Related papers: Geometry of symmetric group-based models

Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…

Many statistical models are algebraic in that they are defined in terms of polynomial constraints, or in terms of polynomial or rational parametrizations. The parameter spaces of such models are typically semi-algebraic subsets of the…

We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes $A$ and $B$, the algorithm computes a transformation $t$ such that with high…

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…

In this note, we characterize the embeddability of generic Kimura 3ST Markov matrices in terms of their eigenvalues. As a consequence, we are able to compute the volume of such matrices relative to the volume of all Markov matrices within…

Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood…

Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

This paper studies the problem of polygonal mapping of buildings by tackling the issue of mask reversibility that leads to a notable performance gap between the predicted masks and polygons from the learning-based methods. We addressed such…

Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…

A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…

Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map --- the collection of joint distributions for a model --- forms the model…

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…

An important application of distance geometry to biochemistry studies the embeddings of the vertices of a weighted graph in the three-dimensional Euclidean space such that the edge weights are equal to the Euclidean distances between…

A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…

Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is…

We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

We revisit the geometry of involutions in groups of finite Morley rank. Our approach unifies and generalises numerous results, both old and recent, that have exploited this geometry; though in fact, we prove much more. We also conjecture…

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…