal is to develop an algorithm for clustering and coding that combines a geometric…

Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…