Technical Report available

[Michael Jordan]

                "Supervised learning and systems with
                      excess degrees of freedom"

                          Michael I. Jordan
                 Massachusetts Institute of Technology

                    COINS Technical Report 88-27

ABSTRACT

When many outputs of an adaptive system have equivalent effects on 
the environment, the problem of finding appropriate actions given 
desired results is ill-posed.  For supervised learning algorithms, the 
ill-posedness of such ``inverse learning problems'' implies a certain
flexibility---during training, there are in general many possible target 
vectors corresponding to each input vector.  To allow supervised learning
algorithms to make use of this flexibility, the current paper considers 
how to specify targets by sets of constraints, rather than as particular 
vectors.  Two classes of constraints are distinguished---configurational 
constraints, which define regions of output space in which an output 
vector must lie, and temporal constraints, which define relationships 
between outputs produced at different points in time.  Learning algorithms
minimize a cost function that contains terms for both kinds of constraints.  
This approach to inverse learning is illustrated by a robotics application 
in which a network finds trajectories of inverse kinematic solutions for 
manipulators with excess degrees of freedom.


To obtain a copy, contact:

jordan at wheaties.ai.mit.edu

or 

Ms. Connie Smith
Computer and Information Science
Graduate Research Center
University of Massachusetts
Amherst, MA 01003

smith at cs.umass.edu