Supervised singular value decomposition and its asymptotic properties

Li, Gen; Yang, Dan; Nobel, Andrew B.; Shen, Haipeng

doi:10.1016/j.jmva.2015.02.016

Cited by 45 publications

(46 citation statements)

References 28 publications

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“…Then model (1.4) can be written in a more compact matrix form: (1.5) We treat the loadings G(X) and Γ as realizations of random matrices throughout the paper. This model is also closely related to the supervised singular value decomposition model, recently studied by Li et al (2015). The authors showed that the model is useful in studying the gene expression and single-nucleotide polymorphism (SNP) data, and proposed an EM algorithm for parameter estimation.…”

Section: This Papermentioning

confidence: 99%

Projected Principal Component Analysis in Factor Models

2014

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This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employees principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are related to the projected linear space. When the dimensionality is large, the factors can be estimated accurately even when the sample size is finite. We propose a flexible semi-parametric factor model, which decomposes the factor loading matrix into the component that can be explained by subject-specific covariates and the orthogonal residual component. The covariates' effects on the factor loadings are further modeled by the additive model via sieve approximations. By using the newly proposed Projected-PCA, the rates of convergence of the smooth factor loading matrices are obtained, which are much faster than those of the conventional factor analysis. The convergence is achieved even when the sample size is finite and is particularly appealing in the high-dimension-low-sample-size situation. This leads us to developing nonparametric tests on whether observed covariates have explaining powers on the loadings and whether they fully explain the loadings. The proposed method is illustrated by both simulated data and the returns of the components of the S&P 500 index.

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Section: This Papermentioning

confidence: 99%

Projected Principal Component Analysis in Factor Models

2014

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“…Our ProPrPCA‐Krige model is closely related to the SupSVD model recently proposed by Li, Yang, Nobel, and Shen (). The SupSVD model is expressed as

bold-italicX = bold-italicU {bold-italicV}^{sans-serifT} + bold-italicE

where U = YB + F .…”

Section: Probabilistic Predictive Pcamentioning

confidence: 97%

Probabilistic predictive principal component analysis for spatially misaligned and high‐dimensional air pollution data with missing observations

Larson

Szpiro

2019

Environmetrics

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Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM 2.5 ), in which data are usually not measured at all study locations. PM 2.5 is also a mixture of many different chemical components. Principal component analysis (PCA) can be incorporated to obtain lowerdimensional representative scores of such multipollutant data. Spatial prediction can then be used to estimate these scores at new locations. Recently developed predictive PCA modifies the traditional PCA algorithm to obtain scores with spatial structures that can be well predicted at unmeasured locations. However, these approaches require complete data, whereas multipollutant data tend to have complex missing patterns in practice. We propose probabilistic versions of predictive PCA, which allow for flexible model-based imputation that can account for spatial information and subsequently improve the overall predictive performance.

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“…The SupCP model specified in Section 3.1 reduces to traditional factor analysis without supervision (B = 0) and when K = 1, i.e., when X is a matrix. More generally, when K = 1 SupCP reduces to the SupSVD model [19]. Thus, an alternative strategy of decomposing X is to apply SupSVD to the matricized data X (1) .…”

Section: Special Casesmentioning

confidence: 99%

Supervised multiway factorization

Lock¹,

Li²

2018

Electron. J. Statist.

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We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order array. Such data are increasingly encountered in biomedical research and other fields. We use a novel likelihood-based latent variable representation of the CP factorization, in which the latent variables are informed by additional covariates. We give conditions for identifiability, and develop an EM algorithm for simultaneous estimation of all model parameters. SupCP can be used for dimension reduction, capturing latent structures that are more accurate and interpretable due to covariate supervision. Moreover, SupCP specifies a full probability distribution for a multiway data observation with given covariate values, which can be used for predictive modeling. We conduct comprehensive simulations to evaluate the SupCP algorithm. We apply it to a facial image database with facial descriptors (e.g., smiling / not smiling) as covariates, and to a study of amino acid fluorescence. Software is available at https://github.com/lockEF/SupCP.

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Supervised singular value decomposition and its asymptotic properties

Cited by 45 publications

References 28 publications

Projected Principal Component Analysis in Factor Models

Projected Principal Component Analysis in Factor Models

Probabilistic predictive principal component analysis for spatially misaligned and high‐dimensional air pollution data with missing observations

Supervised multiway factorization

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