Dependent Indian Buffet Processes
Dependent Indian Buffet Processes
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发表时间：
2010-12
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通讯作者：
Sinead Williamson;Peter Orbanz;Zoubin Ghahramani
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作者：
Sinead Williamson;Peter Orbanz;Zoubin Ghahramani
潜变量模型表示观测数据中的隐藏结构。为了解释观测数据随时间、空间或其他协变量变化的分布，我们需要对潜在变量模型进行概括，以明确地捕捉对协变量的依赖性。基于狄利克雷过程的潜在变量模型已经提出了各种这样的推广。我们通过引入一个依赖的印度自助餐过程来解决二元潜在特征模型中对协变量的依赖。该模型为协变量的每个值生成一个具有无限列数的二进制随机矩阵。二元矩阵在协变量集上的演化由一个分层高斯过程模型控制。协方差函数的选择控制了模型的依赖结构和互换性。我们推导了一种用于贝叶斯推理的马尔可夫链蒙特卡罗采样算法，并在合成数据和实际数据上进行了实验。实验结果表明，显式的依赖关系建模显著提高了预测的准确性。
Latent variable models represent hidden structure in observational data. To account for the distribution of the observational data changing over time, space or some other covariate, we need generalizations of latent variable models that explicitly capture this dependency on the covariate. A variety of such generalizations has been proposed for latent variable models based on the Dirichlet process. We address dependency on covariates in binary latent feature models, by introducing a dependent Indian buffet process. The model generates, for each value of the covariate, a binary random matrix with an unbounded number of columns. Evolution of the binary matrices over the covariate set is controlled by a hierarchical Gaussian process model. The choice of covariance functions controls the dependence structure and exchangeability properties of the model. We derive a Markov Chain Monte Carlo sampling algorithm for Bayesian inference, and provide experiments on both synthetic and real-world data. The experimental results show that explicit modeling of dependencies significantly improves accuracy of predictions.