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CPS1488 Willem van den B. et al.
Table 1: Quartiles of the average Wasserstein distance between the Gaussian
approximations and the MCMC approximation.
Method Q1 Median Q3
Laplace approximation 0.80 0.92 1.03
EP-IS with low-rank 0.73 0.83 0.95
regularization
EP-IS with tapering 0.73 0.85 83.21

Table 2: Quartiles of the computation times in seconds for the 20 simulations.
Method Q1 Median Q3
Metropolis algorithm 25.2 25.4 26.9
Laplace approximation 0.2 0.4 1.2
EP-IS with low-rank 13.6 13.9 14.2
regularization
EP-IS with tapering 13.5 13.8 14.4

4. Discussion and Conclusion
The EP factorization exploited that the likelihood from (1) factorized. This
2
factorization is only required along the partitions. The error covariance, σ In in
(1), is therefore not required to be proportional to an identity matrix but can
be any block diagonal matrix whose block structure corresponds with the data
partition used.
EP-IS combines ideas from deterministic and sampling-based posterior
approximations to obtain an accuracy that is closer to the sampling-based
methods with computational cost closer to deterministic methods.

References

1. Aristidou, A., J. Lasenby, Y. Chrysanthou, and A. Shamir (2017). Inverse
kinematics techniques in computer graphics: A survey. Computer
Graphics Forum 37(6), 35–58.
2. Bertero, M. and M. Piana (2006). Inverse problems in biomedical
imaging: Modeling and methods of solution, pp. 1–33. Milano: Springer
Milan.
3. Cornuet, J.-M., J.-M. Marin, A. Miro, and C. P. Robert (2012). Adaptive
multiple importance sampling. Scandinavian Journal of Statistics 39(4),
798–812.
4. Duka, A.-V. (2014). Neural network based inverse kinematics solution for
trajectory tracking of a robotic arm. Procedia Technology 12, 20–27.

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