The following paper from the RISELab has won the “Notable Paper Award” at the 2019 Artificial Intelligence and Statistics (AISTATS) conference: A Swiss Army Infinitesimal Jackknife; Giordano, R., Stephenson, W., Liu, R., Jordan, M. I. & Broderick, T. (2019); In K. Chaudhuri and M. Sugiyama (Eds.), Proceedings of the Twenty-Second Conference on Artificial Intelligence and Statistics (AISTATS), Okinawa, Japan.

## Finite-Size Corrections and Likelihood Ratio Fluctuations in the Spiked Wigner Model

In this paper we study principal components analysis in the regime of high dimensionality and high noise. Our model of the problem is a rank-one deformation of a Wigner matrix where the signal-to-noise ratio (SNR) is of constant order, and we are interested in the fundamental limits of detection of the spike. Our main goal is to gain a fine understanding of the asymptotics for the log-likelihood ratio process, also known as the free energy, as a function of the SNR. Our main results are twofold. We first prove that the free energy has a finite-size correction to its limit—the replica-symmetric formula—which we explicitly compute. This provides a formula for the Kullback-Leibler divergence between the planted and null models. Second, …

**Authors:** Ahmed El Alaoui, Florent Krzakala, Michael Jordan