Consensus‐based sampling
Consensus‐based sampling
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DOI：
10.1111/sapm.12470
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发表时间：
2021-06
影响因子：
2.7
通讯作者：
J. Carrillo;F. Hoffmann;A. Stuart;U. Vaes
中科院分区：
文献类型：
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作者：
J. Carrillo;F. Hoffmann;A. Stuart;U. Vaes
我们提出了一种新的方法，采样和优化任务的基础上随机相互作用的粒子系统。我们解释了如何使用这种方法来实现以下两个目标：（i）从给定的目标分布生成近似样本，以及（ii）优化给定的目标函数。该方法是无导数和仿射不变的，因此非常适合解决由复杂的正向模型定义的逆问题：（i）允许从贝叶斯后验生成样本，（ii）允许确定最大后验估计。我们调查的各种参数的选择，无论是分析和数值模拟的方法所提出的家庭的属性。分析和数值模拟表明，该方法具有潜在的通用优化任务在欧几里得空间，收缩性能的算法建立在适当的条件下，和计算实验表明广泛的盆地的吸引力为各种具体问题。分析和实验也表明了潜在的采样方法在政权中，目标分布是单峰和接近高斯，事实上，我们证明了该方法恢复拉普拉斯近似的措施在某些参数制度，并提供数值证据表明，这拉普拉斯近似吸引了大量的初始条件的例子。
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target distribution and (ii) optimizing a given objective function. The approach is derivative‐free and affine invariant, and is therefore well‐suited for solving inverse problems defined by complex forward models: (i) allows generation of samples from the Bayesian posterior and (ii) allows determination of the maximum a posteriori estimator. We investigate the properties of the proposed family of methods in terms of various parameter choices, both analytically and by means of numerical simulations. The analysis and numerical simulation establish that the method has potential for general purpose optimization tasks over Euclidean space; contraction properties of the algorithm are established under suitable conditions, and computational experiments demonstrate wide basins of attraction for various specific problems. The analysis and experiments also demonstrate the potential for the sampling methodology in regimes in which the target distribution is unimodal and close to Gaussian; indeed we prove that the method recovers a Laplace approximation to the measure in certain parametric regimes and provide numerical evidence that this Laplace approximation attracts a large set of initial conditions in a number of examples.