# Is there a non-linear version of ICA?

"Independent Component Analysis" is this : someone is sampling a random vector $s \in \mathbb{R}^d$ such that all its components $s_i$ are mutually independent and $\mathbb{E}[s_i^4] < 3$ and the observer has access to only a transform of it as $y = Ws + b$ where $W$ is a full rank $d \times d$ matrix and $b \in \mathbb{R}^d$. Now the question is to be able to recover $W$ and $b$ from $i.i.d$ samples of $y$.

• Is there a natural scenario where one looks at a non-linear version of this question? Like one has to recover the non-linear transformation applied to the sampled $s$?
• Of course there is nonlinear ICA. Are you looking for examples of usage? A way to look at results / internals? – Evil Apr 8 '16 at 15:55
• Thanks! Has there been any recent work on this? Like what is the state of the art of doing this recovery and/or use? – gradstudent Apr 12 '16 at 21:33
• Like in the linear ICA we can recover W and b. I guess there is an analogous question of function recovery in the non-linear case too? – gradstudent Apr 12 '16 at 22:02
• I am not getting you! In linear ICA we do recover W and b. So we do get the "mixing matrix" W. What is your question? – gradstudent Apr 13 '16 at 2:24
• Has there been any recent work or use of this non-linear ICA? – gradstudent Apr 13 '16 at 3:26