Two-Stage Bayesian Optimization for Scalable Inference in State-Space Models
Two-Stage Bayesian Optimization for Scalable Inference in State-Space Models
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DOI：
10.1109/tnnls.2021.3069172
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发表时间：
2021-04
影响因子：
10.4
通讯作者：
Mahdi Imani;Seyede Fatemeh Ghoreishi
中科院分区：
文献类型：
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作者：
Mahdi Imani;Seyede Fatemeh Ghoreishi
状态空间模型（ssm）是一类丰富的动态模型，在经济学、医疗保健、计算生物学、机器人等领域有着广泛的应用。在ssm建模的动态系统中，适当的分析、控制、学习和决策取决于推断/学习模型的准确性。大多数现有的ssm推理技术只能处理非常小的系统，无法应用于大多数大规模的实际问题。为此，本文介绍了一个两阶段贝叶斯优化（BO）框架，用于在ssm中进行可扩展和高效的推理。提出的框架将原始的大参数空间映射到包含原始空间的小线性组合的简化空间。该简化空间捕获了推理函数中最大的可变性（例如，对数似然或对数后验），通过对由粒子滤波方案近似的推理函数梯度的协方差的特征值分解获得。然后，通过提出的两阶段BO策略实现了推理过程中参数搜索空间的指数缩减，其中第一阶段BO策略在缩减空间中的解指定了第二阶段BO在原始空间中的搜索空间。通过几个实验，包括来自肠道微生物群落的真实宏基因组学数据，证明了该框架的准确性和速度。
State-space models (SSMs) are a rich class of dynamical models with a wide range of applications in economics, healthcare, computational biology, robotics, and more. Proper analysis, control, learning, and decision-making in dynamical systems modeled by SSMs depend on the accuracy of the inferred/learned model. Most of the existing inference techniques for SSMs are capable of dealing with very small systems, unable to be applied to most of the large-scale practical problems. Toward this, this article introduces a two-stage Bayesian optimization (BO) framework for scalable and efficient inference in SSMs. The proposed framework maps the original large parameter space to a reduced space, containing a small linear combination of the original space. This reduced space, which captures the most variability in the inference function (e.g., log likelihood or log a posteriori), is obtained by eigenvalue decomposition of the covariance of gradients of the inference function approximated by a particle filtering scheme. Then, an exponential reduction in the search space of parameters during the inference process is achieved through the proposed two-stage BO policy, where the solution of the first-stage BO policy in the reduced space specifies the search space of the second-stage BO in the original space. The proposed framework’s accuracy and speed are demonstrated through several experiments, including real metagenomics data from a gut microbial community.