HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise

ALPCAH：具有尾部奇异值正则化的样本级异方差PCA

ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularization

本文提出ALPCAH方法，用于估计样本级噪声方差并改进PCA子空间估计，无需分布假设或已知噪声方差，模拟实验验证了其有效性，并与PCA、RPCA和HePPCAT等方法进行了比较。

Asymptotic performance of PCA for high-dimensional heteroscedastic data

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding its performance for data that are both high-dimensional and heteroscedastic. This paper analyzes the statistical performance of PCA in this setting, i.e., for high-dimensional data drawn from a low-dimensional subspace and degraded by heteroscedastic noise. We provide simplified expressions for the asymptotic PCA recovery of the underlying subspace, subspace a…

Towards a Theoretical Analysis of PCA for Heteroscedastic Data

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data. PCA performs well in the presence of moderate noise and even with missing data, but is also sensitive to outliers. PCA is also known to have a phase transition when noise is independent and identically distributed; recovery of the subspace sharply declines at a threshold noise variance. Effective use of PCA requires a rigorous understanding of these behaviors…

Optimally Weighted PCA for High-Dimensional Heteroscedastic Data

Modern data are increasingly both high-dimensional and heteroscedastic. This paper considers the challenge of estimating underlying principal components from high-dimensional data with noise that is heteroscedastic across samples, i.e., some samples are noisier than others. Such heteroscedasticity naturally arises, e.g., when combining data from diverse sources or sensors. A natural way to account for this heteroscedasticity is to give noisier blocks of samples less weight in PCA by using the leading eigenvectors of a weighted sample covariance matrix. We consider the problem of choosing weigh…

Optimal spectral shrinkage and PCA with heteroscedastic noise

This paper studies the related problems of prediction, covariance estimation, and principal component analysis for the spiked covariance model with heteroscedastic noise. We consider an estimator of the principal components based on whitening the noise, and we derive optimal singular value and eigenvalue shrinkers for use with these estimated principal components. Underlying these methods are new asymptotic results for the high-dimensional spiked model with heteroscedastic noise, and consistent estimators for the relevant population parameters. We extend previous analysis on out-of-sample pred…

HeMPPCAT: Mixtures of Probabilistic Principal Component Analysers for Data with Heteroscedastic Noise

Mixtures of probabilistic principal component analysis (MPPCA) is a well-known mixture model extension of principal component analysis (PCA). Similar to PCA, MPPCA assumes the data samples in each mixture contain homoscedastic noise. However, datasets with heterogeneous noise across samples are becoming increasingly common, as larger datasets are generated by collecting samples from several sources with varying noise profiles. The performance of MPPCA is suboptimal for data with heteroscedastic noise across samples. This paper proposes a heteroscedastic mixtures of probabilistic PCA technique …