相关论文: Generative Principal Component Analysis

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

We use Bayesian inference and nested sampling to develop a non-parametric method to reconstruct the primordial power spectrum $P_{\mathcal{R}}(k)$ from Large Scale Structure (LSS) data. The performance of the method is studied by applying…

Probabilistic generative models can be used for compression, denoising, inpainting, texture synthesis, semi-supervised learning, unsupervised feature learning, and other tasks. Given this wide range of applications, it is not surprising…

The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In…

The principal component analysis approach is employed to extract the principal components contained in nuclear mass models for the first time. The effects coming from different nuclear mass models are reintegrated and reorganized in the…

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from…

The goal of generative machine learning is to model the probability distribution underlying a given data set. This probability distribution helps to characterize the generation process of the data samples. While classical generative machine…

We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components…

Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…

Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

We study the long-standing problem of determining the number of principal components in econometric applications from a selective inference perspective. We consider i.i.d. observations from a $p$-dimensional random vector with $p<n$ and…

Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is…