Crthuky

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:

usepackagetabularx
usepackagebooktabs

begintable[H]
 centering
 labeltabla4
 begintabularxtextwidthX
 toprule
 textbfAlgorithm 5: The Baum-Welch algorithm \ midrule
 textbfInitialization: \
 $Theta_0, lbrace O_1:T rbrace$ \
 \
 textbfLooping: \
 textbffor $l = 1,..., l_max$ textbfdo \
 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 $gamma_t (i) = fracalpha_t (i) beta_t (i)sum_j=1^K alpha_t (j) beta_t (j), xi_t (i,j) = fracalpha_t (i) a_ij b_j (O_t+1) beta_t+1(j) sum_i=1^N sum_j=1^N alpha_t(i) a_ij b_j (O_t+1 beta_t (j))$ \
 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 $pi_i = fracgamma_1 (i)sum_j=1^K gamma_1(j), a_ij = fracsum_t=1^T varepsilon_t (i,j) sum_k=1^K sum_t=1^T varepsilon_t (i, k), w_kd = fracsum_t=1^T gamma_t (k, d)sum_t=1^T sum_r=1^D gamma_t (k, r)$\
 vline for $1 leq i leq K, 1 leq j leq K, 1 leq k leq K, 1 leq d leq D$\
 textbfend \
 \
 textbfResult: $lbrace Theta_l rbrace^l_max_l=0 $ \ bottomrule
 endtabularx
endtable