Description Usage Arguments Details Value References See Also
Compute the LOCAL log marginal likelihood of the supplied Bayesian Networks. ie the contribution to the log marginal liklihood from one individual node.
1 2 | localLogScoreNormal(node, parents, logScoreParameters,
cache, checkInput = T)
|
node |
A numeric vector of length 1. The node to compute the local log score for. |
parents |
A numeric vector. The parents of node. |
logScoreParameters |
A list with the following components:
|
cache |
Optionally, provide an environment with cached local scores for this data. |
checkInput |
A logical of length 1, specifying whether to check the inputs to the function. |
Let X be a data matrix with a number of predictors (in columns), and y be an response variable, and that n observations are available for each. For a graph G (since this is local score this is equivalent to an indicator vector), the model used is takes the form y = phi_G * beta + epsilon with epsilon ~ N(0, sigma^{2} I). Note that the data needs to be standardised (zero-meaned).
The design matrix phi_{G} is a column of 1s, and then columns corresponding to each of the parents of the node. No cross-terms are included.
The prior used factorises as p(beta, sigma) = p(beta | sigma)p(sigma), The variance has an uninformative, scale invariant Jeffrey's prior p(sigma) = 1/sigma^2, and the coefficients have a zero-mean Normal prior (a Zellner g-prior), with g = n, so that beta | sigma ~ N(0, g * sigma^2 * (phi'_G phi_G)^-1)
The above specification gives the following marginal likelihood.
P(y | G) propto (1 + n)^(-(eta + 1)/2) * (X' * X - (n/(n + 1)) * X' * phi_G * (phi'_G * phi_G)^(-1) * phi_G * X)^(-n/2)
A numeric vector of length 1, giving the log marginal likelihood. The environment 'cache' will also be updated because its scope is global.
Nott, D. J., & Green, P. J. (2004). Bayesian Variable Selection and the Swendsen-Wang Algorithm. Journal of Computational and Graphical Statistics, 13, 141-157. http://dx.doi.org/10.1198/1061860042958
Smith, M., & Kohn, R. (1996). Nonparametric Regression using Bayesian Variable Selection. Journal of Econometrics, 75, 317-343. http://dx.doi.org/10.1016/0304-4076(95)01763-1.
Geiger, D., & Heckerman, D. (1994). Learning Gaussian Networks. Proceedings of the 10th Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-94), 235-240. http://uai.sis.pitt.edu/displayArticleDetails.jsp?mmnu=1&smnu=2& article_id=509&proceeding_id=10
logScoreNormal
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logScoreNormalOffline
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logScoreNormalIncremental
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