  Many statistical learning problems have recently been shown to be amenable to
Semi-Definite Programming (SDP), with community detection and clustering in
Gaussian mixture models as the most striking instances [javanmard et al.,
2016]. Given the growing range of applications of SDP-based techniques to
machine learning problems, and the rapid progress in the design of efficient
algorithms for solving SDPs, an intriguing question is to understand how the
recent advances from empirical process theory can be put to work in order to
provide a precise statistical analysis of SDP estimators.
  In the present paper, we borrow cutting edge techniques and concepts from the
learning theory literature, such as fixed point equations and excess risk
curvature arguments, which yield general estimation and prediction results for
a wide class of SDP estimators. From this perspective, we revisit some
classical results in community detection from [gu\'edon et al.,2016] and [chen
et al., 2016], and we obtain statistical guarantees for SDP estimators used in
signed clustering, group synchronization and MAXCUT.
