Projection of a Markov Process with Neural Networks
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
In this work we have examined an application fromthe insurance industry. We first reformulate it into aproblem of projecting a markov process. We thendevelop a method of carrying out the projectionmany steps into the future by using a combination ofneural networks trained using a maximum entropyprinciple. This methodology improves on currentindustry standard solution in four key areas:variance, bias, confidence level estimation, and theuse of inhomogeneous data.The neural network aspects of the methodologyinclude the use of a generalization error estimate thatdoes not rely on a validation set. We also developour own approximation to the hessian matrix, whichseems to be significantly better than assuming it tobe diagonal and much faster than calculating itexactly. This hessian is used in the network pruningalgorithm. The parameters of a conditional probabilitydistribution were generated by a neuralnetwork, which was trained to maximize thelog-likelihood plus a regularization term.In preparing the data for training the neural networkswe have devised a scheme to decorrelate inputdimensions completely, even non-linear correlations,which should be of general interest in its own right.The results we found indicate that the bias inherentin the current industry-standard projection techniqueis very significant. This work may be the onlyaccurate measurement made of this important source of error.
Place, publisher, year, edition, pages
2001. , 48 p.
Other Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-48860OAI: oai:DiVA.org:kth-48860DiVA: diva2:458725
Subject / course
Master of Science - Computer Science
UppsokPhysics, Chemistry, Mathematics