Approximate primal-dual fixed-point based langevin algorithms for non-smooth convex potentials

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Ziruo Cai, Jinglai Li, Xiaoqun Zhang
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引用次数: 0

Abstract

The Langevin algorithms are frequently used to sample the posterior distributions in Bayesian inference. In many practical problems, however, the posterior distributions often consist of non-differentiable components, posing challenges for the standard Langevin algorithms, as they require to evaluate the gradient of the energy function in each iteration. To this end, a popular remedy is to utilize the proximity operator, and as a result one needs to solve a proximity subproblem in each iteration. The conventional practice is to solve the subproblems accurately, which can be exceedingly expensive, as the subproblem needs to be solved in each iteration. We propose an approximate primal-dual fixed-point algorithm for solving the subproblem, which only seeks an approximate solution of the subproblem and therefore reduces the computational cost considerably. We provide theoretical analysis of the proposed method and also demonstrate its performance with numerical examples.
非光滑凸势的近似基元-双定点朗文算法
朗文算法常用于贝叶斯推理中的后验分布采样。然而,在许多实际问题中,后验分布往往由不可分的成分组成,这给标准的朗格文算法带来了挑战,因为它们需要在每次迭代中评估能量函数的梯度。为此,一种流行的补救方法是利用接近算子,因此需要在每次迭代中解决一个接近子问题。传统的做法是精确求解子问题,这可能会非常昂贵,因为每次迭代都需要求解子问题。我们提出了一种求解子问题的近似原始双定点算法,该算法只寻求子问题的近似解,因此大大降低了计算成本。我们对所提方法进行了理论分析,并通过数值示例演示了该方法的性能。
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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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