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Polystar_bodies this repository contains supplementary material for the paper approximation of starshaped sets using polynomials by chiara meroni, jared miller, and mauricio velasco (arxiv version). We also prove some higher dimensional analogues. We investigate the expressivity of these function classes and describe the combinatorial and geometric structure of the loss landscape, most.
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We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We prove that polystar bodies are uniformly dense in starshaped sets and obtain asymptotically optimal approximation guarantees. We prove that polystar bodies are uniformly dense in starshaped sets and obtain asymptotically optimal approximation guarantees.
Our algorithm is based on the skeleton algorithm for polyhedral inner approximation by csirmaz (2021).
As there is no known relationship between the coefficients of an arbitrary polynomial and the volume of its sublevel sets,. The advantage of sa, see section 2 for details, is. We develop tools for the construction of. The proof uses a perturbed version of the chebyshev polynomials and an application of the brouwer fixed point.
It provides free access to secondary information on researchers, articles, patents, etc., in science and technology, medicine and pharmacy. In this setting, it is standard to seek a minimum volume outer approximation and/or maximum volume inner approximation. If the weighted sum scalarization can be solved exactly or approximately in polynomial time, our algorithm can find a convex approximation set for an approximation factor arbitrarily close to this solution quality. Compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies.
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Abstract we prove some results on when functions on compact sets k ⊂ c can be approximated by polynomials avoiding values in given sets.
We develop tools for the construction. Numerical analysis authors and titles for recent submissions fri, 5 sep 2025 thu, 4 sep 2025 wed, 3 sep 2025 mon, 1 sep 2025 fri, 29 aug 2025 see today's new changes Compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies.
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