Inferring relevant features: from QFT to PCA

Abstract

In many-body physics, renormalization techniques are used to extract aspects of a statistical or quantum state that are relevant at large scale, or for low energy experiments. Recent works have proposed that these features can be formally identified as those perturbations of the states whose distinguishability most resist coarse-graining. Here, we examine whether this same strategy can be used to identify important features of an unlabeled dataset. This approach indeed results in a technique very similar to kernel PCA (principal component analysis), but with a kernel function that is automatically adapted to the data, or "learned". We test this approach on handwritten digits, and find that the most relevant features are significantly better for classification than those obtained from a simple gaussian kernel.

References in corpus (4)

• PCA meets RG
• Holography as deep learning
• Coarse-grained distinguishability of field interactions
• Inferring effective field observables from a discrete model

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• Signal detection in nearly continuous spectra and symmetry breaking
• Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data
• Functional renormalization group for signal detection and stochastic ergodicity breaking
• Functional Renormalization for Signal Detection: Dimensional Analysis and Dimensional Phase Transition for Nearly Continuous Spectra Effective Field Theory