  Textbook wisdom advocates for smooth function fits and implies that
interpolation of noisy data should lead to poor generalization. A related
heuristic is that fitting parameters should be fewer than measurements (Occam's
Razor). Surprisingly, contemporary machine learning (ML) approaches, cf. deep
nets (DNNs), generalize well despite interpolating noisy data. This may be
understood via Statistically Consistent Interpolation (SCI), i.e. data
interpolation techniques that generalize optimally for big data. In this
article we elucidate SCI using the weighted interpolating nearest neighbors
(wiNN) algorithm, which adds singular weight functions to kNN (k-nearest
neighbors). This shows that data interpolation can be a valid ML strategy for
big data. SCI clarifies the relation between two ways of modeling natural
phenomena: the rationalist approach (strong priors) of theoretical physics with
few parameters and the empiricist (weak priors) approach of modern ML with more
parameters than data. SCI shows that the purely empirical approach can
successfully predict. However data interpolation does not provide theoretical
insights, and the training data requirements may be prohibitive. Complex animal
brains are between these extremes, with many parameters, but modest training
data, and with prior structure encoded in species-specific mesoscale circuitry.
Thus, modern ML provides a distinct epistemological approach different both
from physical theories and animal brains.
