EOD 4/07

Rcodes/simulation/inference_analyze.R

@@ -1,7 +1,9 @@
 require("ggplot2")
+require("tidyr")
+require("dplyr")
 filenames <- list.files(
     path = "./Rcodes/simulation/data/",
-    pattern = "inference_testing_2023-05*",
+    pattern = "inference_testing_2023-07*",
     full.names = TRUE
 )
 col_id_BICLS <- c(11, 16, 23, 30, 37)
@@ -13,7 +15,164 @@ ggplot(data = result_data_frame) +
     aes(x = epsilon_alpha, group = preferred_model, fill = preferred_model) +
     geom_bar()
 
-ggplot(data = result_data_frame) +
+# Build ARI row long table
-    aes(x = , group = preferred_model, fill = preferred_model) +
+ARI_long_table <- result_data_frame %>%
-    geom_bar()
+    # mutate(
+    #     iid_mean_row_ARI = iid_mean_row_ARI - sep_mean_row_ARI,
+    #     pi_mean_row_ARI = pi_mean_row_ARI - sep_mean_row_ARI,
+    #     rho_mean_row_ARI = rho_mean_row_ARI - sep_mean_row_ARI,
+    #     pirho_mean_row_ARI = pirho_mean_row_ARI - sep_mean_row_ARI,
+    #     iid_mean_col_ARI = iid_mean_col_ARI - sep_mean_col_ARI,
+    #     pi_mean_col_ARI = pi_mean_col_ARI - sep_mean_col_ARI,
+    #     rho_mean_col_ARI = rho_mean_col_ARI - sep_mean_col_ARI,
+    #     pirho_mean_col_ARI = pirho_mean_col_ARI - sep_mean_col_ARI,
+    #     ) %>%
+    dplyr::select(
+        c(
+            epsilon_alpha, pi1.1, pi1.2, pi1.3, pi1.4,
+            rho2.1, rho2.2, rho2.3, rho2.4, repetition,
+            # sep_mean_row_ARI, 
+            iid_mean_row_ARI, pi_mean_row_ARI, rho_mean_row_ARI,
+            pirho_mean_row_ARI, 
+            # sep_mean_col_ARI,
+            iid_mean_col_ARI,
+            pi_mean_col_ARI,
+            rho_mean_col_ARI,
+            pirho_mean_col_ARI
+        )
+    ) %>%
+    pivot_longer(
+        cols = c(
+            # sep_mean_row_ARI,
+            iid_mean_row_ARI,
+            pi_mean_row_ARI,
+            rho_mean_row_ARI,
+            pirho_mean_row_ARI,
+            # sep_mean_col_ARI,
+            iid_mean_col_ARI,
+            pi_mean_col_ARI,
+            rho_mean_col_ARI,
+            pirho_mean_col_ARI
+        ),
+        names_to = c("model", "axis"),
+        names_sep = "_mean_",
+        names_transform = list(model = as.factor, axis = as.factor),
+        values_to = "ARI"
+    )
 
+summarised_ARI <- ARI_long_table %>%
+    group_by(
+        epsilon_alpha, model, axis
+    ) %>%
+    summarise(mean_ARI = mean(ARI), sd_ARI = sd(ARI)) 
+
+summarised_ARI %>%
+    filter(axis == "row_ARI") %>%
+    ggplot() +
+    aes(x = epsilon_alpha, y = mean_ARI, color = model) +
+    geom_ribbon(aes(x = epsilon_alpha, ymin = mean_ARI - sd_ARI, ymax = mean_ARI + sd_ARI, fill = model), alpha = 0.2) +
+    geom_line() +
+    geom_point()
+
+summarised_ARI %>%
+    filter(axis == "col_ARI") %>%
+    ggplot() +
+    aes(x = epsilon_alpha, y = mean_ARI, color = model) +
+    geom_ribbon(aes(x = epsilon_alpha, ymin = mean_ARI - sd_ARI, ymax = mean_ARI + sd_ARI, fill = model), alpha = 0.2) +
+    geom_line() +
+    geom_point()
+
+# Build Q long table
+Q1_long_table <- result_data_frame %>%
+    # mutate(
+    #     iid_mean_row_ARI = iid_mean_row_ARI - sep_mean_row_ARI,
+    #     pi_mean_row_ARI = pi_mean_row_ARI - sep_mean_row_ARI,
+    #     rho_mean_row_ARI = rho_mean_row_ARI - sep_mean_row_ARI,
+    #     pirho_mean_row_ARI = pirho_mean_row_ARI - sep_mean_row_ARI,
+    #     iid_mean_col_ARI = iid_mean_col_ARI - sep_mean_col_ARI,
+    #     pi_mean_col_ARI = pi_mean_col_ARI - sep_mean_col_ARI,
+    #     rho_mean_col_ARI = rho_mean_col_ARI - sep_mean_col_ARI,
+    #     pirho_mean_col_ARI = pirho_mean_col_ARI - sep_mean_col_ARI,
+    #     ) %>%
+    dplyr::select(
+        c(
+            epsilon_alpha, pi1.1, pi1.2, pi1.3, pi1.4,
+            rho2.1, rho2.2, rho2.3, rho2.4, repetition,
+            iid_Q1, 
+            pi_Q1,
+            rho_Q1,
+            pirho_Q1
+        )
+    ) %>%
+    pivot_longer(
+        cols = c(
+            iid_Q1,
+            pi_Q1,
+            rho_Q1,
+            pirho_Q1
+        ),
+        names_to = c("model"),
+        names_transform = list(model = as.factor),
+        values_to = "row_blocks"
+    )
+
+Q1_summarised <- Q1_long_table %>%
+    group_by(
+        epsilon_alpha, model
+    ) %>%
+    summarise(mean_row_blocks = mean(row_blocks), sd_row_blocks = sd(row_blocks))
+
+Q1_summarised %>%
+    ggplot() +
+    aes(x = epsilon_alpha, y = mean_row_blocks, color = model) +
+    # geom_ribbon(aes(x = epsilon_alpha, ymin = mean_row_blocks - sd_row_blocks, ymax = mean_row_blocks + sd_row_blocks, fill = model), alpha = 0.2) +
+    geom_hline(yintercept = 4)+
+    geom_line() +
+    geom_point() 
+
+Q2_long_table <- result_data_frame %>%
+    # mutate(
+    #     iid_mean_row_ARI = iid_mean_row_ARI - sep_mean_row_ARI,
+    #     pi_mean_row_ARI = pi_mean_row_ARI - sep_mean_row_ARI,
+    #     rho_mean_row_ARI = rho_mean_row_ARI - sep_mean_row_ARI,
+    #     pirho_mean_row_ARI = pirho_mean_row_ARI - sep_mean_row_ARI,
+    #     iid_mean_col_ARI = iid_mean_col_ARI - sep_mean_col_ARI,
+    #     pi_mean_col_ARI = pi_mean_col_ARI - sep_mean_col_ARI,
+    #     rho_mean_col_ARI = rho_mean_col_ARI - sep_mean_col_ARI,
+    #     pirho_mean_col_ARI = pirho_mean_col_ARI - sep_mean_col_ARI,
+    #     ) %>%
+    dplyr::select(
+        c(
+            epsilon_alpha, pi1.1, pi1.2, pi1.3, pi1.4,
+            rho2.1, rho2.2, rho2.3, rho2.4, repetition,
+            iid_Q2,
+            pi_Q2,
+            rho_Q2,
+            pirho_Q2
+        )
+    ) %>%
+    pivot_longer(
+        cols = c(
+            iid_Q2,
+            pi_Q2,
+            rho_Q2,
+            pirho_Q2
+        ),
+        names_to = c("model"),
+        names_transform = list(model = as.factor),
+        values_to = "row_blocks"
+    )
+
+Q2_summarised <- Q2_long_table %>%
+    group_by(
+        epsilon_alpha, model
+    ) %>%
+    summarise(mean_row_blocks = mean(row_blocks), sd_row_blocks = sd(row_blocks))
+
+Q2_summarised %>%
+    ggplot() +
+    aes(x = epsilon_alpha, y = mean_row_blocks, color = model) +
+    # geom_ribbon(aes(x = epsilon_alpha, ymin = mean_row_blocks - sd_row_blocks, ymax = mean_row_blocks + sd_row_blocks, fill = model), alpha = 0.2) +
+    geom_hline(yintercept = 4) +
+    geom_line() +
+    geom_point()

Rcodes/simulation/inference_check.R

@@ -125,6 +125,10 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
         )
     )
 
+    # Handling a problem with sep_BiSBM$M
+    fitted_bisbmpop_iid$sep_BiSBM$M <- fitted_bisbmpop_iid$M
+    sep_BiSBM <- fitted_bisbmpop_iid$sep_BiSBM
+
     fitted_bisbmpop_pi <- estimate_colBiSBM(
         netlist = netlist,
         colsbm_model = "pi",
@@ -134,7 +138,8 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
             verbosity = 0,
             plot_details = 0,
             nb_cores = parallel::detectCores() - 1
-        )
+        ),
+        sep_BiSBM = sep_BiSBM
     )
 
     fitted_bisbmpop_rho <- estimate_colBiSBM(
@@ -146,7 +151,8 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
             verbosity = 0,
             plot_details = 0,
             nb_cores = parallel::detectCores() - 1
-        )
+        ),
+        sep_BiSBM = sep_BiSBM
     )
 
     fitted_bisbmpop_pirho <- estimate_colBiSBM(
@@ -158,11 +164,12 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
             verbosity = 0,
             plot_details = 0,
             nb_cores = parallel::detectCores() - 1
-        )
+        ),
+        sep_BiSBM = sep_BiSBM
     )
 
     # BICLs
-    sep_BICL <- sum(fitted_bisbmpop_iid$sep_BiSBM$BICL)
+    sep_BICL <- sum(sep_BiSBM$BICL)
     iid_BICL <- fitted_bisbmpop_iid$best_fit$BICL
     pi_BICL <- fitted_bisbmpop_pi$best_fit$BICL
     rho_BICL <- fitted_bisbmpop_rho$best_fit$BICL
@@ -179,13 +186,13 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
         # ax row1  row2
         # ay col1  col2
         rowMeans(sapply(seq.int(model$M), function(m) {
-            c(
+            matrix(c(
                 aricode::ARI(model$Z[[m]][[1]], row_clusterings[[m]]),
                 aricode::ARI(model$Z[[m]][[2]], col_clusterings[[m]])
-            )
+            ), nrow = 2, ncol = 1)
         }))
     }
-    sep_mean_ARIs <- compute_mean_ARI(fitted_bisbmpop_iid$sep_BiSBM)
+    sep_mean_ARIs <- compute_mean_ARI(sep_BiSBM)
     iid_mean_ARIs <- compute_mean_ARI(fitted_bisbmpop_iid$best_fit)
     pi_mean_ARIs <- compute_mean_ARI(fitted_bisbmpop_pi$best_fit)
     rho_mean_ARIs <- compute_mean_ARI(fitted_bisbmpop_rho$best_fit)

Rcodes/simulation/model_selection_analyze.Rmd

@@ -0,0 +1,184 @@
+```{r libraries, echo = FALSE, include = FALSE}
+require("ggplot2")
+require("tidyr")
+require("dplyr")
+require("patchwork")
+require("latex2exp")
+```
+
+```{r import-data, echo = FALSE}
+filenames <- list.files(
+    path = "./data/",
+    pattern = "model_selection_check_batch_report_3_rep_*",
+    full.names = TRUE
+)
+data_list <- lapply(filenames, readRDS)
+result_data_frame <- dplyr::bind_rows(data_list)
+
+result_data_frame$preferred_model <- factor(result_data_frame$preferred_model, levels = c(
+    "sep","iid","pi",
+    "rho","pirho"
+))
+
+# Adding a column accounting for true model iid, pi, rho or pirho
+# result_data_frame <- result_data_frame %>% mutate(true_model = if (all( c(epsilon_pi >0, epsilon_rho > 0) == c(TRUE, TRUE))) print("pirho") else if (all( c(epsilon_pi >0, epsilon_rho > 0) == c(TRUE, FALSE))) print("pi") else if (all( c(epsilon_pi >0, epsilon_rho > 0) == c(F, T))) print("rho") else print("iid"))
+
+```
+
+# Capacity to distinguish $\pi\rho\text{-}colBiSBM$ from $iid\text{-}colBiSBM$ and other variants
+
+The idea of this model selection simulations is to assess how the model select 
+the correct *colBiSBM* model among the possible ones: 
+\textit{iid, pi, rho, pirho}. This difference being based on the row and col
+block proportions.
+
+For this task we choose the same simulation context
+as \cite{chabert-liddellLearningCommonStructures2023}.
+
+Namely $n_{1}^{m} = 90, n_{2}^{m} = 90, Q_1 = Q_2 = 3$, $\bm{\alpha}, \bm{\pi}$
+and $\bm{\rho}$ are set as follows:
+
+\begin{align*}
+    \bm{\alpha} =.25 +  \begin{pmatrix}
+                        3 \eps[\alpha] & 2 \eps[\alpha] & \eps[\alpha] \\
+                        2 \eps[\alpha] & 2 \eps[\alpha] & - \eps[\alpha] \\
+                        \eps[\alpha] & - \eps[\alpha] & \eps[\alpha]
+                    \end{pmatrix}, & & \bm{\pi}^1 = \begin{pmatrix}
+                        \frac{1}{3}, & \frac{1}{3}, & \frac{1}{3}
+                    \end{pmatrix}, & & \bm{\pi}^2 = \sigma\begin{pmatrix}
+                        \frac{1}{3} - \eps[\pi], & \frac{1}{3}, & \frac{1}{3} + \eps[\pi]
+                    \end{pmatrix},\\
+    & & \bm{\rho}^1 = \begin{pmatrix}
+                        \frac{1}{3}, & \frac{1}{3}, & \frac{1}{3}
+                    \end{pmatrix}, & & \bm{\rho}^2 = \sigma\begin{pmatrix}
+                        \frac{1}{3} - \eps[\rho], & \frac{1}{3}, & \frac{1}{3} + \eps[\rho]
+                    \end{pmatrix},
+\end{align*}
+with $\eps[\alpha] = 0.16$, $\eps[\pi]$ and $\eps[\rho]$ taking 9 values equally
+spaced in $\left[ 0, .28\right]$. We simulate 324 different collections for each
+value of $\eps[\pi]$ and $\eps[\rho]$.
+
+$\pi\rho\text{-}colBiSBM$, $\pi\text{-}colBiSBM$, $\rho\text{-}colBiSBM$,
+$iid\text{-}colBiSBM$ and $sep\text{-}colBiSBM$ are put in competition and the
+model with the greater BIC-L is selected as the \emph{preferred model}. 
+
+```{r compute-table, echo = FALSE, include = FALSE}
+model_comparison_eps_pi_rho <- result_data_frame %>%
+    group_by(epsilon_pi, epsilon_rho, preferred_model) %>%
+    summarise(n = n()) %>%
+    mutate(prop_model = n / sum(n))
+
+model_comparison_eps_pi <- result_data_frame %>%
+    group_by(epsilon_pi, preferred_model) %>%
+    summarise(n = n(), rec_Q1 = mean(iid_Q1 + pi_Q1 + rho_Q1 + pirho_Q1)/4) %>%
+    mutate(prop_model = n / sum(n))
+
+model_comparison_eps_rho <- result_data_frame %>%
+    group_by(epsilon_rho, preferred_model) %>%
+    summarise(n = n(), rec_Q2 = mean(iid_Q2 + pi_Q2 + rho_Q2 + pirho_Q2)/4) %>%
+    mutate(prop_model = n / sum(n))
+```
+
+```{r epsilon_plot, echo = FALSE, include = FALSE}
+#| fig.asp = 0.5,
+#| fig.pos = "H",
+#| fig.width = 7,
+#| fig.height = 4,
+#| dpi=300
+
+plot_pi <- model_comparison_eps_pi %>% ggplot() +
+    aes(x = epsilon_pi, y = prop_model, color = preferred_model, 
+    fill = preferred_model) +
+    xlab(TeX("$\\epsilon_{\\pi}$")) +
+    ylab("Model proportions")+
+    geom_col(position = "stack")
+plot_rho <- model_comparison_eps_rho %>% ggplot() +
+    aes(x = epsilon_rho, y = prop_model, color = preferred_model, 
+    fill = preferred_model) +
+    xlab(TeX("$\\epsilon_{\\rho}$")) +
+    ylab("")+
+    geom_col(position = "stack")
+
+ggsave("./img/plot_model_function_eps.png", plot_pi + plot_rho + plot_layout(guides = "collect"))
+```
+
+
+When $\eps[\pi] = 0$, $\bm{\pi}^1 = \bm{\pi}^2$, $\eps[\rho] = 0$ and
+$\bm{\rho}^1 = \bm{\rho}^2$, the generated collection is an 
+$iid\text{-}colBiSBM$. When $\eps[\pi] > 0$ or $\bm{\pi}^1 \neq \bm{\pi}^2$,
+the model is a $\pi\text{-}colBiSBM$.
+When $\eps[\rho] > 0$ or $\bm{\rho}^1 \neq \bm{\rho}^2$,
+the model is a $\rho\text{-}colBiSBM$. 
+Finally, when $\eps[\pi] > 0$ or $\bm{\pi}^1 \neq \bm{\pi}^2$ and
+$\eps[\rho] > 0$ or $\bm{\rho}^1 \neq \bm{\rho}^2$,
+the model is a $\pi\rho\text{-}colBiSBM$.
+
+```{r tables, echo = FALSE}
+kable(
+    (model_comparison_eps_pi %>%
+        select(-one_of("n")) %>%
+        pivot_wider(
+            names_from = preferred_model,
+            values_from = prop_model,
+            values_fill = 0
+        ) %>% group_by(epsilon_pi) %>% 
+        summarise(rec_Q1 = mean(rec_Q1), 
+        iid = sum(iid), 
+        pi = sum(pi), 
+        rho = sum(rho), 
+        pirho = sum(pirho)))[,c(1,3:6, 2)],
+    digits = 2,
+    col.names = c(
+        "$\\eps[\\pi]$",
+        "$iid\\text{-}colBiSBM$",
+        "$\\pi\\text{-}colBiSBM$",
+        "$\\rho\\text{-}colBiSBM$",
+        "$\\pi\\rho\\text{-}colBiSBM$",
+        "Recovered $Q_1$"
+    ), align = "lcccc",
+    caption = "\\label{tab:pi-model-sel}Model selection for varying $\\pi$ mixture parameters"
+)
+kable(
+    (model_comparison_eps_rho %>%
+        select(-one_of("n")) %>%
+        pivot_wider(
+            names_from = preferred_model,
+            values_from = prop_model,
+            values_fill = 0
+        )  %>% group_by(epsilon_rho) %>% 
+        summarise(rec_Q2 = mean(rec_Q2), 
+        iid = sum(iid), 
+        pi = sum(pi), 
+        rho = sum(rho), 
+        pirho = sum(pirho)))[,c(1,3:6, 2)],
+    digits = 2,
+    col.names = c(
+        "$\\eps[\\rho]$",
+        "$iid\\text{-}colBiSBM$",
+        "$\\pi\\text{-}colBiSBM$",
+        "$\\rho\\text{-}colBiSBM$",
+        "$\\pi\\rho\\text{-}colBiSBM$",
+        "Recovered $Q_2$"
+    ), align = "lcccc",
+    caption = "\\label{tab:rho-model-sel}Model selection for varying $\\rho$ mixture parameters"
+)
+```
+
+\begin{figure}[H]
+\includegraphics{./Rcodes/simulation/img/plot_model_function_eps.png}
+\caption{Plot of preferred model in function of $\eps[\pi]$ and $\eps[\rho]$}
+\label{fig:pref_model_func_eps}
+\end{figure}
+
+On the figure \ref{fig:pref_model_func_eps} and tables \ref{tab:pi-model-sel} 
+and \ref{tab:rho-model-sel}, one can see that there is a turning
+point around $\eps[\pi] = 0.2$ (resp. $\eps[\rho] = 0.2$), before which 
+$iid\text{-}colBiSBM$
+and $\rho\text{-}colBiSBM$ (resp. $\pi\text{-}colBiSBM$) are selected most of 
+the times and after $0.2$ the $\pi\text{-}colBiSBM$ (resp.
+$\rho\text{-}colBiSBM$) and 
+$\pi\rho\text{-}colBiSBM$ gets more and more selected, highlighting our
+capacity to recover the simulated structure.
+
+Please note that when "Recovered $Q_1$(or $Q_2$)" is not an integer it's because
+some procedures returned a value other than 3.

Rcodes/simulation/model_selection_analyze.tex

@@ -0,0 +1,379 @@
+\hypertarget{capacity-to-distinguish-pirhotext-colbisbm-from-iidtext-colbisbm-and-other-variants}{%
+\section{\texorpdfstring{Capacity to distinguish
+\(\pi\rho\text{-}colBiSBM\) from \(iid\text{-}colBiSBM\) and other
+variants}{Capacity to distinguish \textbackslash pi\textbackslash rho\textbackslash text\{-\}colBiSBM from iid\textbackslash text\{-\}colBiSBM and other variants}}\label{capacity-to-distinguish-pirhotext-colbisbm-from-iidtext-colbisbm-and-other-variants}}
+
+The idea of this model selection simulations is to assess how the model
+select the correct \emph{colBiSBM} model among the possible ones:
+\textit{iid, pi, rho, pirho}. This difference being based on the row and
+col block proportions.
+
+For this task we choose the same simulation context as
+\cite{chabert-liddellLearningCommonStructures2023}.
+
+Namely \(n_{1}^{m} = 90, n_{2}^{m} = 90, Q_1 = Q_2 = 3\),
+\(\bm{\alpha}, \bm{\pi}\) and \(\bm{\rho}\) are set as follows:
+
+\begin{align*}
+    \bm{\alpha} =.25 +  \begin{pmatrix}
+                        3 \eps[\alpha] & 2 \eps[\alpha] & \eps[\alpha] \\
+                        2 \eps[\alpha] & 2 \eps[\alpha] & - \eps[\alpha] \\
+                        \eps[\alpha] & - \eps[\alpha] & \eps[\alpha]
+                    \end{pmatrix}, & & \bm{\pi}^1 = \begin{pmatrix}
+                        \frac{1}{3}, & \frac{1}{3}, & \frac{1}{3}
+                    \end{pmatrix}, & & \bm{\pi}^2 = \sigma\begin{pmatrix}
+                        \frac{1}{3} - \eps[\pi], & \frac{1}{3}, & \frac{1}{3} + \eps[\pi]
+                    \end{pmatrix},\\
+    & & \bm{\rho}^1 = \begin{pmatrix}
+                        \frac{1}{3}, & \frac{1}{3}, & \frac{1}{3}
+                    \end{pmatrix}, & & \bm{\rho}^2 = \sigma\begin{pmatrix}
+                        \frac{1}{3} - \eps[\rho], & \frac{1}{3}, & \frac{1}{3} + \eps[\rho]
+                    \end{pmatrix},
+\end{align*} with \(\eps[\alpha] = 0.16\), \(\eps[\pi]\) and
+\(\eps[\rho]\) taking 9 values equally spaced in
+\(\left[ 0, .28\right]\). We simulate 324 different collections for each
+value of \(\eps[\pi]\) and \(\eps[\rho]\).
+
+\(\pi\rho\text{-}colBiSBM\), \(\pi\text{-}colBiSBM\),
+\(\rho\text{-}colBiSBM\), \(iid\text{-}colBiSBM\) and
+\(sep\text{-}colBiSBM\) are put in competition and the model with the
+greater BIC-L is selected as the \emph{preferred model}.
+
+When \(\eps[\pi] = 0\), \(\bm{\pi}^1 = \bm{\pi}^2\), \(\eps[\rho] = 0\)
+and \(\bm{\rho}^1 = \bm{\rho}^2\), the generated collection is an
+\(iid\text{-}colBiSBM\). When \(\eps[\pi] > 0\) or
+\(\bm{\pi}^1 \neq \bm{\pi}^2\), the model is a \(\pi\text{-}colBiSBM\).
+When \(\eps[\rho] > 0\) or \(\bm{\rho}^1 \neq \bm{\rho}^2\), the model
+is a \(\rho\text{-}colBiSBM\). Finally, when \(\eps[\pi] > 0\) or
+\(\bm{\pi}^1 \neq \bm{\pi}^2\) and \(\eps[\rho] > 0\) or
+\(\bm{\rho}^1 \neq \bm{\rho}^2\), the model is a
+\(\pi\rho\text{-}colBiSBM\).
+
+\begin{longtable}[]{@{}lccccl@{}}
+\caption{\label{tab:pi-model-sel}Model selection for varying \(\pi\)
+mixture parameters}\tabularnewline
+\toprule
+\begin{minipage}[b]{0.08\columnwidth}\raggedright
+\(\eps[\pi]\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(iid\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(\pi\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering
+\(\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering
+\(\pi\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright
+Recovered \(Q_1\)\strut
+\end{minipage}\tabularnewline
+\midrule
+\endfirsthead
+\toprule
+\begin{minipage}[b]{0.08\columnwidth}\raggedright
+\(\eps[\pi]\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(iid\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(\pi\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering
+\(\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering
+\(\pi\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright
+Recovered \(Q_1\)\strut
+\end{minipage}\tabularnewline
+\midrule
+\endhead
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.65\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.35\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.04\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.66\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.34\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.07\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.64\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.34\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.11\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.63\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.03\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.31\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.03\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.14\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.55\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.12\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.28\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.05\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.18\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.39\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.26\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.21\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.13\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.21\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.23\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.42\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.13\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.23\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.25\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.10\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.56\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.05\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.29\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.02\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.08\columnwidth}\raggedright
+0.28\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.65\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.33\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\bottomrule
+\end{longtable}
+
+\begin{longtable}[]{@{}lccccl@{}}
+\caption{\label{tab:rho-model-sel}Model selection for varying \(\rho\)
+mixture parameters}\tabularnewline
+\toprule
+\begin{minipage}[b]{0.09\columnwidth}\raggedright
+\(\eps[\rho]\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(iid\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(\pi\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering
+\(\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering
+\(\pi\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright
+Recovered \(Q_2\)\strut
+\end{minipage}\tabularnewline
+\midrule
+\endfirsthead
+\toprule
+\begin{minipage}[b]{0.09\columnwidth}\raggedright
+\(\eps[\rho]\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(iid\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering
+\(\pi\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering
+\(\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering
+\(\pi\rho\text{-}colBiSBM\)\strut
+\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright
+Recovered \(Q_2\)\strut
+\end{minipage}\tabularnewline
+\midrule
+\endhead
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.63\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.37\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.04\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.65\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.34\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.00\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.07\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.64\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.33\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.11\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.64\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.31\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.03\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.02\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.14\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.53\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.29\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.11\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.06\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.18\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.42\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.20\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.24\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.14\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.21\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.25\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.12\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.40\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.22\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.25\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.08\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.06\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.58\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.29\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.01\strut
+\end{minipage}\tabularnewline
+\begin{minipage}[t]{0.09\columnwidth}\raggedright
+0.28\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering
+0.01\strut
+\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering
+0.65\strut
+\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering
+0.32\strut
+\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright
+3.00\strut
+\end{minipage}\tabularnewline
+\bottomrule
+\end{longtable}
+
+\begin{figure}[H]
+\includegraphics{./Rcodes/simulation/img/plot_model_function_eps.png}
+\caption{Plot of preferred model in function of $\eps[\pi]$ and $\eps[\rho]$}
+\label{fig:pref_model_func_eps}
+\end{figure}
+
+On the figure \ref{fig:pref_model_func_eps} and tables
+\ref{tab:pi-model-sel} and \ref{tab:rho-model-sel}, one can see that
+there is a turning point around \(\eps[\pi] = 0.2\) (resp.
+\(\eps[\rho] = 0.2\)), before which \(iid\text{-}colBiSBM\) and
+\(\rho\text{-}colBiSBM\) (resp. \(\pi\text{-}colBiSBM\)) are selected
+most of the times and after \(0.2\) the \(\pi\text{-}colBiSBM\) (resp.
+\(\rho\text{-}colBiSBM\)) and \(\pi\rho\text{-}colBiSBM\) gets more and
+more selected, highlighting our capacity to recover the simulated
+structure.
+
+Please note that when ``Recovered \(Q_1\)(or \(Q_2\))'' is not an
+integer it's because some procedures returned a value other than 3.

Rcodes/simulation/model_selection_check.R

@@ -1,7 +1,7 @@
 require("bettermc")
 require("gtools")
 require("tictoc")
-devtools::load_all("R/")
+require("colSBM")
 
 # Network param
 nr <- 90
@@ -89,14 +89,14 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
     current_rho2 <- current_rho2[conditions[s, ]$rho2_order]
 
     netlist_generated <- list(
-        generate_bipartite_network(
+        generate_bipartite_collection(
             nr, nc, pi1, rho1,
-            alpha
+            alpha, M = 1, return_memberships = TRUE
-        ),
+        )[[1]],
-        generate_bipartite_network(
+        generate_bipartite_collection(
             nr, nc, current_pi2, current_rho2,
-            alpha
+            alpha, M = 1, return_memberships = TRUE
-        )
+        )[[1]]
     )
 
     # Extracting the incidence matrices
@@ -116,6 +116,9 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
         )
     )
 
+    fitted_bisbmpop_iid$sep_BiSBM$M <- 2
+    sep_BiSBM <- fitted_bisbmpop_iid$sep_BiSBM
+
     fitted_bisbmpop_pi <- estimate_colBiSBM(
         netlist = netlist,
         colsbm_model = "pi",
@@ -125,7 +128,8 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
             verbosity = 0,
             plot_details = 0,
             nb_cores = parallel::detectCores() - 1
-        )
+        ),
+        sep_BiSBM = sep_BiSBM
     )
 
     fitted_bisbmpop_rho <- estimate_colBiSBM(
@@ -137,7 +141,8 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
             verbosity = 0,
             plot_details = 0,
             nb_cores = parallel::detectCores() - 1
-        )
+        ),
+        sep_BiSBM = sep_BiSBM
     )
 
     fitted_bisbmpop_pirho <- estimate_colBiSBM(
@@ -149,7 +154,8 @@ results <- bettermc::mclapply(seq_len(nrow(conditions)), function(s) {
             verbosity = 0,
             plot_details = 0,
             nb_cores = parallel::detectCores() - 1
-        )
+        ), 
+        sep_BiSBM = sep_BiSBM
     )
 
     # BICLs

Rmd2Latex-fragment.R

@@ -3,7 +3,7 @@ require("knitr")
 create_latex <- function(f) {
     knitr::knit(f, "/tmp/tmp-outputfile.md")
     newname <- paste0(tools::file_path_sans_ext(f), ".tex")
-    mess <- paste("pandoc -f markdown -t latex -p -o", shQuote(newname), "/tmp/tmp-outputfile.md")
+    mess <- paste("pandoc --extract-media=./img -f markdown -t latex -p -o", shQuote(newname), "/tmp/tmp-outputfile.md")
     system(mess)
 }
 args <- commandArgs(trailingOnly = TRUE)

presentation_UMR.tex

@@ -54,6 +54,12 @@ chercheurs et des maîtres de conférences, a été pour moi très enrichissant.
 stage s'inscrit dans la construction de mon parcours professionnel en validant
 le désir que je présentais de faire de la recherche.
 
+Par ailleurs, divers projets entrepris au sein du laboratoire ont permis de
+nouer des relations amicales en dehors des heures de travail. Par exemple, le
+projet de construction d'une borne d'arcade pour le laboratoire, impulsé par
+Julien Chiquet, a été une expérience extrêmement agréable et captivante à
+laquelle prendre part.
+
 J'ai particulièrement apprécié la disponibilité de toutes les personnes de
 l'unité qui n'ont jamais hésité à se rendre disponible pour répondre à mes
 questions.

rapport.tex

@@ -20,6 +20,7 @@
 \usepackage{longtable}
 \usepackage{rotating} % For allowing to rotate figures
 \usepackage{svg} % To allow svg inclusions
+\usepackage{float} % To allow Pandoc to control figure placement
 
 %% Bibliography
 \usepackage[style=apa,citestyle=authoryear-comp]{biblatex}
@@ -64,6 +65,7 @@
 
 % Nouvelles commandes
 \newcommand{\Tau}{\mathcal{T}}
+\newcommand{\eps}[1][]{\ensuremath{\epsilon_{#1}}}
 
 % titre et auteur
 \title{Rapport de stage dans l'UMR MIA Paris-Saclay}
@@ -1058,6 +1060,7 @@ We illustrate our capacity to perform a partition of a collection for all
 colBiSBM models in \ref{sec:network-clustering-of-simulated-networks}.
 
 \chapter{Simulation studies}\label{chap:simulation-studies}
+\include{Rcodes/simulation/model_selection_analyze}
 \section{Network clustering of simulated networks}\label{sec:network-clustering-of-simulated-networks}
 
 \chapter{Applications}