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Baum Welch algorithm description

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0

I am trying to replicate this table, on the Baum Welch algorithm, for Hidden Markov Models. I can not put expressions in the center, I'm trying with begin {align *} ... end {align *}, but the problem is that the vertical line is deleted. Somebody could help me?

Expected Output:

usepackage{tabularx}

usepackage{booktabs}



begin{table}[H]

    centering

    label{tabla4}

    begin{tabularx}{textwidth}{X}

        toprule

        textbf{Algorithm 5:} The Baum-Welch algorithm \ midrule

        textbf{Initialization:} \

         $Theta_0, lbrace O_{1:T} rbrace$  \

        \

        textbf{Looping:} \

        textbf{for} $l = 1,..., l_{max}$ textbf{do} \

          vline   1. Forward-Backward calculations:\

          vline \

          vline   $alpha_1 (i) = pi_i b_i (O_1),  beta_T (i) = 1$, \

          vline   $alpha_t (i) = left[ sum_{j=1}^K alpha_{t-1} (j) a_{ji} right] b_j (O_t),  beta_t (i) = sum_{j=1}^K a_{ij} b_j (O_{t+1}) beta_{t+1} (j)$\

          vline   for $1 leq i leq K,  1 leq t leq T-1$\

          vline \

          vline   2. E-step: \

          vline \

          vline   $gamma_t (i) = frac{alpha_t (i) beta_t (i)}{sum_{j=1}^K alpha_t (j) beta_t (j)},  xi_t (i,j) = frac{alpha_t (i) a_{ij} b_j (O_{t+1}) beta_{t+1}(j) }{sum_{i=1}^N sum_{j=1}^N alpha_t(i) a_{ij} b_j (O_{t+1} beta_t (j))}$ \

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq t leq T-1$\

          vline   \

          vline   3. M-step: \

          vline   \

          vline   $pi_i = frac{gamma_1 (i)}{sum_{j=1}^K gamma_1(j)},  a_{ij} = frac{sum_{t=1}^T varepsilon_t (i,j)}{ sum_{k=1}^K sum_{t=1}^T varepsilon_t (i, k)},  w_{kd} = frac{sum_{t=1}^T gamma_t (k, d)}{sum_{t=1}^T sum_{r=1}^D gamma_t (k, r)}$\

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq k leq K, 1 leq d leq D$\

        textbf{end} \

        \

        textbf{Result:} $lbrace Theta_l rbrace^{l_{max}}_{l=0} $ \ bottomrule

    end{tabularx}

end{table}

tabularx booktabs

share

asked 4 mins ago

Rafael DíazRafael Díaz

1012

New contributor

Rafael Díaz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

add a comment | 

0

I am trying to replicate this table, on the Baum Welch algorithm, for Hidden Markov Models. I can not put expressions in the center, I'm trying with begin {align *} ... end {align *}, but the problem is that the vertical line is deleted. Somebody could help me?

Expected Output:

usepackage{tabularx}

usepackage{booktabs}



begin{table}[H]

    centering

    label{tabla4}

    begin{tabularx}{textwidth}{X}

        toprule

        textbf{Algorithm 5:} The Baum-Welch algorithm \ midrule

        textbf{Initialization:} \

         $Theta_0, lbrace O_{1:T} rbrace$  \

        \

        textbf{Looping:} \

        textbf{for} $l = 1,..., l_{max}$ textbf{do} \

          vline   1. Forward-Backward calculations:\

          vline \

          vline   $alpha_1 (i) = pi_i b_i (O_1),  beta_T (i) = 1$, \

          vline   $alpha_t (i) = left[ sum_{j=1}^K alpha_{t-1} (j) a_{ji} right] b_j (O_t),  beta_t (i) = sum_{j=1}^K a_{ij} b_j (O_{t+1}) beta_{t+1} (j)$\

          vline   for $1 leq i leq K,  1 leq t leq T-1$\

          vline \

          vline   2. E-step: \

          vline \

          vline   $gamma_t (i) = frac{alpha_t (i) beta_t (i)}{sum_{j=1}^K alpha_t (j) beta_t (j)},  xi_t (i,j) = frac{alpha_t (i) a_{ij} b_j (O_{t+1}) beta_{t+1}(j) }{sum_{i=1}^N sum_{j=1}^N alpha_t(i) a_{ij} b_j (O_{t+1} beta_t (j))}$ \

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq t leq T-1$\

          vline   \

          vline   3. M-step: \

          vline   \

          vline   $pi_i = frac{gamma_1 (i)}{sum_{j=1}^K gamma_1(j)},  a_{ij} = frac{sum_{t=1}^T varepsilon_t (i,j)}{ sum_{k=1}^K sum_{t=1}^T varepsilon_t (i, k)},  w_{kd} = frac{sum_{t=1}^T gamma_t (k, d)}{sum_{t=1}^T sum_{r=1}^D gamma_t (k, r)}$\

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq k leq K, 1 leq d leq D$\

        textbf{end} \

        \

        textbf{Result:} $lbrace Theta_l rbrace^{l_{max}}_{l=0} $ \ bottomrule

    end{tabularx}

end{table}

tabularx booktabs

share

asked 4 mins ago

Rafael DíazRafael Díaz

1012

New contributor

Rafael Díaz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

add a comment | 

I am trying to replicate this table, on the Baum Welch algorithm, for Hidden Markov Models. I can not put expressions in the center, I'm trying with begin {align *} ... end {align *}, but the problem is that the vertical line is deleted. Somebody could help me?

Expected Output:

usepackage{tabularx}

usepackage{booktabs}



begin{table}[H]

    centering

    label{tabla4}

    begin{tabularx}{textwidth}{X}

        toprule

        textbf{Algorithm 5:} The Baum-Welch algorithm \ midrule

        textbf{Initialization:} \

         $Theta_0, lbrace O_{1:T} rbrace$  \

        \

        textbf{Looping:} \

        textbf{for} $l = 1,..., l_{max}$ textbf{do} \

          vline   1. Forward-Backward calculations:\

          vline \

          vline   $alpha_1 (i) = pi_i b_i (O_1),  beta_T (i) = 1$, \

          vline   $alpha_t (i) = left[ sum_{j=1}^K alpha_{t-1} (j) a_{ji} right] b_j (O_t),  beta_t (i) = sum_{j=1}^K a_{ij} b_j (O_{t+1}) beta_{t+1} (j)$\

          vline   for $1 leq i leq K,  1 leq t leq T-1$\

          vline \

          vline   2. E-step: \

          vline \

          vline   $gamma_t (i) = frac{alpha_t (i) beta_t (i)}{sum_{j=1}^K alpha_t (j) beta_t (j)},  xi_t (i,j) = frac{alpha_t (i) a_{ij} b_j (O_{t+1}) beta_{t+1}(j) }{sum_{i=1}^N sum_{j=1}^N alpha_t(i) a_{ij} b_j (O_{t+1} beta_t (j))}$ \

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq t leq T-1$\

          vline   \

          vline   3. M-step: \

          vline   \

          vline   $pi_i = frac{gamma_1 (i)}{sum_{j=1}^K gamma_1(j)},  a_{ij} = frac{sum_{t=1}^T varepsilon_t (i,j)}{ sum_{k=1}^K sum_{t=1}^T varepsilon_t (i, k)},  w_{kd} = frac{sum_{t=1}^T gamma_t (k, d)}{sum_{t=1}^T sum_{r=1}^D gamma_t (k, r)}$\

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq k leq K, 1 leq d leq D$\

        textbf{end} \

        \

        textbf{Result:} $lbrace Theta_l rbrace^{l_{max}}_{l=0} $ \ bottomrule

    end{tabularx}

end{table}

tabularx booktabs

share

asked 4 mins ago

Rafael DíazRafael Díaz

1012

New contributor

Rafael Díaz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

usepackage{tabularx}

usepackage{booktabs}



begin{table}[H]

    centering

    label{tabla4}

    begin{tabularx}{textwidth}{X}

        toprule

        textbf{Algorithm 5:} The Baum-Welch algorithm \ midrule

        textbf{Initialization:} \

         $Theta_0, lbrace O_{1:T} rbrace$  \

        \

        textbf{Looping:} \

        textbf{for} $l = 1,..., l_{max}$ textbf{do} \

          vline   1. Forward-Backward calculations:\

          vline \

          vline   $alpha_1 (i) = pi_i b_i (O_1),  beta_T (i) = 1$, \

          vline   $alpha_t (i) = left[ sum_{j=1}^K alpha_{t-1} (j) a_{ji} right] b_j (O_t),  beta_t (i) = sum_{j=1}^K a_{ij} b_j (O_{t+1}) beta_{t+1} (j)$\

          vline   for $1 leq i leq K,  1 leq t leq T-1$\

          vline \

          vline   2. E-step: \

          vline \

          vline   $gamma_t (i) = frac{alpha_t (i) beta_t (i)}{sum_{j=1}^K alpha_t (j) beta_t (j)},  xi_t (i,j) = frac{alpha_t (i) a_{ij} b_j (O_{t+1}) beta_{t+1}(j) }{sum_{i=1}^N sum_{j=1}^N alpha_t(i) a_{ij} b_j (O_{t+1} beta_t (j))}$ \

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq t leq T-1$\

          vline   \

          vline   3. M-step: \

          vline   \

          vline   $pi_i = frac{gamma_1 (i)}{sum_{j=1}^K gamma_1(j)},  a_{ij} = frac{sum_{t=1}^T varepsilon_t (i,j)}{ sum_{k=1}^K sum_{t=1}^T varepsilon_t (i, k)},  w_{kd} = frac{sum_{t=1}^T gamma_t (k, d)}{sum_{t=1}^T sum_{r=1}^D gamma_t (k, r)}$\

          vline   for $1 leq i leq K,  1 leq j leq K,  1 leq k leq K, 1 leq d leq D$\

        textbf{end} \

        \

        textbf{Result:} $lbrace Theta_l rbrace^{l_{max}}_{l=0} $ \ bottomrule

    end{tabularx}

end{table}

share

asked 4 mins ago

Rafael DíazRafael Díaz

1012

New contributor

Rafael Díaz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share

asked 4 mins ago

Rafael DíazRafael Díaz

1012

New contributor

Rafael Díaz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 4 mins ago

Rafael DíazRafael Díaz

1012

New contributor

Rafael Díaz is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 4 mins ago

Rafael DíazRafael Díaz

1012