Nonlinear canonical analysis and independence tests

Dauxois, Jacques; Nkiet, Guy Martial

doi:10.1214/aos/1024691242

Cited by 35 publications

(39 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These principal components can be used to construct an orthogonal decomposition of the joint density. Dauxois and Nkiet (1998) use canonical analysis as a test of independence between two random vectors and Darolles, Florens, and Gourieroux (2000) use it produce a test of reversibility. Their statistical tests are based on the restrictions that reversibility imposes on the canonical analysis.…”

Section: Testing Symmetrymentioning

confidence: 99%

Operator Methods for Continuous-Time Markov Processes

Aı̈t-Sahalia

Hansen

Scheinkman

2010

Handbook of Financial Econometrics: Tools and Techniques

View full text Add to dashboard Cite

Section: Testing Symmetrymentioning

confidence: 99%

Operator Methods for Continuous-Time Markov Processes

Aı̈t-Sahalia

Hansen

Scheinkman

2010

Handbook of Financial Econometrics: Tools and Techniques

View full text Add to dashboard Cite

“…In some applications, it is possible to build sequences of finite-dimensional subspaces having the previous property (see [6,8]). Then, a regularised approximation is feasible because of the finite dimension.…”

Section: The Latter Inequality Shows That (R (N)mentioning

confidence: 99%

“…is the complete nonincreasing sequence of the squared canonical coefficients derived from the centered nonlinear canonical analysis (NLCA) of X 1 and X 2 (see, e.g., [6,7] This class of measures of association was introduced in [6] and has the properties given below. …”

Section: Nonlinear Association Between Random Variablesmentioning

confidence: 99%

“…Thus, the class defined by (7.11) can be seen as a particular class of measures of dependence. Examples of measures of this class are provided in [6].…”

Section: )mentioning

confidence: 99%

“…In this latter work, it is seen that these measures can be expressed as nondecreasing symmetric functions of the canonical correlation coefficients. Moreover, a class of measures of association which are related to the nonlinear canonical analysis have recently been introduced (see [6]). However, a question arises: Knowing that both linear and nonlinear canonical analysis are particular cases of the general notion of canonical analysis (CA) of Hilbertian subspaces [7], is it possible to define a notion of measure of association for Hilbertian subspaces that allows one to obtain the previous classical measures of association as particular cases?…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Measures of Association for Hilbertian Subspaces and Some Applications

Dauxois

Nkiet

2002

Journal of Multivariate Analysis

Self Cite

View full text Add to dashboard Cite

Measures of association are introduced for Hilbertian subspaces, that are defined by a few axioms and are shown to be symmetric nondecreasing functions of the canonical coefficients. When particular subspaces are considered, classical measures of association are obtained as particular cases. Moreover, the proposed framework allows one to introduce new approaches for measuring partial noncorrelation, partial independence and linear predictability of a stationary process.

show abstract

Semi-supervised Laplacian Regularization of Kernel Canonical Correlation Analysis

Blaschko

Lampert

Gretton

Machine Learning and Knowledge Discovery in Databases

View full text Add to dashboard Cite

Kernel canonical correlation analysis (KCCA) is a dimensionality reduction technique for paired data. By finding directions that maximize correlation, KCCA learns representations that are more closely tied to the underlying semantics of the data rather than noise. However, meaningful directions are not only those that have high correlation to another modality, but also those that capture the manifold structure of the data. We propose a method that is simultaneously able to find highly correlated directions that are also located on high variance directions along the data manifold. This is achieved by the use of semi-supervised Laplacian regularization of KCCA. We show experimentally that Laplacian regularized training improves class separation over KCCA with only Tikhonov regularization, while causing no degradation in the correlation between modalities. We propose a model selection criterion based on the Hilbert-Schmidt norm of the semi-supervised Laplacian regularized cross-covariance operator, which we compute in closed form.

show abstract

Nonlinear canonical analysis and independence tests

Cited by 35 publications

References 9 publications

Operator Methods for Continuous-Time Markov Processes

Operator Methods for Continuous-Time Markov Processes

Measures of Association for Hilbertian Subspaces and Some Applications

Semi-supervised Laplacian Regularization of Kernel Canonical Correlation Analysis

Contact Info

Product

Resources

About