Solving inverse problems using an EM approach to density estimation

Zoubin Ghahramani, Dept. of Brain & Cognitive Sciences,
Massachusetts Institute of Technology, Cambridge, MA 02139

This paper proposes density estimation as a feasible approach to the wide class of learning problems where traditional function approximation methods fail. These problems generally involve learning the inverse of causal systems, specifically when the inverse is a non-convex mapping. We demonstrate the approach through three case studies: the inverse kinematics of a three-joint planar arm, the acoustics of a four-tube articulatory model, and the localization of multiple objects from sensor data.

The learning algorithm presented differs from regression-based algorithms in that no distinction is made between input and output variables; the joint density is estimated via the EM algorithm and can be used to represent any input/output map by forming the conditional density of the output given the input.

In M.C. Mozer, P. Smolensky, D.S. Touretzky, J.L. Elman, & A.S. Weigend (eds.), Proceedings of the 1993 Connectionist Models Summer School. pp. 316--323. Hillsdale, NJ: Erlbaum Associates, 1994. gzipped postscript.

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