6533b833fe1ef96bd129b98d
RESEARCH PRODUCT
Signal-to-noise ratio in reproducing kernel Hilbert spaces
Gustau Camps-vallsLuis Gómez-chovaRaul Santos-rodriguezsubject
Noise model02 engineering and technologySNR010501 environmental sciences01 natural sciencesKernel principal component analysisSenyal Teoria del (Telecomunicació)Signal-to-noise ratioArtificial Intelligence0202 electrical engineering electronic engineering information engineeringHeteroscedastic0105 earth and related environmental sciencesMathematicsNoise (signal processing)Dimensionality reductionKernel methodsSignal classificationSupport vector machineKernel methodKernel (statistics)Anàlisi funcionalSignal ProcessingFeature extraction020201 artificial intelligence & image processingSignal-to-noise ratioComputer Vision and Pattern RecognitionAlgorithmSoftwareImatges ProcessamentReproducing kernel Hilbert spaceCausal inferencedescription
This paper introduces the kernel signal-to-noise ratio (kSNR) for different machine learning and signal processing applications}. The kSNR seeks to maximize the signal variance while minimizing the estimated noise variance explicitly in a reproducing kernel Hilbert space (rkHs). The kSNR gives rise to considering complex signal-to-noise relations beyond additive noise models, and can be seen as a useful signal-to-noise regularizer for feature extraction and dimensionality reduction. We show that the kSNR generalizes kernel PCA (and other spectral dimensionality reduction methods), least squares SVM, and kernel ridge regression to deal with cases where signal and noise cannot be assumed independent. We give computationally efficient alternatives based on reduced-rank Nyström and projection on random Fourier features approximations, and analyze the bounds of performance and its stability. We illustrate the method through different examples, including nonlinear regression, nonlinear classification in channel equalization, nonlinear feature extraction from high-dimensional spectral satellite images, and bivariate causal inference. Experimental results show that the proposed kSNR yields more accurate solutions and extracts more noise-free features when compared to standard approaches.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-09-01 |