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%\author{Yuan Qi\\
%        yuanqi@media.mit.edu}
%\title{6.891 Course Proposal: Study of Bayesian Approximation for Relevance Vector Machine}
%\date{Oct. 15, 2000}
\topmargin 1in
\begin{document}
%\maketitle

\begin{center} \Large{6.899 Term Paper: } \\
Yuan Qi\\
yuanqi@media.mit.edu\\
March 20, 2002
\end{center}

\section{Introduction}

The past decade has witnessed many new theories and applications for 
statistical machine learning. However, most of statistical machine 
learning techniques are 
for a predetermined situation; it is static 
and inflexible; it has flat structure and only deal with attribute 
(random variable) without any concept of objects. To some extent,
these limitations make it hard to apply Bayesian networks to
representing complex, 
structured, and flexible domains. On the other hand, first order logic
or relational data model have been used in AI and database communities
to have a more expressive representation for data relations. But for
learning and inference purposes, they suffer from the disability of
modeling the uncertenty of the world.

To address those problems, an interesting research direction is combining 
relational data model or first order logic  with probablity to have
probablistic relational learning.
On one side, researchers  have 
introduced probability directly into the proof 
procedure of logic programmings, for example, 
stochastic logic programs (SLP)~\cite{}. On the other hand, researchers have
combined relational data model with probablity
in a way more like extensions of Bayesian networks, for example,
 probabilistic relational models (PRM)~\cite{KolPfe98} and  Bayesian logic 
programs \cite{KerRae2000}. 
In this paper, we try to utilize these new models to address some
machine learning problems.

The paper contains two slightly diverse topics. First, we 
propose  new methods of sampling the Bayesian
network structures using stochastic logic programs. Then we 
present a new algorithm for classifying texts based on  probabilistic 
relational models. This two topics will be discussed in part 1 and 2
of this paper respectively.

\section{Part 1: Sampling BN Structures using SLP}


An SLP can efficiently define a prior over Bayesian nets as follows~\cite{}.

bn([],[],[]). \\
bn([RV|RVs],BN,AncBN):- \\
 bn(RVs, BN2, AncBN2,
 connect_no_cycles(RV,BN2,AncBN2,BN,AncBN).

\% An edge: RV parent of H 
1/3:: which_edge([H|T],RV,[H-RV|Rest]) `:-
choose_edges(T,RV,Rest).
\% An edge: H parent of RV
1/3:: which_edge([H|T],RV,[RV-H|Rest]) `:-
choose_edges(T,RV,Rest).
\% No edge
1/3:: which_edge([_H|T],RV,Rest) `:-
choose_edges(T,RV,Rest).

Cussens \cite{}, and Angelopoulos and Cussens \cite{}  use SLP
 for sampling Bayesian model structures. They use the
 Metropolis-Hasting algorithm to sample from the 


Second, I plan to study some existed approaches for combing attribute
and relational learning \cite{KerRae2000,KolPfe98,NgoHad96}. Among them, Bayesian logic programs \cite{KerRae2000} and probabilistic relational models \cite{KolPfe98}
are especially interesting to me. 

Third, I can either write a review paper on investigating those approaches and 
related learning methods \cite{GetFriKolPfe2001}, or try to develop 
classification and clustering techniques for relational data based on
these existed models.

In short, I think it is promising to combine attribute and relational learning
from a Bayesian perspective. Some initial works have been done in this
direction. I hope my work could add more interesting results to this
research direction.

\section{Part 2: Relational Bayesian Text Classification}

\section{Conclusions}

\section{Alternative Plans}

\begin{thebibliography}{99}
\bibitem{KerRae2000} Kristian Kersting and Luc de Raedt, "Bayesian Logic Programs." In J. Cussens and A. Frisch, editors, Work-in-Progress Reports of the Tenth International Conference on Inductive Logic Programming, London, 2000. 
\bibitem{NgoHad96} Liem Ngo and Peter Haddawy, "Answering Queries from Context-Sensitive Probabilistic Knowledge Bases." Theoretical Computer Science, 1996. 
\bibitem{KolPfe98}Daphne Koller and Avi Pfeffer, "Probabilistic Frame-Based systems." In Proceedings of the Fifteenth National Conference on Artificial Intelligence, 1998. 
\bibitem{GetFriKolPfe2001}  L. Getoor, N. Friedman, D. Koller, and
A. Pfeffer , Learning Probabilistic Relational Models,Invited
contribution to the book Relational Data Mining, S. Dzeroski and
N. Lavrac, Eds., Springer-Verlag, 2001.
\bibitem{WanMer2000}
E. A. Wan and R. van der Merwe, "The Unscented Kalman Filter for Nonlinear Estimation," in Proc. of IEEE Symposium 2000 (AS-SPCC),
Lake Louise, Alberta, Canada,
Oct. 2000. http://citeseer.nj.nec.com/wan00unscented.html  
\bibitem{Mac2000}
 D. J. MacKay,
  Probable Networks and Plausible Predictions - A Review of Practical Bayesian Methods for Supervised Neural Networks,
Network (IOPP), 2000.
\bibitem{Mac2000}
 D. J. MacKay,
  Probable Networks and Plausible Predictions - A Review of Practical Bayesian Methods for Supervised Neural Networks,
Network (IOPP), 2000.


\end{thebibliography}

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