\relax 
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {1}Introduction}{1}}
\citation{weiss:systems}
\citation{maron:hoeffding}
\citation{maron:hoeffding}
\citation{moore:schemata}
\citation{maron:thesis}
\citation{dasarathy:collection}
\citation{cleveland:lwr}
\citation{moore:brute-force}
\citation{aha:thesis}
\citation{fix:nonparametric}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {1.1}Lazy learning algorithms}{3}}
\newlabel{sec-lazy-learning}{{1.1}{3}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {1.1.1}{\string\pit\space k}-nearest-neighbors}{3}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {1.1.2}Weighted distance metric}{4}}
\citation{maron:thesis}
\citation{moore:brute-force}
\citation{cleveland:lwr}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {1.1.3}Kernel regression}{5}}
\newlabel{equation:weighting}{{1}{5}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {1.1.4}Local regression and local weighted regression}{5}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {1.2}Determining the accuracy of a model}{5}}
\citation{efron:statistical}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {1.3}Summary}{6}}
\citation{maron:hoeffding}
\citation{press:recipes}
\citation{atkeson:approximating,lowe:95}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {2}Previous approaches}{7}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {2.1}Brute force}{7}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {2.2}Descent methods}{7}}
\citation{press:recipes}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {1}{\ignorespaces Example of local minima in model selection}}{8}}
\newlabel{local-minima}{{2.2}{8}}
\citation{goldberg:genetic}
\citation{kirkpatrick:annealing}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {2.3}Genetic algorithms and simulated annealing}{9}}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {3}Racing: Hoeffding and Bayes}{9}}
\citation{hoeffding:bound}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {3.1}Hoeffding races}{10}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {3.1.1}Hoeffding's Bound}{10}}
\newlabel{equation:hoeffding}{{2}{10}}
\newlabel{equation:epsilon}{{3}{10}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2}{\ignorespaces Use of Hoeffding's bound to eliminate LBs}}{11}}
\newlabel{example}{{2}{11}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {3.1.2}Hoeffding races}{11}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {3.1.3}Ending the race}{12}}
\@writefile{toc}{\string\contentsline\space {subsubsection}{\string\numberline\space {3.1.4}Proof of correctness}{12}}
\newlabel{equation1}{{5}{12}}
\citation{omohundro:suggestion}
\citation{haussler:genpac}
\newlabel{equation2}{{12}{13}}
\citation{schm:msrn}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {3.2}Bayesian races}{14}}
\newlabel{eq:ejj}{{16}{14}}
\citation{wlch:thsg}
\citation{box:blocking}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {3}{\ignorespaces The posterior distributions on the errors of four models involved in a race. The lower the error the better, so it seems very unlikely that model 4 will turn out to be better than model 2 at the end of the race. Thus model 4 is eliminated at this point.}}{15}}
\newlabel{race-fourgauss.ps}{{3.2}{15}}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {4}Extensions}{15}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {4.1}Bounding errors}{16}}
\newlabel{sec-bounding-errors}{{4.1}{16}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {4.2}Shrinking the intervals}{16}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {4}{\ignorespaces Example of how to shrink the interval bounds}}{17}}
\newlabel{shrink-example}{{4}{17}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {4.3}Eliminating indistinguishable models}{17}}
\citation{box:blocking}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {4.4}Blocking}{18}}
\citation{maron:hoeffding}
\citation{murphy:repository}
\citation{schaal:openloop}
\citation{zhang:protein}
\citation{energy:shootout}
\citation{moore:forward}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {5}Empirical results of Hoeffding and Bayesian racing}{19}}
\@writefile{lot}{\string\contentsline\space {table}{\string\numberline\space {1}{\ignorespaces  Results of various races.}}{21}}
\newlabel{results}{{1}{21}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {5}{\ignorespaces Scaling of Hoeffding races vs. brute force}}{22}}
\newlabel{hoeff-vs-brute}{{5}{22}}
\citation{maron:thesis}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {5.1}Segmenting Magnetic Resonance Images}{23}}
\citation{moore:brute-force}
\citation{mllr:sbst}
\citation{crn:grdy,jhn:irrl,sklk:prtt}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {6}Racing for relevant attributes}{24}}
\citation{moore:schemata}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {6.1}Schemata search}{25}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {6.2}Experiments}{27}}
\@writefile{lot}{\string\contentsline\space {table}{\string\numberline\space {2}{\ignorespaces Syntax Of the Multivariate Functions In Experiments}}{28}}
\newlabel{tab:syntax}{{2}{28}}
\citation{moore:brute-force}
\citation{haussler:genpac}
\citation{kaelbling:thesis}
\citation{rivest:bandit}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {6}{\ignorespaces Comparing the conventional forward sequential selection algorithm against its racing counterparts, and against schemata search (which has no forwards-backwards bias).}}{30}}
\newlabel{forward}{{6}{30}}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {7}Conclusion}{30}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {7.1}Related Work}{30}}
\citation{gratch:bandit}
\citation{grtc:lrnn}
\citation{box:blocking}
\citation{greiner:palo}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {7}{\ignorespaces Comparing the conventional backward elimination algorithm against its racing counterparts, and against schemata search (which has no forwards-backwards bias).}}{31}}
\newlabel{backward}{{7}{31}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {7.2}Future Work}{32}}
\bibdata{paper}
\bibcite{aha:thesis}{\citeauthoryear {Aha}{1990}}
\bibcite{atkeson:approximating}{\citeauthoryear {Atkeson}{1990}}
\bibcite{box:blocking}{\citeauthoryear {Box \bgroup \pem {}et al.\egroup }{1978}}
\bibcite{crn:grdy}{\citeauthoryear {Caruana and Freitag}{1994}}
\bibcite{cleveland:lwr}{\citeauthoryear {Cleveland \bgroup \pem {}et al.\egroup }{1988}}
\bibcite{dasarathy:collection}{\citeauthoryear {Dasarathy}{1991}}
\bibcite{efron:statistical}{\citeauthoryear {Efron and Tibshirani}{1991}}
\bibcite{fix:nonparametric}{\citeauthoryear {Fix and Hodges}{1951}}
\bibcite{goldberg:genetic}{\citeauthoryear {Goldberg}{1989}}
\bibcite{grtc:lrnn}{\citeauthoryear {Gratch \bgroup \pem {}et al.\egroup }{1993}}
\bibcite{gratch:bandit}{\citeauthoryear {Gratch}{1994}}
\bibcite{greiner:palo}{\citeauthoryear {Greiner and Jurisica}{1992}}
\bibcite{haussler:genpac}{\citeauthoryear {Haussler}{1992}}
\bibcite{hoeffding:bound}{\citeauthoryear {Hoeffding}{1963}}
\bibcite{jhn:irrl}{\citeauthoryear {John \bgroup \pem {}et al.\egroup }{1994}}
\bibcite{kaelbling:thesis}{\citeauthoryear {Kaelbling}{1990}}
\bibcite{kirkpatrick:annealing}{\citeauthoryear {Kirkpatrick \bgroup \pem {}et al.\egroup }{1983}}
\bibcite{energy:shootout}{\citeauthoryear {Kreider and Haberl}{1993}}
\bibcite{lowe:95}{\citeauthoryear {Lowe}{1995}}
\bibcite{maron:hoeffding}{\citeauthoryear {Maron and Moore}{1994}}
\bibcite{maron:thesis}{\citeauthoryear {Maron}{1994}}
\bibcite{mllr:sbst}{\citeauthoryear {Miller}{1990}}
\bibcite{moore:schemata}{\citeauthoryear {Moore and Lee}{1994}}
\bibcite{moore:brute-force}{\citeauthoryear {Moore \bgroup \pem {}et al.\egroup }{1992}}
\bibcite{moore:forward}{\citeauthoryear {Moore}{1992}}
\bibcite{murphy:repository}{\citeauthoryear {Murphy and Aha}{1995}}
\bibcite{omohundro:suggestion}{\citeauthoryear {Omohundro}{1993}}
\bibcite{press:recipes}{\citeauthoryear {Press \bgroup \pem {}et al.\egroup }{1992}}
\bibcite{rivest:bandit}{\citeauthoryear {Rivest and Yin}{1993}}
\bibcite{schaal:openloop}{\citeauthoryear {Schaal and Atkeson}{1993}}
\bibcite{schm:msrn}{\citeauthoryear {Schmitt}{1969}}
\bibcite{sklk:prtt}{\citeauthoryear {Skalak}{1994}}
\bibcite{weiss:systems}{\citeauthoryear {Weiss and Kulikowski}{1991}}
\bibcite{wlch:thsg}{\citeauthoryear {Welch}{1937}}
\bibcite{zhang:protein}{\citeauthoryear {Zhang \bgroup \pem {}et al.\egroup }{1992}}
\bibstyle{named}
