Statistical Inference with Unnormalized Models
Posted on (Update: )
This post is based on the talk given by T. Kanamori at the 11th ICSA International Conference on Dec. 22nd, 2019.
Problem Setting
Estimation Models
Other divergences: density-power divergences, pseudo spherical divergence, etc. => robust estimators
Different from the intractable models talked in the MCMC, which only aims to get a sample from the untractable model, but here we need to get a (MLE) estimate of the parameter.
Proposed Approach
where the variational representation of KL divergences is that
where the Stein operator is defined by
Theoretical Properties
more details can be found in the M-estimator.
the calculation procedure is as follows:
Numerical Experiments
Conclusion
