modeling including conditional random fields crfs maximum entropy methods graphical models and maximum likelihood estimation an embodiment can include upper bounding a partition function using a quadratic function and optimizing parameters using the bounding fig1 is a flow chart of an example method for parameter optimization using a partition function bound in accordance with at least one embodiment in particular at 102 initial parameters are provided to a system at 104 a feature function e g u0192 y is provided to the system and at 106 an a priori probability function e g h y is provided to the system at 108 the system computes a quadratic upper bound on a partition function as described below at 110 the system tests a loop index if the end of the index has been reached processing continues to 112 otherwise processing continues to 108 at 112 the quadratic parameters of the partition function bound are provided for downstream processing the mathematical basis for partition function bounding e g as shown in fig1 is set forth below which is parameterized by a vector u03b8 u03b5 d of dimensionality d u03b5z here u0192 u03c9 d is any vector valued function mapping an input y to some arbitrary vector the prior h u03c9 is a fixed non negative measure the partition function z u03b8 is a scalar that ensures that p y u03b8 normalizes i e z u03b8 u03c3 y h y exp u03b8 t u0192 y assume that the number of configurations of y is u03c9 n and is finite the partition function is clearly log convex in u03b8 and a linear lower bound is given via jensen 39 s inequality as mentioned above.