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108 lines
4.1 KiB
108 lines
4.1 KiB
3 years ago
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\chapter{Route/Trajectory Prediction}
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\label{ch:03_xxx}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Section}
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\label{sec:0301_xxx}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[H]
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\centering
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\tikz{ %
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%Define nodes
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\node[obs] (x) {$\mv{x}_n^{(j)}$};
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\node[latent, above=of x] (s) {$s_n^{(j)}$};
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\node[latent, left=of s] (s0) {$s_0$};
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\node[latent, left=of s0] (pi) {$\mv{\pi}_{\mv{i}}$};
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\node[latent, below=of pi] (theta) {$\theta_{\mv{i}}$};
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\node[latent, left=of pi] (alpha) {$\alpha$};
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\node[latent, left=of theta] (H) {$H$};
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\node[latent, left=of H] (lambda) {$\lambda$};
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\node[latent, above=of pi] (beta) {$\beta$};
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\node[latent, left=of beta] (gamma) {$\gamma$};
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\node[latent, above=of s] (z) {$z^{(j)}$};
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\node[latent, right=of z] (rho) {$\rho$};
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\node[latent, right=of rho] (eta) {$\eta$};
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\node[const, left=of gamma,yshift=0.25cm] (gamma_a) {$\gamma_a$};
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\node[const, left=of gamma,yshift=-0.25cm] (gamma_b) {$\gamma_b$};
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\node[const, left=of alpha,yshift=0.25cm] (alpha_a) {$\alpha_a$};
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\node[const, left=of alpha,yshift=-0.25cm] (alpha_b) {$\alpha_b$};
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\edge {gamma_a} {gamma};
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\edge {gamma_b} {gamma};
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\edge {alpha_a} {alpha};
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\edge {alpha_b} {alpha};
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\factor[left=of eta] {eta_rho} {GEM()} {} {} ; %
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\factor[left=of rho] {rho_z} {Cat()} {} {} ;
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\factor[right=of gamma] {gamma_beta} {GEM()} {} {} ; %
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\factor[above=of x] {x_s} {right:$F(\theta_{s_n^{(j)}})$} {} {} ; %
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\factor[left=of H] {lambda_H} {NIW} {} {} ; %
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%\factor[above=of f,yshift=0.7cm] {rf} {Cat} {} {} ;
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%\factor[above=of pi, yshift=0.4cm] {pi-f} {left:Dir} {} {} ;
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%\factor[above=of t, yshift=0.5cm] {t-f} {left:Beta} {} {} ; %
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%\factor[right=of p, xshift=0.5cm] {p-f} {Dir} {} {} ; %
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%\factor[above=of d, yshift=0.4cm] {d-f} {right:Dir} {} {} ; %
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%Connect the nodes
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\edge {s0} {s} ;
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\edge {s} {x} ;
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\edge {z} {s} ;
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\edge {rho} {z} ;
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\edge {eta} {rho} ;
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\edge {lambda} {H} ;
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\edge {H} {theta} ;
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\edge {alpha} {pi} ;
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\edge {beta} {pi} ;
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\edge {gamma} {beta} ;
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%\edge {pi} {s} ;
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\path (pi) edge [bend left,->] (s) ;
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%\path (theta) edge [bend left,->] (x) ;
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\edge {theta} {x} ;
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%\factoredge {gamma} {d-f} {d} ;
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%\factoredge {alpha} {p-f} {p}; %
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%\factoredge {p} {t-f} {t}; %
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%\factoredge {beta} {pi-f} {pi} ;
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%\factoredge {pi} {yf} {y} ;
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%\factoredge {d} {rf} {f} ;
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%\gate {y-gate} {(yf)(yf-caption)} {t}
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%\gate {f-gate} {(rf)(rf-caption)} {t}
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%Plates
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\plate [inner sep=0.25cm,xshift=1.2mm,yshift=0.15cm] {sx} {(s)(x)} {$N_j$}; %
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{\tikzset{plate caption/.append style={above=-1.2cm of #1.south east }}
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\plate [inner sep=0.45cm,yshift=0.4cm] {sxz} {(s)(x)(z)} {$J$};}
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\plate [inner sep=0.35cm, color=black,
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fill=black,
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fill opacity=0.1,
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text opacity=1] {pitheta} {(pi)(theta)} {$\infty$};
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\node[latent, left=of s0,fill=white] (pi) {$\mv{\pi}_{\mv{i}}$};
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\node[latent, below=of pi,fill=white] (theta) {$\theta_{\mv{i}}$};
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%{\tikzset{plate caption/.append style={above=5pt of #1.north west}} ... }
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%{\tikzset{plate caption/.append style={above=5pt of #1.north east}} ... }
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%{\tikzset{plate caption/.append style={above=5pt of #1.south west}}
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%\plate [inner sep=0.2cm, xshift=-0.2cm, color=red] {pM} {(beta)(pi)(yf)(y)(rf)(f)} {M workers} ;}
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%\plate [inner sep=0.2cm, xshift=-0.05cm, yshift=0.15cm, color=brown] {pJi} {(y)(f)} {$J_i$}
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}
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\end{figure}
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\begin{align}
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\mv{i} = [l,k]
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\end{align}
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$l$ represents the l'th HMM (e.g. for trajectory classification) and state $k$ respectively.
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%==============================================================================
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\subsection{Subsection}
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\label{subsec:030101_xxx}
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%==============================================================================
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