On decompositional algorithms for uniform sampling from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si10.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math>-spheres and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math>-balls

Harman, Radoslav; Lacko, Vladimír

doi:10.1016/j.jmva.2010.06.002

Cited by 57 publications

(7 citation statements)

References 25 publications

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“…A family of methods, using the beta distribution, were developed for higher dimensional spheres [10,11,12,13,14]. The relationship between these efficient methods was presented by Harman and Vladimir [15].…”

Section: Introductionmentioning

confidence: 99%

The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems

Peake

Trevelyan

Coates

2014

Engineering Analysis with Boundary Elements

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Section: Introductionmentioning

confidence: 99%

The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems

Peake

Trevelyan

Coates

2014

Engineering Analysis with Boundary Elements

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“…For the sampling in a hyperellipsoid, samples can be generated via (Harman & Lacko 2010;Gammell & Barfoot 2014)…”

Section: Training Setmentioning

confidence: 99%

CoLFI: Cosmological Likelihood-free Inference with Neural Density Estimators

Wang,

Cheng,

et al. 2023

ApJS

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In previous works, we proposed to estimate cosmological parameters with an artificial neural network (ANN) and a mixture density network (MDN). In this work, we propose an improved method called a mixture neural network (MNN) to achieve parameter estimation by combining ANN and MDN, which can overcome shortcomings of the ANN and MDN methods. Besides, we propose sampling parameters in a hyperellipsoid for the generation of the training set, which makes the parameter estimation more efficient. A high-fidelity posterior distribution can be obtained using  ( 10 2 ) forward simulation samples. In addition, we develop a code named CoLFI for parameter estimation, which incorporates the advantages of MNN, ANN, and MDN, and is suitable for any parameter estimation of complicated models in a wide range of scientific fields. CoLFI provides a more efficient way for parameter estimation, especially for cases where the likelihood function is intractable or cosmological models are complex and resource-consuming. It can learn the conditional probability density p( θ ∣ d ) using samples generated by models, and the posterior distribution p( θ ∣ d 0) can be obtained for a given observational data d 0. We tested the MNN using power spectra of the cosmic microwave background and Type Ia supernovae and obtained almost the same result as the Markov Chain Monte Carlo method. The numerical difference only exists at the level of  ( 10 − 2 σ ) . The method can be extended to higher-dimensional data.

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“…Suppose that the index set J consists of s elements. First, we generate the vector δ in the s-sphere defined as B = {δ ∈ R s : |δ| = R} with some predefined radius R. There are several methods for the uniform sampling of points δ in the s-sphere with the unit radius R = 1, for example, [87,88]. Then every generated point is multiplied by R. Moreover, we take vectors δ only from a part of the s-sphere.…”

Section: Perturbation Of Embeddings and The Instance Reconstructionmentioning

confidence: 99%

Explanation of Siamese Neural Networks for Weakly Supervised Learning

Utkin

Kovalev

Kasimov

2020

cai

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A new method for explaining the Siamese neural network (SNN) as a black-box model for weakly supervised learning is proposed under condition that the output of every subnetwork of the SNN is a vector which is accessible. The main problem of the explanation is that the perturbation technique cannot be used directly for input instances because only their semantic similarity or dissimilarity is known. Moreover, there is no an "inverse" map between the SNN output vector and the corresponding input instance. Therefore, a special autoencoder is proposed, which takes into account the proximity of its hidden representation and the SNN outputs. Its pre-trained decoder part as well as the encoder are used to reconstruct original instances from the SNN perturbed output vectors. The important features of the explained instances are determined by averaging the corresponding changes of the reconstructed instances. Numerical experiments with synthetic data and with the well-known dataset MNIST illustrate the proposed method.

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On decompositional algorithms for uniform sampling from n-spheres and n-balls

Cited by 57 publications

References 25 publications

The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems

The equal spacing of N points on a sphere with application to partition-of-unity wave diffraction problems

CoLFI: Cosmological Likelihood-free Inference with Neural Density Estimators

Explanation of Siamese Neural Networks for Weakly Supervised Learning

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