Semi-supervised Wavelet Thresholding and Applications
نویسندگان
چکیده
Under the general regression setup, yi = gi + ǫi, we are interested in estimating a possibly multivariate regression function g. The wavelet thresholding is a simple operation in the wavelet domain that selects the subset of wavelet coefficients corresponding to an estimator of g when back-transformed. We propose the selection of this subset in a semi-supervised fashion, in which a neighbor structure and classification function appropriate for wavelet domains are utilized. The unlabeled coefficients are considered to be connected to neighboring coefficients and fall on a low dimensional manifold in the space of all wavelet coefficients. The decision to include a coefficient in the model depends not only on its magnitude but also on the labeled and unlabeled coefficients from its neighborhood. The theoretical properties of the method are discussed and its performance is demonstrated on simulated examples.
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