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Nonlinear multi-output regression on unknown input manifold. (English) Zbl 1386.68133

Summary: Consider unknown smooth function which maps high-dimensional inputs to multidimensional outputs and whose domain of definition is unknown low-dimensional input manifold embedded in an ambient high-dimensional input space. Given training dataset consisting of “input-output” pairs, regression on input manifold problem is to estimate the unknown function and its Jacobian matrix, as well to estimate the input manifold. By transforming high-dimensional inputs in their low-dimensional features, initial regression problem is reduced to certain regression on feature space problem. The paper presents a new geometrically motivated method for solving both interrelated regression problems.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
62G08 Nonparametric regression and quantile regression
62H25 Factor analysis and principal components; correspondence analysis
68T10 Pattern recognition, speech recognition
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