Optimality of Least-squares for Classification in Gaussian-Mixture Models

摘要: We consider the problem of learning coefficients a linear classifier through Empirical Risk Minimization with convex loss function in high-dimensional setting. In particular, we introduce an approach to characterize best achievable classification risk among losses, when data points follow standard Gaussian-mixture model. Importantly, prove that square achieves minimum for this Our numerical illustrations verify theoretical results and show they are accurate even relatively small dimensions.