A Limitation of V-Matrix based Methods

To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are inconsistent. In particular, we would like to present that the constrained quadratic optimization problem for conditional probability estimation using V-matrix method may not have a consistent solution always. A limitation of V-matrix based (Direct) Method of Solving Conditional Probability Function V-Matrix method of estimation of conditional probability function was defined in [1]. Here we present a limitationof thesame. Since the kernel matrices are known to be positive semi-definite, the constrains matrices for the above Quadratic Programming (QP) problem may not have full rank and there is no guarantee that the constraints will be consistent, hence no solution could be found.