Learning Polynomial Transformations via Generalized Tensor Decompositions

We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form f(x), where x∼N(0,Ir) is hidden and f: ℝr → ℝd is a function where every output coordinate is a low-degree polynomial, the goal is to learn the distribution over f(x). One can think of this as a simple model for learning deep generative models, namely pushforwards of Gaussians under two-layer neural networks with polynomial activations, though the learning problem is mathematically natural in its own right.