## Universal Prediction Band via Semi-Definite Programming

This paper proposes a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification.

This paper proposes a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification.

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the sampling nature of the data. We introduce the moment-adjusted stochastic gradient descents, a new stochastic optimization method for statistical inference.