19. The storage medium as set forth in claim 18 , wherein the optimization function is configured to optimize a softmax function of the form ⅇ β k T ⁢ x ∑ k ′ = 1 K ⁢ ⅇ β k ′ T ⁢ x .
19. The storage medium as set forth in claim 18 , wherein the optimization function is configured to optimize a softmax function of the form ⅇ β k T ⁢ x ∑ k ′ = 1 K ⁢ ⅇ β k ′ T ⁢ x . 21. The storage medium as set forth in claim 19 , wherein the upper bounding a sum of exponentials by a product of sigmoids comprises upper bounding an expectation of the softmax function of the form E Q [e β k T x ] where Q(β k ) denotes a probability density function (pdf) over the parameters β and E Q [ . . . ] denotes an expectation with respect to Q.