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• W2972719005 abstract "We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a submanifold defined by a yao{sufficiently smooth non-linear map}. The observation noise is additive Gaussian. Our main result shows that the residual of the model fit, by solving a non-linear least-square problem, follows a (possibly noncentral) $chi^2$ distribution. The parameters of the $chi^2$ distribution are related to the model order and dimension of the problem. We further present a method to select the model orders sequentially. We demonstrate the broad application of the general theory in machine learning and signal processing, including determining the rank of low-rank (possibly complex-valued) matrices and tensors from noisy, partial, or indirect observations, determining the number of sources in signal demixing, and potential applications in determining the number of hidden nodes in neural networks." @default.
• W2972719005 created "2019-09-19" @default.
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• W2972719005 date "2019-09-11" @default.
• W2972719005 modified "2023-10-16" @default.
• W2972719005 title "Goodness-of-fit tests on manifolds" @default.
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• W2972719005 doi "https://doi.org/10.48550/arxiv.1909.05229" @default.
• W2972719005 hasPublicationYear "2019" @default.
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