# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/displaystylex_{ik}(1-pi_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle x_{ik} (1 - \pi_{ik})$">|; 

$key = q/displaystylethetainQ;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle \theta \in Q$">|; 

$key = q/displaystylevarepsilon={((kappa=0.788,upsilon=0.924),1)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle \varepsilon = \{ ((\kappa=0.788,\upsilon=0.924),1) \}$">|; 

$key = q/partialR;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$ \partial R$">|; 

$key = q/|Q|;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$ \vert Q\vert$">|; 

$key = q/displaystylepsi(theta,x_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle \psi(\theta,x_{ik})$">|; 

$key = q/kappa=0.788;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$ \kappa=0.788$">|; 

$key = q/displaystylepi_{ik}=kappa^{x_{ik}}timesupsilon^{k-x_{ik}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle \pi_{ik} = \kappa^{x_{ik}} \times \upsilon^{k-x_{ik}}$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$ R$">|; 

$key = q/displaystyleb(psi)=lnint_ye^{psibullety}a(y)dy;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="192" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle b(\psi) = \ln \int_y e^{\psi \bullet y} a(y) dy$">|; 

$key = q/includegraphics[width=0.7textwidth]{slashhomeslashleighfslashstaticslashPaper-PostCompslashblocks};LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="91" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="\includegraphics[width=0.7\textwidth]{/home/leighf/static/Paper-PostComp/blocks}">|; 

$key = q/displaystylefrac{e^{psi(theta,x_{ik})}x_{ik}(1-pi_{ik})}{1+e^{psi(theta,x_{ik})}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle \frac{e^{\psi(\theta,x_{ik})} x_{ik} (1 - \pi_{ik})}{1+e^{\psi(\theta,x_{ik})}}$">|; 

$key = q/displaystylea(y);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle a(y)$">|; 

$key = q/displaystylefrac{int_Rh(theta)f(x|theta)KL(theta,hat{theta}),dtheta}{int_Rh(theta)f(x|theta),dtheta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="73" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \frac{\int_R h(\theta) f(x\vert\theta) KL(\theta,\hat{\theta})   d\theta}{\int_R h(\theta) f(x\vert\theta)   d\theta}$">|; 

$key = q/argmin_{hat{theta}inQ}E_{h(theta)}left[KL(theta,hat{theta})right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$ argmin_{\hat{\theta} \in Q} E_{h(\theta)} \left[ KL(\theta,\hat{\theta}) \right]$">|; 

$key = q/err;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$ err$">|; 

$key = q/includegraphics[width=0.6textwidth]{slashhomeslashleighfslashstaticslashPaper-PostCompslashdogs1};LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="257" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="\includegraphics[width=0.6\textwidth]{/home/leighf/static/Paper-PostComp/dogs1}">|; 

$key = q/k-1;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$ k-1$">|; 

$key = q/log_e2;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$ \log_e 2$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$ x$">|; 

$key = q/hat{theta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="23" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$ \hat{\theta}$">|; 

$key = q/displaystylehat{theta}=argmin_{hat{theta}inR}E_{h(theta)}left[KL(theta,hat{theta})right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \hat{\theta} = argmin_{\hat{\theta} \in R} E_{h(\theta)} \left[ KL(\theta,\hat{\theta}) \right]$">|; 

$key = q/upsilon;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$ \upsilon$">|; 

$key = q/displaystyle(alpha,beta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle (\alpha,\beta)$">|; 

$key = q/w_7=0.01;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$ w_7 = 0.01$">|; 

$key = q/pi_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$ \pi_i$">|; 

$key = q/[0,1];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$ [0,1]$">|; 

$key = q/I(theta)proptoh(theta)f(x|theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$ I(\theta) \propto h(\theta) f(x\vert\theta)$">|; 

$key = q/displaystyletheta;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle \theta$">|; 

$key = q/pi_{k}=pi_{k-1}kappa;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$ \pi_{k}=\pi_{k-1} \kappa$">|; 

$key = q/displaystyleS={theta_t:t=1,...,N};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle S = \{ \theta_t : t = 1,...,N \}$">|; 

$key = q/displaystyle=Phi(alpha+betax_i);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\displaystyle = \Phi (\alpha + \beta x_i)$">|; 

$key = q/displaystylefrac{sum_{thetainQ}f(x|theta)^{-1}KL(theta,hat{theta})}{sum_{thetainQ}f(x|theta)^{-1}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \frac{\sum_{\theta \in Q} f(x\vert\theta)^{-1} KL(\theta,\hat{\theta})}{\sum_{\theta \in Q} f(x\vert\theta)^{-1}}$">|; 

$key = q/displaystyleKL(psi,hat{psi});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle KL(\psi,\hat{\psi})$">|; 

$key = q/displaystyle-H(psi)-E_{psi}left[loga(y)right]+b(hat{psi})-hat{psi}bulletE_{psi}y;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle -H(\psi) - E_{\psi}\left[ \log a(y) \right] + b(\hat{\psi}) - \hat{\psi} \bullet E_{\psi} y$">|; 

$key = q/{displaymath}{array}{c@{hspace{14pt}}c}includegraphics[width=0.45textwidth]{slasbfRegion13pointestimate(w_{13}<0.01)}{array}{displaymath};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="713" HEIGHT="523" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="\begin{displaymath}\begin{array}{c@{\hspace{14pt}}c}
\includegraphics[width=0.45...
...\bf Region 13 point estimate ($w_{13} &lt; 0.01$)} \\\\
\end{array}\end{displaymath}">|; 

$key = q/-logp;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$ -\log p$">|; 

$key = q/displaystylefrac{partialb(psi(theta,x_{ik}))}{partialpsi};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle \frac{\partial b(\psi(\theta,x_{ik}))}{\partial \psi}$">|; 

$key = q/displaystyleapprox;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle \approx$">|; 

$key = q/-logp_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$ -\log p_i$">|; 

$key = q/argmin_{theta_i}MessLen(theta_i,x);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$ argmin_{\theta_i} MessLen(\theta_i,x)$">|; 

$key = q/displaystyledhat{theta}^{(k)}=left[{array}{c}dhat{vartheta_0}^{(k)}vdotsdhat{varrtheta_d}}Bigllvert_{hat{theta}^{(k)}}right){array}right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="486" HEIGHT="121" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle d\hat{\theta}^{(k)} = \left[ \begin{array}{c} d\hat{\vartheta_0}^...
...t{\vartheta_d}} \Bigl\lvert_{\hat{\theta}^{(k)}} \right) \ \end{array} \right]$">|; 

$key = q/displaystyle-b(psi)+b(hat{psi})+(psi-hat{psi})bulletnablab(psi);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="269" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle -b(\psi) + b(\hat{\psi}) + (\psi - \hat{\psi}) \bullet \nabla b(\psi)$">|; 

$key = q/displaystyleerr(theta')=1-frac{sum_{thetainR}h(theta)+h(theta')}{h(theta')}logfrsum_{thetainR}h(theta)+h(theta')}{sum_{thetainR}h(theta)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle err(\theta') = 1 - \frac{\sum_{\theta \in R} h(\theta) + h(\theta...
...frac{\sum_{\theta \in R} h(\theta) + h(\theta')}{\sum_{\theta \in R} h(\theta)}$">|; 

$key = q/displaystyleJ=left[{array}{ccc}sum_{thetainQ}f(x|theta)^{-1}left(frac{partial^2Krtheta_d}}Bigllvert_{hat{theta}^{(k)}}right){array}right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="620" HEIGHT="121" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle J = \left[ \begin{array}{ccc} \sum_{\theta \in Q} f(x\vert\theta)...
...\hat{\vartheta_d}} \Bigl\lvert_{\hat{\theta}^{(k)}} \right) \end{array} \right]$">|; 

$key = q/x_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$ x_i$">|; 

$key = q/displaystyle=-logleft(int_Rh(theta),dthetaright)-frac{int_Rh(theta)cdotlogf(x|theta),dtheta}{int_Rh(theta),dtheta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle = - \log \left( \int_R h(\theta)   d\theta \right) - \frac{\int_R h(\theta) \cdot \log f(x\vert\theta)   d\theta}{\int_R h(\theta)   d\theta}$">|; 

$key = q/alpha=log(kappa);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$ \alpha=\log(\kappa)$">|; 

$key = q/x_{ik};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$ x_{ik}$">|; 

$key = q/k-x_{ik};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$ k-x_{ik}$">|; 

$key = q/displaystylevarepsilon={(theta_1,antilog(-MessLen(theta_1,x))),...,(theta_K,antilog(-MessLen(theta_K,x)))};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="611" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle \varepsilon = \{ (\theta_1,antilog(- MessLen(\theta_1,x))),...,(\theta_K,antilog(- MessLen(\theta_K,x))) \}$">|; 

$key = q/i^{mbox{th}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="25" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$ i^{\mbox{th}}$">|; 

$key = q/displaystylevarepsilon={(hat{theta}_{logit},0.03),(hat{theta}_{probit},0.07),(hat{theta}_{cloglog},0.9)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="366" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$\displaystyle \varepsilon = \{ (\hat{\theta}_{logit},0.03), (\hat{\theta}_{probit},0.07),(\hat{\theta}_{cloglog},0.9) \}$">|; 

$key = q/dhat{theta}^{(k)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="23" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$ d\hat{\theta}^{(k)}$">|; 

$key = q/err(.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$ err(.)$">|; 

$key = q/displaystylelogfrac{pi_{ik}}{1-pi_{ik}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="50" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle \log \frac{\pi_{ik}}{1 - \pi_{ik}}$">|; 

$key = q/h(.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$ h(.)$">|; 

$key = q/{figure}algorithm{{Pseudo-codeforoptimisingtheMMLDmessagelengthintheunimodallike{theta_i}{Block{{i{={i+1{Block{algorithm{{figure};MSF=1.6;LFS=12;FSF=1.6;AAF;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="556" HEIGHT="637" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="\begin{figure}\begin{algorithm}{Pseudo-code for optimising the MMLD message leng...
...\theta_i \}$\end{Block}\\\\
$i$ \= $i + 1$\end{Block}\end{algorithm}\end{figure}">|; 

$key = q/displaystyleE_{h(theta)}left[KL(theta,hat{theta})right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="137" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle E_{h(\theta)}\left[ KL(\theta,\hat{\theta}) \right]$">|; 

$key = q/displaystyle-b(psi)+b(hat{psi})+(psi-hat{psi})bulletE_{psi}y;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle -b(\psi) + b(\hat{\psi}) + (\psi - \hat{\psi}) \bullet E_{\psi} y$">|; 

$key = q/displaystylefrac{partialpsi(theta,x_{ik})}{partialalpha};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \frac{\partial \psi(\theta,x_{ik})}{\partial \alpha}$">|; 

$key = q/displaystylefrac{e^{psi(theta,x_{ik})}(j-x_{ik})(1-pi_{ik})}{1+e^{psi(theta,x_{ik})}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle \frac{e^{\psi(\theta,x_{ik})} (j-x_{ik}) (1 - \pi_{ik})}{1+e^{\psi(\theta,x_{ik})}}$">|; 

$key = q/displaystylelog(pi_{ik})=alphax_{ik}+beta(k-x_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle \log(\pi_{ik}) = \alpha x_{ik} + \beta (k-x_{ik})$">|; 

$key = q/displaystyleapprox-frac{sum_{thetainQ}h(theta)I(theta)^{-1}logf(x|theta)}{sum_{t|theta)^{-1}logf(x|theta)}{sum_{thetainQ}f(x|theta)^{-1}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="506" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \approx - \frac{ \sum_{\theta \in Q} h(\theta) I(\theta)^{-1} \lo...
...rt\theta)^{-1} \log f(x\vert\theta) }{\sum_{\theta \in Q} f(x\vert\theta)^{-1}}$">|; 

$key = q/displaystyle=-logleft(sum_{thetainR}h(theta)right)-frac{sum_{thetainR}h(theta)cdotlogf(x|theta)}{sum_{thetainR}h(theta)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\displaystyle = - \log \left( \sum_{\theta \in R} h(\theta) \right) - \frac{\su...
...eta \in R} h(\theta) \cdot \log f(x\vert\theta)}{\sum_{\theta \in R} h(\theta)}$">|; 

$key = q/displaystyleE_{h(theta)f(x|theta)}left[KL(theta,hat{theta})right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle E_{h(\theta)f(x\vert\theta)}\left[ KL(\theta,\hat{\theta}) \right]$">|; 

$key = q/J;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$ J$">|; 

$key = q/displaystyle-logf(x|theta)Bigllvert_{thetainpartialR}=-frac{int_Rh(theta)logf(x|theta),dtheta}{int_Rh(theta),dtheta}+1;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="374" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle - \log f(x\vert\theta) \Bigl\lvert_{\theta \in \partial R} = - \f...
...t_R h(\theta) \log f(x\vert\theta)   d\theta}{\int_R h(\theta)   d\theta} + 1$">|; 

$key = q/hat{theta}=(hat{vartheta_1},...,hat{vartheta_d});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$ \hat{\theta} = (\hat{\vartheta_1},...,\hat{\vartheta_d})$">|; 

$key = q/pi_k;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$ \pi_k$">|; 

$key = q/U={Q_1,...,Q_K};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$ U = \{ Q_1,...,Q_K \}$">|; 

$key = q/f(x|theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$ f(x\vert\theta)$">|; 

$key = q/upsilon=0.924;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$ \upsilon=0.924$">|; 

$key = q/displaystyleapprox-logleft(frac{frac{1}{N}sum_{thetainQ}h(theta)I(theta)^{-1}}{finQ}f(x|theta)^{-1}}{sum_{thetainS}f(x|theta)^{-1}}right);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle \approx -\log \left( \frac{ \frac{1}{N} \sum_{\theta \in Q} h(\th...
...\in Q} f(x\vert\theta)^{-1}}{\sum_{\theta \in S} f(x\vert\theta)^{-1} } \right)$">|; 

$key = q/KL(.|.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$ KL(.\vert.)$">|; 

$key = q/displaystyleint_Rh(theta)KL(theta,hat{theta}),dtheta;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle \int_R h(\theta) KL(\theta,\hat{\theta})   d\theta$">|; 

$key = q/I(.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$ I(.)$">|; 

$key = q/displaystylefrac{e^{psi(theta,x_{ik})}}{1+e^{psi(theta,x_{ik})}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle \frac{e^{\psi(\theta,x_{ik})}}{1+e^{\psi(\theta,x_{ik})}}$">|; 

$key = q/displaystyle1;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle 1$">|; 

$key = q/displaystyle=frac{e^{alpha+betax_i}}{1+alpha+betax_i};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\displaystyle = \frac{e^{\alpha + \beta x_i}}{1 + \alpha + \beta x_i}$">|; 

$key = q/h(theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$ h(\theta)$">|; 

$key = q/f(.|.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$ f(.\vert.)$">|; 

$key = q/displaystyleerr(theta')approx1-frac{sum_{thetainQ}f(x|theta)^{-1}+f(x|theta')^{-1}+f(x|theta')^{-1}}{sum_{thetainQ}f(x|theta)^{-1}}right);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="613" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle err(\theta') \approx 1 - \frac{\sum_{\theta \in Q} f(x\vert\theta...
...{-1} + f(x\vert\theta')^{-1}}{\sum_{\theta \in Q} f(x\vert\theta)^{-1}} \right)$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$ p$">|; 

$key = q/displaystyle(k-x_{ik})(1-pi_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle (k-x_{ik}) (1 - \pi_{ik})$">|; 

$key = q/theta^{(0)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$ \theta^{(0)}$">|; 

$key = q/{displaymath}{array}{c@{hspace{14pt}}c}multicolumn{2}{c}{includegraphics[width=0fPosteriormean(point-wise)estimate.}}{array}{displaymath};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="831" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="\begin{displaymath}\begin{array}{c@{\hspace{14pt}}c}
\multicolumn{2}{c}{\include...
...box{\bf Posterior mean (point-wise) estimate.}} \\\\
\end{array}\end{displaymath}">|; 

$key = q/displaystylep(y|psi)=a(y)e^{psibullety-b(psi)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="43" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle p(y\vert\psi) = a(y) e^{\psi \bullet y - b(\psi)}$">|; 

$key = q/N=2048;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$ N=2048$">|; 

$key = q/displaystyleb(psi(theta,x_{ik}));MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle b(\psi(\theta,x_{ik}))$">|; 

$key = q/pi_{k}=pi_{k-1}upsilon;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$ \pi_{k}=\pi_{k-1} \upsilon$">|; 

$key = q/kappa;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$ \kappa$">|; 

$key = q/displaystyleJtimesdhat{theta}^{(k)}=-r;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle J \times d\hat{\theta}^{(k)} = -r$">|; 

$key = q/displaystyle-logf(x|theta)le-frac{sum_{thetainQ}logf(x|theta)f(x|theta)^{-1}}{sum_{thetainQ}f(x|theta)^{-1}}+1-err(theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle -\log f(x\vert\theta) \le - \frac{\sum_{\theta \in Q} \log f(x\ve...
...vert\theta)^{-1} }{\sum_{\theta \in Q} f(x\vert\theta)^{-1} } + 1 - err(\theta)$">|; 

$key = q/p_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$ p_i$">|; 

$key = q/K;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$ K$">|; 

$key = q/lambda=0.5;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$ \lambda = 0.5$">|; 

$key = q/-logf(x|theta_i);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$ -\log f(x\vert\theta_i)$">|; 

$key = q/k;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$ k$">|; 

$key = q/displaystylefrac{partialb(psi(theta,x_{ik}))}{partialalpha};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \frac{\partial b(\psi(\theta,x_{ik}))}{\partial \alpha}$">|; 

$key = q/displaystylefrac{partialpsi(theta,x_{ik})}{partialbeta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\displaystyle \frac{\partial \psi(\theta,x_{ik})}{\partial \beta}$">|; 

$key = q/logf(x|theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$ \log f(x\vert\theta)$">|; 

$key = q/sigma=2.5;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$ \sigma = 2.5$">|; 

$key = q/beta=log(upsilon);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$ \beta=\log(\upsilon)$">|; 

$key = q/displaystylelog(1+e^pi_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle \log (1+e^\pi_{ik})$">|; 

$key = q/displaystyleMessLen(theta_i,x)=-logp_i-logf(x|theta_i);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\displaystyle MessLen(\theta_i,x) = -\log p_i - \log f(x\vert\theta_i)$">|; 

$key = q/f;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$ f$">|; 

$key = q/w_1=0.42;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$ w_1 = 0.42$">|; 

$key = q/displaystyleKL(theta,hat{theta})lefrac{sum_{theta'inQ}f(x|theta')^{-1}KL(theta',at{theta})}{sum_{theta'inQ}f(x|theta')^{-1}}+1-err(theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="75" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\displaystyle KL(\theta,\hat{\theta}) \le \frac{\sum_{\theta' \in Q} f(x\vert\t...
...',\hat{\theta}) }{\sum_{\theta' \in Q} f(x\vert\theta')^{-1}} + 1 - err(\theta)$">|; 

$key = q/theta_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$ \theta_i$">|; 

$key = q/Q;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$ Q$">|; 

$key = q/N=128;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$ N=128$">|; 

$key = q/displaystylefrac{partialb(psi(theta,x_{ik}))}{partialbeta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle \frac{\partial b(\psi(\theta,x_{ik}))}{\partial \beta}$">|; 

$key = q/displaystyle=1-e^{-e^{alpha+betax_i}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\displaystyle = 1 - e^{- e^{\alpha + \beta x_i}}$">|; 

$key = q/displaystyle=;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle =$">|; 

$key = q/displaystylepi_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \pi_i$">|; 

$key = q/{figure}algorithm{{Pseudo-codeforoptimisingtheMMLDmessagelengthinthevariabledimeeBlock{Block{Block{Block{Block{algorithm{{figure};MSF=1.6;LFS=12;FSF=1.6;AAF;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="556" HEIGHT="626" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="\begin{figure}\begin{algorithm}{Pseudo-code for optimising the MMLD message leng...
...nd{Block}\end{Block}\end{Block}\end{Block}\end{Block}\end{algorithm}\end{figure}">|; 

$key = q/displaystylefrac{1}{|Q|}sum_{thetainQ}KL(theta,hat{theta});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \frac{1}{\vert Q\vert} \sum_{\theta \in Q} KL(\theta,\hat{\theta})$">|; 

$key = q/{displaymath}{array}{c@{hspace{14pt}}c}includegraphics[width=0.45textwidth]{slas&mbox{bfRegion9pointestimate(w<0.01)}{array}{displaymath};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="678" HEIGHT="317" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="\begin{displaymath}\begin{array}{c@{\hspace{14pt}}c}
\includegraphics[width=0.45...
...\mbox{\bf Region 9 point estimate ($w &lt; 0.01$)} \\\\
\end{array}\end{displaymath}">|; 

$key = q/displaystylevarepsilon={(theta_1,w_1),...,(theta_K,w_K)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\displaystyle \varepsilon = \{ (\theta_1,w_1),...,(\theta_K,w_K) \}$">|; 

$key = q/hat{theta}^{(k+1)}=hat{theta}^{(k)}+dhat{theta}^{(k)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$ \hat{\theta}^{(k+1)} = \hat{\theta}^{(k)} + d\hat{\theta}^{(k)}$">|; 

1;

