Dimensionality reduction to maximize prediction generalization capability. (arXiv:2003.00470v2 [stat.ML] UPDATED)

Generalization of time series prediction remains an important open issue in
machine learning, wherein earlier methods have either large generalization
error or local minima. We develop an analytically solvable, unsupervised
learning scheme that extracts the most informative components for predicting
future inputs, termed predictive principal component analysis (PredPCA). Our
scheme can effectively remove unpredictable noise and minimize test prediction
error through convex optimization. Mathematical analyses demonstrate that,
provided with sufficient training samples and sufficiently high-dimensional
observations, PredPCA can asymptotically identify …

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