NIPS2009_0224_slide - model. Figure 1. An example of...

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Gaussian process regression with Student- t likelihood jarno.vanhatalo@tkk.fi pasi.jylanki@tkk.fi aki.vehtari@tkk.fi A B HELSINKI UNIVERSITY OF TECHNOLOGY Department of Biomedical Engineering and Computational Science A robust observation model, such as the Student- t distribution, reduces the influence of outlying observations and improves the predictions. The problem, however, is the analyti- cally intractable inference. We utilize the Laplace approximation for approximate inference and compare our approach to VB and MCMC scheme (a) Gaussian observation model. (b) Student- t observation
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Unformatted text preview: model. Figure 1. An example of regression with outliers by Neal (1997). • All the methods (Laplace, VB, MCMC) are similar in predictive performance • VB underestimates variance more than Laplace approximation • The Laplace approximation is the fastest and MCMC the slowest (c) Neal data (d) Friedman data Figure 2. Scatter plot of the posterior mean (up-per row) and variance (lower row) of the latent variables. In each figure, left plot is for MCMC (x-axis) vs the Laplace approximation (y-axis) and the right plot is MCMC vs. VB....
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