Paper available by ftp

[Zoubin Ghahramani]

FTP-host: psyche.mit.edu
FTP-filename: /pub/zoubin.cmss.ps.Z

The following paper is very closely related to Chris M Bishop's
recently announced paper on MIXTURE DENSITY NETWORKS. It also
addresses the problem of learning multi-valued mappings such as those
that arise in inverse kinematics, acoustics, object localization, etc.
The approach also involves learning a mixture density, though it does
not combine that with the use of a feedforward network.

-----------------------------------------------------------------------------
				   
 Solving Inverse Problems Using an EM Approach to Density Estimation
				   
			  Zoubin Ghahramani

	       Department of Brain & Cognitive Sciences
		Massachusetts Institute of Technology
			 Cambridge, MA 02139
				   
			zoubin at psyche.mit.edu
				   
			       Abstract

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.

--------------------------------------------------------------------
ftp instructions:

% ftp psyche.mit.edu
login: anonymous
password: <login-name>
ftp> cd pub
ftp> binary
ftp> get zoubin.cmss.ps.Z
ftp> bye
% uncompress zoubin.cmss.ps.Z
% lpr zoubin.cmss.ps

-------------------------------------------------------------------- 
Matlab code for the EM mixture algorithms for real, binary, and
classification problems for both complete and incomplete data (*) is
also available by anonymous ftp from the same site:

ftp> get zoubin.EMcode.README
ftp> get zoubin.EMcode.tar.Z

Please email me if you intend to use the code so I can keep you
updated with newer releases and  possibly C++ and CM5 code.

(*) cf. Ghahramani & Jordan 1993, "Supervised learning from incomplete
data using an EM approach":
ftp> get zoubin.nips93.ps.Z

--------------------------------------------------------------------

Zoubin Ghahramani