论文标题
贝叶斯特征分配模型的粒子吉布斯采样
Particle-Gibbs Sampling For Bayesian Feature Allocation Models
论文作者
论文摘要
贝叶斯特征分配模型是一种流行的工具，用于建模具有组合潜在结构的数据。这些模型中的精确推断通常是棘手的，因此从业者通常将马尔可夫链蒙特卡洛（MCMC）方法应用于后推断。使用最广泛的MCMC策略依赖于特征分配矩阵的元素明智的吉布斯更新。这些元素明智的更新可能效率低下，因为功能通常密切相关。为了克服这个问题，我们开发了一个Gibbs采样器，该采样器可以单个动作更新功能分配矩阵的整行。但是，对于具有大量功能的模型，随着计算复杂性在特征数量上呈指数尺度，该采样器是不切实际的。我们开发了一个粒子吉布斯采样器，该采样器的靶向与行明智的吉布斯更新相同，但具有仅在特征数量中线性增长的计算复杂性。我们使用来自一系列功能分配模型的合成数据将提出方法的性能与标准Gibbs采样器进行比较。我们的结果表明，使用PG方法的行明智更新可以显着提高特征分配模型的采样器的性能。
Bayesian feature allocation models are a popular tool for modelling data with a combinatorial latent structure. Exact inference in these models is generally intractable and so practitioners typically apply Markov Chain Monte Carlo (MCMC) methods for posterior inference. The most widely used MCMC strategies rely on an element wise Gibbs update of the feature allocation matrix. These element wise updates can be inefficient as features are typically strongly correlated. To overcome this problem we have developed a Gibbs sampler that can update an entire row of the feature allocation matrix in a single move. However, this sampler is impractical for models with a large number of features as the computational complexity scales exponentially in the number of features. We develop a Particle Gibbs sampler that targets the same distribution as the row wise Gibbs updates, but has computational complexity that only grows linearly in the number of features. We compare the performance of our proposed methods to the standard Gibbs sampler using synthetic data from a range of feature allocation models. Our results suggest that row wise updates using the PG methodology can significantly improve the performance of samplers for feature allocation models.
