MAP.LinearGaussianGaussian: Maximum A Posteriori (MAP) estimate of a "LinearGaussianGaussian" object

Description

Generate the MAP estimate of mu in following model structure: $$x \sim Gaussian(A z + b, Sigma)$$ $$z \sim Gaussian(m,S)$$ Where Sigma is known. A is a $dimx x dimz$ matrix, x is a $dimx x 1$ random vector, z is a $dimz x 1$ random vector, b is a $dimm x 1$ vector. Gaussian() is the Gaussian distribution. See ?dGaussian for the definition of Gaussian distribution. The model structure and prior parameters are stored in a "LinearGaussianGaussian" object. The MAP estimates are:

$z_MAP = argmax p(z|m,S,A,b,x,Sigma)$

Usage

# S3 method for LinearGaussianGaussian
MAP(obj, ...)

Arguments

obj

A "LinearGaussianGaussian" object.

...

Additional arguments to be passed to other inherited types.

Value

numeric vector, the MAP estimate of "z".

References

Murphy, Kevin P. Machine learning: a probabilistic perspective. MIT press, 2012.

Examples

Run this code

# NOT RUN {
obj <- LinearGaussianGaussian(gamma=list(Sigma=matrix(c(2,1,1,2),2,2),
                                         m=c(0.2,0.5,0.6),S=diag(3)))
x <- rGaussian(100,mu = runif(2),Sigma = diag(2))
A <- matrix(runif(6),2,3)
b <- runif(2)
ss <- sufficientStatistics(obj,x=x,A=A,b=b)
## update prior into posterior
posterior(obj=obj,ss=ss)
## get the MAP estimate of z
MAP(obj)
# }