12. A method for facilitating statistical modeling in an artificial intelligence application, comprising: employing a processor executing computer-executable instructions stored on a computer-readable storage medium to implement the following acts: receiving at least one data set representing an outcome, the at least one data set having incomplete observation data for a set of variables with at least one continuous variable; utilizing the data set and probabilistic inference to determine parameter gradients for a log-likelihood of a conditional Gaussian (CG) graphical model over those variables; representing the CG graphical model as a recursive exponential mixed model (REMM); determining a conditional Gaussian regression in the REMM representation model; utilizing a chain rule to transform a resulting parameter gradient expression into a parameter representation of c, β, and σ, representing an intercept, coefficients, and variance, respectively for a regression on continuous parents; employing probabilistic inference to determine quantities in the parameter gradient expression; converting a resulting parameterization into a non-exponential representation; utilizing a propagation scheme on the non-exponential parameterization in order to compute at least one gradient; assigning, for all families (X v ,X pa(v) ) where X v is a continuous variable, each configuration of discrete parent variables x d pa(v) a sum vector and a sum of squares matrix for expected posterior statistics associated with conditional distributions for the continuous variable and its continuous parents (X v ,X c pa(v) ) given configurations of discrete parents; For each data case in a data set: utilizing a propagation scheme for Bayesian networks with conditional Gaussian distributions to determine a mean vector and a covariance matrix associated with a posterior marginal distribution for all families (X v ,X pa(v) ), where X v is a continuous variable; employing posterior conditional means and variances to determine expected values (x v *,x c pa(v) *) and ((x v x v )*, (x v x c pa(v) )*, (x v x c pa(v) ′)*, (x c pa(v) ′X c pa(v) )*) for continuous variables in each of these families given each configuration of discrete variables in the respective families; adding the expected values to the sum and the sum of squares expected posterior statistics; and determining the parameter gradients utilizing a formula for a sample of incomplete observations; employing the CG graphical model to deduce a cause of the given outcome in an artificial intelligence application; and displaying the deduced cause on a display device.
12. A method for facilitating statistical modeling in an artificial intelligence application, comprising: employing a processor executing computer-executable instructions stored on a computer-readable storage medium to implement the following acts: receiving at least one data set representing an outcome, the at least one data set having incomplete observation data for a set of variables with at least one continuous variable; utilizing the data set and probabilistic inference to determine parameter gradients for a log-likelihood of a conditional Gaussian (CG) graphical model over those variables; representing the CG graphical model as a recursive exponential mixed model (REMM); determining a conditional Gaussian regression in the REMM representation model; utilizing a chain rule to transform a resulting parameter gradient expression into a parameter representation of c, β, and σ, representing an intercept, coefficients, and variance, respectively for a regression on continuous parents; employing probabilistic inference to determine quantities in the parameter gradient expression; converting a resulting parameterization into a non-exponential representation; utilizing a propagation scheme on the non-exponential parameterization in order to compute at least one gradient; assigning, for all families (X v ,X pa(v) ) where X v is a continuous variable, each configuration of discrete parent variables x d pa(v) a sum vector and a sum of squares matrix for expected posterior statistics associated with conditional distributions for the continuous variable and its continuous parents (X v ,X c pa(v) ) given configurations of discrete parents; For each data case in a data set: utilizing a propagation scheme for Bayesian networks with conditional Gaussian distributions to determine a mean vector and a covariance matrix associated with a posterior marginal distribution for all families (X v ,X pa(v) ), where X v is a continuous variable; employing posterior conditional means and variances to determine expected values (x v *,x c pa(v) *) and ((x v x v )*, (x v x c pa(v) )*, (x v x c pa(v) ′)*, (x c pa(v) ′X c pa(v) )*) for continuous variables in each of these families given each configuration of discrete variables in the respective families; adding the expected values to the sum and the sum of squares expected posterior statistics; and determining the parameter gradients utilizing a formula for a sample of incomplete observations; employing the CG graphical model to deduce a cause of the given outcome in an artificial intelligence application; and displaying the deduced cause on a display device. 13. The method of claim 12 further comprising: employing the parameter gradients in a gradient-based optimization process that iteratively adapts parameters of a model to improve incomplete data likelihood.