# 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||;
$key = q/displaystylethetainQ;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylevarepsilon={((kappa=0.788,upsilon=0.924),1)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/partialR;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/|Q|;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylepsi(theta,x_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/kappa=0.788;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylepi_{ik}=kappa^{x_{ik}}timesupsilon^{k-x_{ik}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/R;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleb(psi)=lnint_ye^{psibullety}a(y)dy;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/includegraphics[width=0.7textwidth]{slashhomeslashleighfslashstaticslashPaper-PostCompslashblocks};LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystylea(y);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$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||;
$key = q/err;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/includegraphics[width=0.6textwidth]{slashhomeslashleighfslashstaticslashPaper-PostCompslashdogs1};LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/k-1;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/log_e2;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/x;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/hat{theta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/upsilon;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyle(alpha,beta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/w_7=0.01;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/pi_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/[0,1];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/I(theta)proptoh(theta)f(x|theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyletheta;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/pi_{k}=pi_{k-1}kappa;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleS={theta_t:t=1,...,N};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyle=Phi(alpha+betax_i);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystyleKL(psi,hat{psi});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$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||;
$key = q/-logp;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{partialb(psi(theta,x_{ik}))}{partialpsi};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleapprox;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/-logp_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/argmin_{theta_i}MessLen(theta_i,x);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$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||;
$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||;
$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||;
$key = q/x_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/alpha=log(kappa);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/x_{ik};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/k-x_{ik};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/i^{mbox{th}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/dhat{theta}^{(k)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/err(.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylelogfrac{pi_{ik}}{1-pi_{ik}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/h(.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystyleE_{h(theta)}left[KL(theta,hat{theta})right];MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystylefrac{partialpsi(theta,x_{ik})}{partialalpha};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystylelog(pi_{ik})=alphax_{ik}+beta(k-x_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$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||;
$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||;
$key = q/J;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/hat{theta}=(hat{vartheta_1},...,hat{vartheta_d});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/pi_k;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/U={Q_1,...,Q_K};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/f(x|theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/upsilon=0.924;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/KL(.|.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleint_Rh(theta)KL(theta,hat{theta}),dtheta;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/I(.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystyle1;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyle=frac{e^{alpha+betax_i}}{1+alpha+betax_i};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/h(theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/f(.|.);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/p;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyle(k-x_{ik})(1-pi_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/theta^{(0)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystylep(y|psi)=a(y)e^{psibullety-b(psi)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/N=2048;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleb(psi(theta,x_{ik}));MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/pi_{k}=pi_{k-1}upsilon;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/kappa;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleJtimesdhat{theta}^{(k)}=-r;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/p_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/K;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/lambda=0.5;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/-logf(x|theta_i);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/k;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{partialb(psi(theta,x_{ik}))}{partialalpha};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{partialpsi(theta,x_{ik})}{partialbeta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/logf(x|theta);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/sigma=2.5;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/beta=log(upsilon);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylelog(1+e^pi_{ik});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyleMessLen(theta_i,x)=-logp_i-logf(x|theta_i);MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/f;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/w_1=0.42;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/theta_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/Q;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/N=128;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylefrac{partialb(psi(theta,x_{ik}))}{partialbeta};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyle=1-e^{-e^{alpha+betax_i}};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystyle=;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/displaystylepi_i;MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystylefrac{1}{|Q|}sum_{thetainQ}KL(theta,hat{theta});MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$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||;
$key = q/displaystylevarepsilon={(theta_1,w_1),...,(theta_K,w_K)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
$key = q/hat{theta}^{(k+1)}=hat{theta}^{(k)}+dhat{theta}^{(k)};MSF=1.6;LFS=12;AAT;NTR/;
$cached_env_img{$key} = q||;
1;