Variational message passing

Because every child must be conjugate to its parent, this has limited the types of distributions that can be used in the model. For example, the parents of a [[Gaussian distribution]] must be a [[Gaussian distribution]] (corresponding to the [[Mean]]) and a [[gamma distribution]] (corresponding to the precision, or one over $\backslash sigma$ in more common parameterizations). Discrete variables can have [[Dirichlet distribution|Dirichlet]] parents, and [[Poisson distribution|Poisson]] and [[Exponential distribution|exponential]] nodes must have [[gamma distribution|gamma]] parents. More recently, VMP has been extended to handle models that violate this conditional conjugacy constraint.{{cite journal |last1=Knowles |first1=David A. |last2=Minka |first2=Thomas P. |date=2011 |title=Non-conjugate Variational Message Passing for Multinomial and Binary Regression |journal=NeurIPS |volume= |issue= |pages= |doi= |access-date= | url=https://proceedings.neurips.cc/paper/2011/file/5c936263f3428a40227908d5a3847c0b-Paper.pdf}}

Because every child must be conjugate to its parent, this has limited the types of distributions that can be used in the model. For example, the parents of a [[Gaussian distribution]] must be a [[Gaussian distribution]] (corresponding to the [[Mean]]) and a [[gamma distribution]] (corresponding to the precision, or one over $\backslash sigma$ in more common parameterizations). Discrete variables can have [[Dirichlet distribution|Dirichlet]] parents, and [[Poisson distribution|Poisson]] and [[Exponential distribution|exponential]] nodes must have [[gamma distribution|gamma]] parents. More recently, VMP has been extended to handle models that violate this conditional conjugacy constraint.{{cite journal |last1=Knowles |first1=David A. |last2=Minka |first2=Thomas P. |date=2011 |title=Non-conjugate Variational Message Passing for Multinomial and Binary Regression |journal=NeurIPS |volume= |issue= |pages= |doi= |access-date= | url=https://proceedings.neurips.cc/paper/2011/file/5c936263f3428a40227908d5a3847c0b-Paper.pdf}}

== Literature ==

* {{Cite Q | Q139488859 }}

*{{Cite thesis |type=PhD |title=Variational Algorithms for Approximate Bayesian Inference |url=http://www.cs.toronto.edu/~beal/thesis/beal03.pdf |last=Beal |first=M.J. |year=2003 |publisher=Gatsby Computational Neuroscience Unit, University College London |access-date=2007-02-15 |archive-url=https://web.archive.org/web/20050428173705/http://www.cs.toronto.edu/~beal/thesis/beal03.pdf |archive-date=2005-04-28 |url-status=dead }}

==References==

==References==

{{Reflist}}

{{Reflist}}

*{{cite journal |first1=J.M. |last1=Winn |first2=C. |last2=Bishop |title=Variational Message Passing |journal=Journal of Machine Learning Research |volume=6 |pages=661–694 |year=2005 |url=http://www.johnwinn.org/Publications/papers/VMP2004.pdf |format=PDF}}

*{{Cite thesis |type=PhD |title=Variational Algorithms for Approximate Bayesian Inference |url=http://www.cs.toronto.edu/~beal/thesis/beal03.pdf |last=Beal |first=M.J. |year=2003 |publisher=Gatsby Computational Neuroscience Unit, University College London |access-date=2007-02-15 |archive-url=https://web.archive.org/web/20050428173705/http://www.cs.toronto.edu/~beal/thesis/beal03.pdf |archive-date=2005-04-28 |url-status=dead }}

==External links==

==External links==