关键词: 复拟随机变量, 准范数, 复经验风险最小化原则, 关键定理, 收敛速度的界, 神经网络

Abstract: Firstly，the definitions of complex quasi-random variable and primary norm are introduced.Next the concepts and some properties of the mathematical expectation and variance of complex quasi-random variables are provided.Secondly，for complex quasi-random variables we discuss a number of fundamental concepts such as e.g.，Markov’s inequalities，Chebyshev’s inequalities and a Khinchine’s law of large numbers.Finally，the definitions of the complex empirical risk functional，the complex expected risk functional，and complex empirical risk minimization principle on quasi-probability measure space are proposed.Then the key theorem of learning theory based on complex quasi-random samples is proved，and the bounds on the rate of uniform convergence of learning process are constructed.The investigations will help lay essential theoretical foundations for the systematic and comprehensive development of the complex quasi-statistical learning theory.

Key words: complex quasi-random variable, primary norm, complex empirical risk minimization principle, key theorem, the bounds on the rate of convergence, neural network