Estimating the number of signals using principal component analysis

Virta, Joni; Nordhausen, Klaus

doi:10.1002/sta4.231

Cited by 9 publications

(16 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Again, as it is risky to base the decision here on one lag τ only, that is, on AMUSE alone, pooling information is again a safer choice. The pooled "SOBI" eigenvalues are defined as Matilainen et al (2018); Virta and Nordhausen (2021) for this purpose is…”

Section: Estimation Of Q In Inmmentioning

confidence: 99%

“…where Matilainen et al (2018) suggested bootstrapping strategies to get the distribution of t k under H 0k , and Virta and Nordhausen (2021) showed that under quite broad assumptions for a time series of length T, T j T j p −q ð Þ 2 t q converges to a χ 2 Virta and Nordhausen (2021) also showed that successive testing can be used to get a consistent estimate for q.…”

Section: Estimation Of Q In Inmmentioning

confidence: 99%

See 1 more Smart Citation

A review of second‐order blind identification methods

Pan

Matilainen

Taskinen

et al. 2021

WIREs Computational Stats

Self Cite

View full text Add to dashboard Cite

Second-order source separation (SOS) is a data analysis tool which can be used for revealing hidden structures in multivariate time series data or as a tool for dimension reduction. Such methods are nowadays increasingly important as more and more high-dimensional multivariate time series data are measured in numerous fields of applied science. Dimension reduction is crucial, as modeling such high-dimensional data with multivariate time series models is often impractical as the number of parameters describing dependencies between the component time series is usually too high. SOS methods have their roots in the signal processing literature, where they were first used to separate source signals from an observed signal mixture. The SOS model assumes that the observed time series (signals) is a linear mixture of latent time series (sources) with uncorrelated components. The methods make use of the second-order statistics-hence the name "second-order source separation." In this review, we discuss the classical SOS methods and their extensions to more complex settings. An example illustrates how SOS can be performed.

show abstract

Section: Estimation Of Q In Inmmentioning

confidence: 99%

Section: Estimation Of Q In Inmmentioning

confidence: 99%

A review of second‐order blind identification methods

Pan

Matilainen

Taskinen

et al. 2021

WIREs Computational Stats

Self Cite

View full text Add to dashboard Cite

show abstract

“…If r < r, then we may fail to capture all relevant information in L. On the other hand, if r > r, then the estimate L will overfit the training data, potentially leading to downstream overfitting in the ensemble. In general, estimating r is a challenging task [Wold, 1978, Peres-Neto et al, 2005, Choi et al, 2017, Virta and Nordhausen, 2019.…”

Section: Crc-l: Training a Classifier On The Latent Signalsmentioning

confidence: 99%

Separating and reintegrating latent variables to improve classification of genomic data

Payne¹,

Gagnon-Bartsch²

2020

Preprint

View full text Add to dashboard Cite

Genomic datasets contain the effects of various unobserved biological variables in addition to the variable of primary interest. These latent variables often affect a large number of features (e.g., genes) and thus give rise to dense latent variation, which presents both challenges and opportunities for classification. Some of these latent variables may be partially correlated with the phenotype of interest and therefore helpful, while others may be uncorrelated and thus merely contribute additional noise. Moreover, whether potentially helpful or not, these latent variables may obscure weaker effects that impact only a small number of features but more directly capture the signal of primary interest. We propose the cross-residualization classifier to better account for the latent variables in genomic data. Through an adjustment and ensemble procedure, the cross-residualization classifier essentially estimates the latent variables and residualizes out their effects, trains a classifier on the residuals, and then re-integrates the the latent variables in a final ensemble classifier. Thus, the latent variables are accounted for without discarding any potentially predictive information that they may contribute. We apply the method to simulated data as well as a variety of genomic datasets from multiple platforms. In general, we find that the cross-residualization classifier performs well relative to existing classifiers and sometimes offers substantial gains.

show abstract

“…This signal subspace can be straightforwardly estimated with PCA as long as one knows its dimension d which is, however, usually unknown in practice. Numerous procedures for determining the dimension have been proposed, see Jolliffe (2002) for a review and, e.g., Schott (2006); Nordhausen et al (2016); Virta and Nordhausen (2019) for asymptotic tests and Beran and Srivastava (1985); Dray (2008); Luo and Li (2016) for bootstrap-and permutation-based techniques. Simplest of these methods is perhaps the test of sub-sphericity based on the test statistics, Tn,j = m2,p−j(Sn) m1,p−j(Sn) 2 − 1, j = 0, .…”

Section: Introductionmentioning

confidence: 99%

Testing for subsphericity when $n$ and $p$ are of different asymptotic order

Virta¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this short note, we extend a classical test of subsphericity, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional regime where the signal eigenvalues of the covariance matrix diverge to infinity and either p/n → 0 or p/n → ∞.In the latter case we further require that the divergence of the eigenvalues is suitably fast in a specific sense. Our work can be seen to complement that of Schott ( 2006) who established equivalent results in the regime p/n → γ ∈ (0, ∞). Simulations are used to demonstrate the results, providing also evidence that the test might be further extendable to a wider asymptotic setting.

show abstract

Estimating the number of signals using principal component analysis

Cited by 9 publications

References 24 publications

A review of second‐order blind identification methods

A review of second‐order blind identification methods

Separating and reintegrating latent variables to improve classification of genomic data

Testing for subsphericity when $n$ and $p$ are of different asymptotic order

Contact Info

Product

Resources

About