SEMIDEFINITE PROGRAMMING AND MULTIVARIATE CHEBYSHEV BOUNDS

Abstract Chebyshev inequalities provide bounds on the probability of a set based on known expected values of certain functions, for example, known power moments. In some important cases these bounds can be efficiently computed via convex optimization. We discuss one particular type of generalized Chebyshev bound, a lower bound on the probability of a set defined by strict quadratic inequalities, given the mean and the covariance of the distribution. We present a semidefinite programming formulation, give an interpretation of the dual problem, and describe some applications.