Monday, March 10, 2014 - 3:05pm
1 hour (actually 50 minutes)
Bayesian approaches to statistical model selection requires the evaluation of the marginal likelihood integral, which, in general, is difficult to obtain. When the statistical model is regular, it is well-known that the marginal likelihood integral can be approximated using a function of the maximized log-likelihood function and the dimension of the model. When the model is singular, Sumio Watanabe has shown that an approximation of the marginal likelihood integral can be obtained through resolution of singularities, a result that has intimately tied machine learning and Bayesian model selection to computational algebraic geometry. This talk will be an introduction to singular learning theory with the factor analysis model as a running example.