  Motivated by the sampling problems and heterogeneity issues common in high-
dimensional big datasets, we consider a class of discordant additive index
models. We propose method of moments based procedures for estimating the
indices of such discordant additive index models in both low and
high-dimensional settings. Our estimators are based on factorizing certain
moment tensors and are also applicable in the overcomplete setting, where the
number of indices is more than the dimensionality of the datasets. Furthermore,
we provide rates of convergence of our estimator in both high and
low-dimensional setting. Establishing such results requires deriving tensor
operator norm concentration inequalities that might be of independent interest.
Finally, we provide simulation results supporting our theory. Our contributions
extend the applicability of tensor methods for novel models in addition to
making progress on understanding theoretical properties of such tensor methods.
