Related papers: Algebraic geometry of Poisson regression
The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in…
We consider the optimal design problem for a comparison of two regression curves, which is used to establish the similarity between the dose response relationships of two groups. An optimal pair of designs minimizes the width of the…
The objective of this paper is to provide, for the problem of univariate symmetry (with respect to specified or unspecified location), a concept of optimality, and to construct tests achieving such optimality. This requires embedding…
This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
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…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
Classical regression has a simple geometric description in terms of a projection of the training labels onto the column space of the design matrix. However, for over-parameterized models -- where the number of fit parameters is large enough…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
We present a Python package together with a practical guide for the implementation of a lightweight diversity-enhanced genetic algorithm (GA) approach for the exploration of multi-dimensional parameter spaces. Searching a parameter space…
To facilitate the design and optimization of nanomaterials for a given application it is necessary to understand the relationship between structure and physical properties. For large nanomaterials, there is imprecise structural information…
We consider the problem of how to assign treatment in a randomized experiment, in which the correlation among the outcomes is informed by a network available pre-intervention. Working within the potential outcome causal framework, we…
The gamma model is a generalized linear model for gamma-distributed outcomes. The model is widely applied in psychology, ecology or medicine. In this paper we focus on gamma models having a linear predictor without intercept. For a specific…
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the $3$-dimensional Poisson algebras. In addition, we study the…
In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…