大规模贝叶斯压缩感知中的高效变分推理
Efficient variational inference in large-scale Bayesian compressed sensing
摘要：
我们从概率的角度研究重尾先验下的线性模型。贝叶斯压缩感知框架中的焦点转向捕获潜在变量的完整后验分布，而不是像标准确定性方法那样计算单个稀疏最可能（MAP）解决方案，这允许量化估计不确定性并使用最大似然学习模型参数。稀疏线性模型下的精确后验分布是很难得到的，我们集中于变分贝叶斯技术来近似它，重复计算高斯方差是变分技术在大规模问题中应用的一个关键要求，也是主要的计算瓶颈。我们利用最近提出的扰动和MAP算法从高斯马尔可夫随机场（GMRF）绘制精确的样本。我们的论文的主要技术贡献是表明，估计高斯方差使用相对较少的数量，这样有效地抽取的随机样本是更有效的替代通用方差估计技术。通过将方差估计的问题减少到标准优化原语，所得到的变分算法是完全可扩展的和可并行的，允许贝叶斯计算在非常大规模的问题中具有与常规点估计技术相同的存储器和时间复杂度要求。我们用图像去模糊的实验来说明这些想法。
英文摘要：
We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing framework shifts towards capturing the full posterior distribution on the latent variables, which allows quantifying the estimation uncertainty and learning model parameters using maximum likelihood. The exact posterior distribution under the sparse linear model is intractable and we concentrate on variational Bayesian techniques to approximate it. Repeatedly computing Gaussian variances turns out to be a key requisite and constitutes the main computational bottleneck in applying variational techniques in large-scale problems. We leverage on the recently proposed Perturb-and-MAP algorithm for drawing exact samples from Gaussian Markov random fields (GMRF). The main technical contribution of our paper is to show that estimating Gaussian variances using a relatively small number of such efficiently drawn random samples is much more effective than alternative general-purpose variance estimation techniques. By reducing the problem of variance estimation to standard optimization primitives, the resulting variational algorithms are fully scalable and parallelizable, allowing Bayesian computations in extremely large-scale problems with the same memory and time complexity requirements as conventional point estimation techniques. We illustrate these ideas with experiments in image deblurring.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
