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Related papers: Experimental Design Using Interlacing Polynomials

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Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…

Machine Learning · Statistics 2019-09-27 Tyler R. Scott , Karl Ridgeway , Michael C. Mozer

This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…

Algebraic Geometry · Mathematics 2011-11-30 Yongbi Li

A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…

Mathematical Physics · Physics 2007-05-23 N. Gurappa , Prasanta K. Panigrahi , T. Shreecharan

We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…

Statistics Theory · Mathematics 2023-12-27 Alen Alexanderian

In this article, an adaption of an algorithm for the creation of experimental designs by Lekivetz and Jones (2015) is suggested, dealing with constraints around randomization. Split-plot design of experiments is used, when the levels of…

Methodology · Statistics 2020-03-24 Thomas Muehlenstaedt , Maria Lanzerath

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

Data Structures and Algorithms · Computer Science 2024-11-26 Antonios Antoniadis , Marek Eliáš , Adam Polak , Moritz Venzin

We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…

Data Structures and Algorithms · Computer Science 2020-07-28 Kuan Cheng , Zhengzhong Jin , Xin Li , Yu Zheng

We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…

Optimization and Control · Mathematics 2026-01-19 Ahmed Attia

Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…

Symbolic Computation · Computer Science 2010-07-20 Daniel S. Roche

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975) 57-70].…

Statistics Theory · Mathematics 2014-01-30 Holger Dette , Viatcheslav B. Melas , Petr Shpilev

In this paper, we study relations among several types of Eulerian polynomials from a combinatorial viewpoint. We establish an identity between the restricted Eulerian polynomials of types $A$ and $B$. As an application, we present a…

Combinatorics · Mathematics 2026-03-04 Zhong-Xue Zhang

We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical…

Combinatorics · Mathematics 2014-05-06 Jose Rodriguez

We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…

Numerical Analysis · Mathematics 2020-01-22 Nick Dexter , Hoang Tran , Clayton Webster

We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this…

Machine Learning · Statistics 2024-02-26 Fengyi Li , Ayoub Belhadji , Youssef Marzouk

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…

Numerical Analysis · Mathematics 2018-09-21 Nicola A. Nodargi

We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality…

Computation · Statistics 2013-11-12 Selin Damla Ahipasaoglu

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

Artificial Intelligence · Computer Science 2012-12-12 David Ephraim Larkin

A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size $n$ subject to cardinality constraint $k$; the algorithm is based upon the idea of interlacing two…

Data Structures and Algorithms · Computer Science 2019-10-28 Alan Kuhnle

We propose a method for constructing optimal block designs for experiments on networks. The response model for a given network interference structure extends the linear network effects model to incorporate blocks. The optimality criteria…

Methodology · Statistics 2019-11-26 Vasiliki Koutra , Steven G. Gilmour , Ben M. Parker

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…

Numerical Analysis · Mathematics 2024-07-03 Alen Alexanderian , Ruanui Nicholson , Noemi Petra
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