# LaTeX2HTML 96.1 (Feb 5, 1996)
# Associate images original text with physical files.

$key = q/{_inline}$x_i,i=1,ldots,m${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=111 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline252" SRC="img4.gif"  > '; 
$key = q/{_inline}$w_rmML${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=30 HEIGHT=15 ALIGN=MIDDLE ALT="tex2html_wrap_inline260" SRC="img9.gif"  > '; 
$key = q/{_inline}$bfA=bfUoperatornamediag(lambda_i)bfV^rmT${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=130 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline268" SRC="img13.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlesplitphantomintpbig(y^(n+1);SPMamp;big|(x^(1),ldots,x^(n+1),y^(1),ldots,y^(n),hatsigma^2big)propto;SPMamp;intpbig(y^(n+1)big|x^(1),ldots,x^(n+1),y^(1),ldots,y^(n),hatsigma^2big)pbig(w|calD,hatsigma^2big)d^m+1wpropto;SPMamp;intpbig(y^(n+1)big|x^(n+1),w,hatsigma^2big)pbig(y^(1),ldots,y^(n)big|x^(1),ldots,x^(n),w,hatsigma^2big)d^m+1wpropto;SPMamp;intexpBig(!!-fracbig(f_w(x^(n+1))-y^(n+1)big)^22hatsigma^2-frac12(w-tildew_rmML)^rmTtildebfA(w-tildew_rmML)Big)d^m+1w.split{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=629 HEIGHT=147 ALIGN=MIDDLE ALT="displaymath329" SRC="img27.gif"  > '; 
$key = q/{_inline}$f_tildew_rmML(x)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=54 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline310" SRC="img29.gif"  > '; 
$key = q/{_inline}$x^(n+1)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=41 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap_inline308" SRC="img26.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlehatmu=f_tildew_rmML(x^(n+1))qquadtextandqquadhate^2=hatsigma^2+(x^(n+1))^rmTtildebfA^-1x^(n+1).labeleq:mv{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=563 HEIGHT=20 ALIGN=MIDDLE ALT="displaymath331" SRC="img28.gif"  > '; 
$key = q/{_inline}$O(nm^2+m^3)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=94 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline312" SRC="img31.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlehatsigma^2=frac1n-ksum_c=1^nbig(f_tildew_rmML(x^(c))-y^(c)big)^2labeleq:noise{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=472 HEIGHT=44 ALIGN=MIDDLE ALT="displaymath327" SRC="img24.gif"  > '; 
$key = q/{_inline}$tildebfA^-1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=27 HEIGHT=15 ALIGN=BOTTOM ALT="tex2html_wrap_inline280" SRC="img17.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middletildew_rmML=tildebfA^-1bfb.labeleq:wml{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=398 HEIGHT=18 ALIGN=MIDDLE ALT="displaymath325" SRC="img23.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlesplitlogpbig(y^(n+1)=t^(n+1)big|x^(1),ldots,x^(n+1),y^(1),ldots,y^(n),hatsigma^2big)=hspace2cm-0.5log(2pihate^2)-frac(hatmu-t)^22hate^2.splitlabeleq:dens{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=598 HEIGHT=58 ALIGN=MIDDLE ALT="displaymath333" SRC="img30.gif"  > '; 
$key = q/{_inline}$x_m+1equiv1.0${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=77 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline254" SRC="img5.gif"  > '; 
$key = q/{_inline}$nleqm+1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=70 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline306" SRC="img25.gif"  > '; 
$key = q/{_inline}$lambda_i;SPMlt;10^-6max_j(lambda_j)${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=133 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline290" SRC="img21.gif"  > '; 
$key = q/{_inline}$bfU${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=12 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline270" SRC="img14.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlepbig(y^(1),ldots,y^(n)big|x^(1),ldots,x^(n),w,sigma^2big)proptoprod_c=1^nexpBig(!!-fracbig(f_w(x^(c))-y^(c)big)^22sigma^2Big).{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=594 HEIGHT=47 ALIGN=MIDDLE ALT="displaymath317" SRC="img8.gif"  > '; 
$key = q/{_inline}$calD={x^(i),y^(i)|i=1ldotsn}${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=175 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline256" SRC="img6.gif"  > '; 
$key = q/{_inline}$bfV${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=13 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline272" SRC="img15.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlesplitfracpartialE(w)partialw_j=bf0;;Rightarrow;;sum_c=1^nbig(sum_i=1^m+1w_i^phantom(x_i^(c)-y_phantomi^(c)big)x_j^(c)=bf0;;Rightarrow;;w_rmML=bfA^-1bfbhspace2cmmboxwhere;;bfA_ii'=sum_c=1^nx_i^(c)x_i'^(c),quadbfb_i=sum_c=1^ny_phantomi^(c)x_i^(c),quadi,i'=1,ldots,m+1.splitlabelel{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=631 HEIGHT=94 ALIGN=MIDDLE ALT="displaymath321" SRC="img11.gif"  > '; 
$key = q/{_inline}$w_m+1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=36 HEIGHT=16 ALIGN=MIDDLE ALT="tex2html_wrap_inline250" SRC="img3.gif"  > '; 
$key = q/{_inline}$lambda${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=8 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline274" SRC="img16.gif"  > '; 
$key = q/{_inline}$sigma^2${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=14 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline258" SRC="img7.gif"  > '; 
$key = q/{_inline}$10^-6${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=31 HEIGHT=14 ALIGN=BOTTOM ALT="tex2html_wrap_inline294" SRC="img22.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middleE(w)=sum_c=1^nbig(f_w(x^(c))-y^(c)big)^2,{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=454 HEIGHT=44 ALIGN=MIDDLE ALT="displaymath319" SRC="img10.gif"  > '; 
$key = q/{_inline}$1lambda_i=0${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=57 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline282" SRC="img18.gif"  > '; 
$key = q/{_inline}$w_i,i=1,ldots,m+1${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=141 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline246" SRC="img2.gif"  > '; 
$key = q/{_inline}$bfA${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=12 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline264" SRC="img12.gif"  > '; 
$key = q/{_inline}$lambda_i${_inline}/;
$cached_env_img{$key} = ' <IMG WIDTH=11 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline286" SRC="img19.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middlef_w(x)=sum_i=1^m+1x_iw_i,{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=412 HEIGHT=46 ALIGN=MIDDLE ALT="displaymath315" SRC="img1.gif"  > '; 
$key = q/{displaymath}htmlimagealign=middletildebfA^-1=bfVoperatornamediag(1lambda_i)bfU^rmT.labeleq:ta{displaymath}/;
$cached_env_img{$key} = ' <IMG WIDTH=433 HEIGHT=20 ALIGN=MIDDLE ALT="displaymath323" SRC="img20.gif"  > '; 

1;

