# Expectation Propagation - The Essential Minimum

Taken from Vehtari et al. (2014). Assume that you can factorize your target distribution $f(\theta) \propto \prod_{k=0}^K f_k(\theta)$ Approximate target distribution using a distribution with a similar factorization, called the global approximation $g(\theta) \propto \prod_{k=0}^K g_k(\theta)$ At each iteration of the algorithm, and for every factor $$k=1, \ldots, K$$ form the cavity distribution by removing $$k^{\text{th}}$$ term from the global approximation $g_{-k} \propto \frac{g(\theta)}{g_k(\theta)}$ also form the tilted distribution by including $$f_k(\theta)$$ to the cavity distribution (in place of $$g_k(\theta)$$) $g_{\backslash k}(\theta) \propto f_k(\theta) g_{-k}(\theta)$ The algorithm updates the site approximation $$g_k(\theta)$$ so that the new global approximation approximates the tilted distribution $g_k(\theta)^{\text{new}}g_{-k}(\theta) \approx f_k(\theta)g_{-k}(\theta)$

# Bibliography

Vehtari, Aki, Andrew Gelman, Tuomas Sivula, Pasi Jylänki, Dustin Tran, Swupnil Sahai, Paul Blomstedt, John P. Cunningham, David Schiminovich, and Christian Robert. 2014. “Expectation Propagation as a Way of Life: A Framework for Bayesian Inference on Partitioned Data.” ##### Mauro Camara Escudero
###### Computational Statistics and Data Science Ph.D.

My research interests include approximate manifold sampling and generative models.