HePPCAT: Probabilistic PCA for Data With Heteroscedastic Noise
HePPCAT: Probabilistic PCA for Data With Heteroscedastic Noise
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DOI：
10.1109/tsp.2021.3104979
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发表时间：
2021-01
影响因子：
5.4
通讯作者：
David Hong;Kyle Gilman;L. Balzano;J. Fessler
中科院分区：
文献类型：
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作者：
David Hong;Kyle Gilman;L. Balzano;J. Fessler
主成分分析（PCA）是一种用于降低数据维度的经典且普遍的方法，但对于在现代应用中日益常见的异构数据而言，它并非最优选择。PCA对所有样本一视同仁，因此当噪声在样本间具有异方差性时（例如当样本来自不同质量的数据源时就会出现这种情况），其效果就会变差。本文开发了一种概率PCA变体，通过将异构性纳入统计模型来对其进行估计和考虑。与同方差情形不同，由此产生的非凸优化问题似乎无法通过奇异值分解来解决。本文开发了一种异方差概率PCA技术（HePPCAT），它使用高效的交替最大化算法来联合估计潜在因素和未知的噪声方差。模拟实验说明了算法的相对速度、考虑异方差性的益处以及该问题看似有利的优化情况。对环境空气质量数据进行的实际数据实验表明，与不考虑异方差性的技术相比，HePPCAT能够给出更好的PCA估计。
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so degrades when the noise is heteroscedastic across samples, as occurs, e.g., when samples come from sources of heterogeneous quality. This paper develops a probabilistic PCA variant that estimates and accounts for this heterogeneity by incorporating it in the statistical model. Unlike in the homoscedastic setting, the resulting nonconvex optimization problem is not seemingly solved by singular value decomposition. This paper develops a heteroscedastic probabilistic PCA technique (HePPCAT) that uses efficient alternating maximization algorithms to jointly estimate both the underlying factors and the unknown noise variances. Simulation experiments illustrate the comparative speed of the algorithms, the benefit of accounting for heteroscedasticity, and the seemingly favorable optimization landscape of this problem. Real data experiments on environmental air quality data show that HePPCAT can give a better PCA estimate than techniques that do not account for heteroscedasticity.