Title: Computational and statistical limits in high dimensional independent component analysis
Authors: Arnab Auddy - Columbia University (United States) [presenting]
Ming Yuan - Columbia University (United States)
Abstract: The independent components analysis (ICA) model is a popular semiparametric model where one observes a d-dimensional vector $X=AS$ for an unknown invertible mixing matrix $A$ and a random vector $S$ consisting of independent components. Despite its usage in a variety of applications, existing statistical results in such models are restricted to the case of fixed dimension $d$. We will address the issues of computability and statistical inference in the ICA model when $d$ is allowed to grow. We will first see that there exists a computational limit, in terms of the sample size $n$ and the dimension $d$, below which it is computationally hard to recover any column of $A$. On the other hand, if we are above this limit, it is, in fact, possible to estimate the columns of $A$ at a parametric rate, without estimating the unknown marginal distributions of $S$. Additionally, we show that our estimators are asymptotically normal (for sufficiently large $d$ and $n$) whenever we are above the computational limit.