Concise Formulas for the Area and Volume of a Hyperspherical Cap

By S. Li. 2011

433 citations recorded by the source corpus.

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On combining machine learning with decision making (2011, background): “Proof See Li (2011) and references therein.”
Theory of Disagreement-Based Active Learning (2014, neutral): “that Ck(u) = (1)2λ k(Bk(r))I2u r −u(2) r2 ( k+1 2 , 1 2 ) [Li, 2011], where Iy(a, b) =”
On the Quality of the Initial Basin in Overspecified Neural Networks (2015, methodology): “The surface area of a hyperspherical cap of radius θ is given by the formula: ([Li, 2011])”
Coresets for Scalable Bayesian Logistic Regression (2016, neutral): “It follows from [23, Eq.”
Exponential Lower Bounds for Batch Reinforcement Learning: Batch RL can be Exponentially Harder than Online RL (2020, background): “For the proof, see (Li, 2011) where φ in their notation is the half-angle of the hypersector and sin φ = 1−cos2 φ = 1− b.”
Learning visual biases from human imagination (2014, background): “While this angle is not very restrictive in low dimensions, it becomes much more restrictive as the number of dimensions increases [21].”