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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning 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An Approximate Approach to E-optimal Designs for Weighted Polynomial Regression by Using Tchebycheff Systems and Orthogonal Polynomials
Takuma Takeuchi, Hiroto Sekido · 2013-03-19 · via math.ST updates on arXiv.org

In statistics, experimental designs are methods for making efficient experiments. E-optimal designs are the multisets of experimental conditions which minimize the maximum axis of the confidence ellipsoid of estimators. The aim of this thesis is to propose a new algorithm for constructing E-optimal designs approximately for weighted polynomial regression with a nonnegative weight function. First, an algorithm to calculate E-optimal designs for weighted polynomial regression of particular weight functions is discussed. Next a new algorithm for constructing E-optimal designs approximately is proposed. Notions of the Tchebycheff systems and orthogonal polynomials are used in the proposed algorithm. Finally in this thesis, the results of numerical examples are shown in order to verify the accuracy of the E-optimal designs computed by the proposed algorithm.

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