probability . The approximation has the basic property that it is a factorized distribution, i.e. a product of two or more independent distributions over disjoint subsets of the unobserved variables. Partition the unobserved variables into two or more subsets, over which the independent factors will be derived. There is no universal procedure for doing this; creating too many subsets yields a poor approximation, while creating too few makes the entire variational Bayes procedure intractable. Typically, the first split is to separate the parameters and latent variables; often, this is enough by itself to produce a tractable result. Assume that the partitions are called . For a given partition , write down the formula for the best approximating distribution using the basic equation . Fill in the formula for the joint probability distribution using the graphical model. Any component conditional distributions that don't involve any of the variables in can be ignored; they will be folded into the constant term. Simplify the formula and apply the expectation operator, following the above example. Ideally, this should simplify into expectations of basic functions of variables not in (e.g. first or second raw moments, expectation of a logarithm, etc.). In order for the variational Bayes procedure to work well, these expectations should generally be expressible analytically as functions of the parameters and/or hyperparameters of the distributions of these variables. In all cases, these expectation terms are constants with respect to the variables in the current partition. The functional form of the formula with respect to the variables in the current partition indicates the type of distribution. In particular, exponentiating the formula generates the probability density function (PDF) of the distribution (or at least, something proportional to it, with unknown normalization constant). In order for the overall method to be tractable, it should be possible to recognize the functional form as belonging to a known distribution. Significant mathematical manipulation may be required to convert the formula into a form that matches the PDF of a known distribution. When this can be done, the normalization constant can be reinstated by definition, and equations for the parameters of the known distribution can be derived by extracting the appropriate parts of the formula. When all expectations can be replaced analytically with functions of variables not in the current partition, and the PDF put into a form that allows identification with a known distribution, the result is a set