How to estimate weak spikes is a fundamental problem in high-dimensional data analysis, where the empirical eigenvalue approach is known to be significantly biased. To correct the bias, we may use random matrix theory to derive the precise asymptotical behavior of the empirical eigenvalues, but such an approach is quite hard and so far researchers are only able to solve the idealized GOE case.

We developed a new approach where we first use the cycle count statistics to estimate the order-m moments of the spikes for m=1,2,..., and then use these moments to estimate the spikes. In a setting much broader than the GOE case, we show that our approaches are consistent with algebraic rates. To implement our approaches, we must address a long lasting problem: how to efficiently compute the cycle count statistics. We solve it with a humAI approach where we combine complicated graph theory with the intelligence of AI.