TY - JOUR
AU - Saniee, Iraj
AB - Abstract: We show that a collection of Gaussian mixture models (GMMs) in $R^{n}$ can be optimally classified using $O(n)$ neurons in a neural network with two hidden layers (deep neural network), whereas in contrast, a neural network with a single hidden layer (shallow neural network) would require at least $O(\exp(n))$ neurons or possibly exponentially large coefficients. Given the universality of the Gaussian distribution in the feature spaces of data, e.g., in speech, image and text, our result sheds light on the observed efficiency of deep neural networks in practical classification problems.
TI - Efficient Deep Learning of GMMs
JF - Statistics
DA - 2019-02-15
UR - https://www.deepdyve.com/lp/arxiv-cornell-university/efficient-deep-learning-of-gmms-CYB2QNvu8c
VL - 2019
IS - 1902
DP - DeepDyve
ER -