fix: TSIR vs GMLM -> R to TikZ plot

AOS-accepted/plots/sim-tsir-reg-vs-gmlm.tex

@@ -0,0 +1,98 @@
+\documentclass[border=0cm]{standalone}
+
+\usepackage{tikz}
+\usepackage{pgfplots}
+\usepackage{bm}
+
+\definecolor{gmlm}{RGB}{0,0,0}
+\definecolor{tsir}{RGB}{255,50,50}
+
+\pgfplotsset{
+    compat=newest,
+    every axis/.style={
+        grid=both,
+        grid style={gray, dotted},
+        label style={font=\tiny},
+        tick label style={font=\tiny}
+    },
+    % every axis plot/.append style={
+    %     mark = *,
+    %     mark size = 1pt,
+    %     line width=0.8pt
+    % }
+}
+\tikzset{
+    legend entry/.style={
+        mark = *,
+        mark size = 1pt,
+        mark indices = {2},
+        line width=0.8pt
+    }
+}
+
+\begin{document}
+\begin{tikzpicture}[>=latex]
+
+    \begin{axis}[
+        name=p1, % ymin = -60, ymax = 60
+        width=7.5cm, height=5cm,
+        xticklabel=\empty
+    ]
+        \addplot[color = tsir] table[x = time, y = tsir.reg.beta] {tsir-vs-gmlm-1.csv};
+        \addplot[color = gmlm] table[x = time, y = gmlm.beta] {tsir-vs-gmlm-1.csv};
+    \end{axis}
+    \node[anchor = base west, yshift = 0.3em] at (p1.north west) {
+        Time
+    };
+    \node[anchor = south, xshift = -1.5em, rotate = 90] at (p1.west) {
+        $\widehat{\beta}_1$
+    };
+
+    \begin{axis}[
+        name=p2,
+        width=7.5cm, height=5cm,
+        anchor=north west, at={(p1.below south west)}, yshift=0.4em
+    ]
+        \addplot[color = tsir] table[x = time, y = tsir.reg.Gamma] {tsir-vs-gmlm-1.csv};
+        \addplot[color = gmlm] table[x = time, y = gmlm.Gamma] {tsir-vs-gmlm-1.csv};
+    \end{axis}
+    \node[anchor = south, xshift = -1.5em, rotate = 90] at (p2.west) {
+        $\widehat{\Gamma}_1$
+    };
+    \node[anchor = north, yshift = -1em] at (p2.south) {
+        Time [s]
+    };
+
+    \begin{axis}[
+        name=p3,
+        width=7.5cm, height=5cm,
+        anchor=north west, at={(p1.right of north east)}, xshift=1cm,
+        xticklabel=\empty
+    ]
+        \addplot[color = gmlm, dotted, mark = *, mark size = 1pt] table[x = sensor, y = gmlm.beta] {tsir-vs-gmlm-2.csv};
+        \addplot[color = tsir, dotted, mark = *, mark size = 1pt] table[x = sensor, y = tsir.reg.beta] {tsir-vs-gmlm-2.csv};
+    \end{axis}
+    \node[anchor = base west, yshift = 0.3em] at (p3.north west) {
+        Sensors
+    };
+    \node[anchor = south, xshift = -1em, rotate = 90] at (p3.west) {
+        $\widehat{\beta}_2$
+    };
+
+    \begin{axis}[
+        name=p4,
+        width=7.5cm, height=5cm,
+        anchor=north west, at={(p3.below south west)}, yshift=0.4em
+    ]
+        \addplot[color = gmlm, dotted, mark = *, mark size = 1pt] table[x = sensor, y = gmlm.Gamma] {tsir-vs-gmlm-2.csv};
+        \addplot[color = tsir, dotted, mark = *, mark size = 1pt] table[x = sensor, y = tsir.reg.Gamma] {tsir-vs-gmlm-2.csv};
+    \end{axis}
+    \node[anchor = south, xshift = -1em, rotate = 90] at (p4.west) {
+        $\widehat{\Gamma}_2$
+    };
+    \node[anchor = north, yshift = -1em] at (p4.south) {
+        Sensor Index
+    };
+
+\end{tikzpicture}
+\end{document}

AOS-accepted/plots/sim-tsir-vs-gmlm.tex

@@ -0,0 +1,98 @@
+\documentclass[border=0cm]{standalone}
+
+\usepackage{tikz}
+\usepackage{pgfplots}
+\usepackage{bm}
+
+\definecolor{gmlm}{RGB}{0,0,0}
+\definecolor{tsir}{RGB}{255,50,50}
+
+\pgfplotsset{
+    compat=newest,
+    every axis/.style={
+        grid=both,
+        grid style={gray, dotted},
+        label style={font=\tiny},
+        tick label style={font=\tiny}
+    },
+    % every axis plot/.append style={
+    %     mark = *,
+    %     mark size = 1pt,
+    %     line width=0.8pt
+    % }
+}
+\tikzset{
+    legend entry/.style={
+        mark = *,
+        mark size = 1pt,
+        mark indices = {2},
+        line width=0.8pt
+    }
+}
+
+\begin{document}
+\begin{tikzpicture}[>=latex]
+
+    \begin{axis}[
+        name=p1, % ymin = -60, ymax = 60
+        width=7.5cm, height=5cm,
+        xticklabel=\empty
+    ]
+        \addplot[color = tsir] table[x = time, y = tsir.beta] {tsir-vs-gmlm-1.csv};
+        \addplot[color = gmlm] table[x = time, y = gmlm.beta] {tsir-vs-gmlm-1.csv};
+    \end{axis}
+    \node[anchor = base west, yshift = 0.3em] at (p1.north west) {
+        Time
+    };
+    \node[anchor = south, xshift = -1.5em, rotate = 90] at (p1.west) {
+        $\widehat{\beta}_1$
+    };
+
+    \begin{axis}[
+        name=p2,
+        width=7.5cm, height=5cm,
+        anchor=north west, at={(p1.below south west)}, yshift=0.4em
+    ]
+        \addplot[color = tsir] table[x = time, y = tsir.Gamma] {tsir-vs-gmlm-1.csv};
+        \addplot[color = gmlm] table[x = time, y = gmlm.Gamma] {tsir-vs-gmlm-1.csv};
+    \end{axis}
+    \node[anchor = south, xshift = -1.5em, rotate = 90] at (p2.west) {
+        $\widehat{\Gamma}_1$
+    };
+    \node[anchor = north, yshift = -1em] at (p2.south) {
+        Time [s]
+    };
+
+    \begin{axis}[
+        name=p3,
+        width=7.5cm, height=5cm,
+        anchor=north west, at={(p1.right of north east)}, xshift=1cm,
+        xticklabel=\empty
+    ]
+        \addplot[color = gmlm, dotted, mark = *, mark size = 1pt] table[x = sensor, y = gmlm.beta] {tsir-vs-gmlm-2.csv};
+        \addplot[color = tsir, dotted, mark = *, mark size = 1pt] table[x = sensor, y = tsir.beta] {tsir-vs-gmlm-2.csv};
+    \end{axis}
+    \node[anchor = base west, yshift = 0.3em] at (p3.north west) {
+        Sensors
+    };
+    \node[anchor = south, xshift = -1em, rotate = 90] at (p3.west) {
+        $\widehat{\beta}_2$
+    };
+
+    \begin{axis}[
+        name=p4,
+        width=7.5cm, height=5cm,
+        anchor=north west, at={(p3.below south west)}, yshift=0.4em
+    ]
+        \addplot[color = gmlm, dotted, mark = *, mark size = 1pt] table[x = sensor, y = gmlm.Gamma] {tsir-vs-gmlm-2.csv};
+        \addplot[color = tsir, dotted, mark = *, mark size = 1pt] table[x = sensor, y = tsir.Gamma] {tsir-vs-gmlm-2.csv};
+    \end{axis}
+    \node[anchor = south, xshift = -1em, rotate = 90] at (p4.west) {
+        $\widehat{\Gamma}_2$
+    };
+    \node[anchor = north, yshift = -1em] at (p4.south) {
+        Sensor Index
+    };
+
+\end{tikzpicture}
+\end{document}

AOS-accepted/supplement.tex

@@ -849,7 +849,7 @@ TSIR suffers substantial loss in predictive accuracy in the full 2D EEG data (se
 \begin{figure}
     \centering
     \caption{\label{fig:TSIRvsGMLM}TSIR in red vs. GMLM in black}
-    \includegraphics[width = \textwidth]{plots/tsir_eeg_2d_bad_perf.pdf}
+    \includegraphics{plots/sim-tsir-vs-gmlm.pdf}
 \end{figure}
 
 To observe this in practice, we took the full 2D EEG data (only the S1 stimulus) and computed $\widehat{\mat{\Gamma}}^{\mathrm{TSIR}}_1, \widehat{\mat{\Gamma}}^{\mathrm{TSIR}}_2$, $\widehat{\mat{\Sigma}}^{\mathrm{TSIR}}_1, \widehat{\mat{\Sigma}}^{\mathrm{TSIR}}_2$ from which we computed the reductions $\widehat{\mat{\beta}}^{\mathrm{TSIR}}_1$ and $\widehat{\mat{\beta}}^{\mathrm{TSIR}}_2$. For comparison, we used GMLM to estimate the reduction matrices $\widehat{\mat{\beta}}^{\mathrm{GMLM}}_1$, $\widehat{\mat{\beta}}^{\mathrm{GMLM}}_2$ and the scatter matrices $\widehat{\mat{\Omega}}^{\mathrm{GMLM}}_1$, $\widehat{\mat{\Omega}}^{\mathrm{GMLM}}_2$. We also computed the GMLM analog of the standardized reductions $\widehat{\mat{\Gamma}}^{\mathrm{GMLM}}_1 = (\widehat{\mat{\Omega}}^{\mathrm{GMLM}}_1)^{-1}\widehat{\mat{\beta}}_1^{\mathrm{GMLM}}$ and $\widehat{\mat{\Gamma}}^{\mathrm{GMLM}}_2 = (\widehat{\mat{\Omega}}^{\mathrm{GMLM}}_2)^{-1}\widehat{\mat{\beta}}_2^{\mathrm{GMLM}}$. We next plotted in \cref{fig:TSIRvsGMLM} the estimated reductions $\widehat{\mat{\beta}}^{\mathrm{GMLM}}_1$, $\widehat{\mat{\beta}}^{\mathrm{GMLM}}_2$, $\widehat{\mat{\Gamma}}^{\mathrm{GMLM}}_1$, $\widehat{\mat{\Gamma}}^{\mathrm{GMLM}}_2$ in black and  $\widehat{\mat{\beta}}^{\mathrm{TSIR}}_1$, $\widehat{\mat{\beta}}^{\mathrm{TSIR}}_2$, $\widehat{\mat{\Gamma}}^{\mathrm{TSIR}}_1$, $\widehat{\mat{\Gamma}}^{\mathrm{TSIR}}_2$ in red (with appropriate scaling). Since the estimates of the reductions $\widehat{\mat{\beta}}_j$'s are completely different between GMLM and TSIR but the estimates of the standardized reductions $\mat{\Gamma}_j$'s agree to a high degree, we conclude that the loss of estimation accuracy happens in the final calculations that %That is in computing the estimates of the reductions $\mat{\beta}_j = \mat{\Sigma}_j^{-1}\mat{\Gamma}$, which 
@@ -858,9 +858,9 @@ involve the inversion of the severely ill-conditioned mode-wise estimated covari
 To check whether our conjecture holds, we introduced a regularization term similar to the regularization employed in GMLM to the mode-wise sample covariances $\mat{\Sigma}_j$ in TSIR. As can be seen in \cref{fig:TSIRregvsGMLM}, this produced roughly the same reductions $\widehat{\mat{\beta}}_j$ as well as the $\widehat{\mat{\Gamma}}_j$.
 
 \begin{figure}
-\caption{TSIR (reg) in red vs. GMLM in black}
+    \centering
-\label{fig:TSIRregvsGMLM}
+    \caption{\label{fig:TSIRregvsGMLM}TSIR (reg) in red vs. GMLM in black}
-    \includegraphics[width = \textwidth]{plots/tsir_regularized.pdf}
+    \includegraphics{plots/sim-tsir-reg-vs-gmlm.pdf}
 \end{figure}
 
 To further study the relationship between GMLM and TSIR, we first  consider a setting in which GMLM and TSIR are theoretically equivalent. We assume that $Y$ is categorical, $\ten{X}\mid Y = y$ is multi-linear normal and the reduction $\ten{R}(\ten{X})$ is one-dimensional. Additionally, $\mat{\Omega}_j$ is assumed to be positive definite but \emph{not} further constrained. Under these assumptions, GMLM and TSIR are equivalent since %Even though GMLM minimizes the log-likelihood and TSIR minimizes a squared error loss, 
@@ -1043,40 +1043,6 @@ The results of our analysis above agree with the configuration of the chess boar
 
 \end{appendix}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Support information, if any,             %%
-%% should be provided in the                %%
-%% Acknowledgements section.                %%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\begin{acks}[Acknowledgments]
-%The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.
-%\end{acks}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Funding information, if any,             %%
-%% should be provided in the                %%
-%% funding section.                         %%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \begin{funding}
-% Both authors were partially supported by the Vienna Science and Technology Fund (WWTF) [10.47379/ICT19018] and the Austrian Science Fund (FWF) research
-% project P 30690-N35.
-% \end{funding}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% Supplementary Material, including data   %%
-%% sets and code, should be provided in     %%
-%% {supplement} environment with title      %%
-%% and short description. It cannot be      %%
-%% available exclusively as external link.  %%
-%% All Supplementary Material must be       %%
-%% available to the reader on Project       %%
-%% Euclid with the published article.       %%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \begin{supplement}
-% \stitle{???}
-% \sdescription{???.}
-% \end{supplement}
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%                  The Bibliography                       %%
 %%                                                         %%

sim/sim_efficiency.R

@@ -101,11 +101,11 @@ with(merge(
     suffixes = c("", ".sd"),
     all = FALSE
 ), {
-    plot(range(pj), 0:1, type = "n",
+    par(mar = c(4.1, 4.1, 0.1, 0.1))
-        main = "Simulation -- Efficiency Gain",
+    plot(range(pj), 0:1, type = "n", main = "", xlab = "", ylab = "", xaxt = "n", bty = "n")
-        xlab = expression(tilde(p)),
+    axis(1, at = sort(unique(pj)))
-        ylab = expression(d(B, hat(B)))
+    title(ylab = expression(d(B, hat(B))), line = 2.5)
-    )
+    title(xlab = expression(tilde(p)), line = 2.5)
     for (sz in sort(unique(sample.size))) {
         i <- order(pj)[(sample.size == sz)[order(pj)]]
         i <- i[!(is.na(lm[i]) | is.na(lm.sd[i]))]
@@ -132,4 +132,17 @@ with(merge(
         lines(pj[i], mani[i], type = "b", pch = 16, col = "#006e18", lty = lty.idx, lwd = 2)
         lty.idx <- lty.idx + 1L
     }
+    legend(23, 0.8,
+        legend = c(
+            "Linear Model of Y | vec(X)",
+            "GMLM of vec(X) | Y",
+            "GMLM of X | Y",
+            "GMLM of X | Y + constraint"
+        ),
+        col = c("#cf7d03", "#b30303", "#002d8d", "#006e18"),
+        fill = paste0(c("#cf7d03", "#b30303", "#002d8d", "#006e18"), "50"),
+        lwd = 2, lty = 1, bty = "n"
+    )
 })
+
+dev.copy2pdf(file = "sim_efficiency.pdf", width = 12, height = 6)

tensorPredictors/R/gmlm_tensor_normal.R

@@ -112,7 +112,6 @@ gmlm_tensor_normal <- function(X, F, sample.axis = length(dim(X)),
                 min_max <- range(eigen(Sigmas[[j]], TRUE, TRUE)$values)
                 # The condition is approximately `kappa(Sigmas[[j]]) > reg.threshold`
                 if (min_max[2] > reg.threshold * min_max[1]) {
-                    cat(sprintf("\033[2mReg (%d): cond(Sigma_%d) = %f\033[0m\n", iter, j, min_max[2] / min_max[1]))
                     diag(Sigmas[[j]]) <- diag(Sigmas[[j]]) + reg.factor * min_max[2]
                 }
             }