In Marie-PerrotDockes/VariSel: Perform variable selection for different model types
knitr::opts_chunk$set(dev = "cairo_pdf", message = 'hide', warning = FALSE, cache = TRUE)
library(VariSel)
library(tidyverse)
library(extrafont)
library(ggsci)
require(tidymodels)
require(furrr)
require(rlang)
require(patchwork)
loadfonts()
theme_set(theme_bw() + theme_bw() +
theme(strip.background = element_rect(fill = "white"),
text = element_text(face="bold", family="LM Roman 10", size=16) ))
scale_colour_discrete <- function(...)scale_color_uchicago()
scale_fill_discrete <- function(...)scale_fill_uchicago()
A simple vision of the immune system :
\framesubtitle{Or how Astérix and Obélix can kick-off the Romans}
```{tikz, tikz-ex2, fig.cap = "DC Th dialogue", fig.ext = 'pdf', echo =FALSE}
\definecolor{vert}{RGB}{ 109,205,89}
\definecolor{bleu}{RGB}{93,139,172}
\definecolor{marron}{RGB}{172,126,93}
\definecolor{marronfonce}{RGB}{120,88,65}
\definecolor{i1}{RGB}{122,181,168}
\definecolor{i2}{RGB}{122,165,181}
\definecolor{i3}{RGB}{122,181,139}
\definecolor{dc}{RGB}{173,220,153}
\definecolor{dc2}{RGB}{123, 87, 229}
\definecolor{lt}{RGB}{153,173,220}
\definecolor{pert}{RGB}{220,153,173}
\tikzstyle{line} = [draw, -latex, color = marron, line width=1pt]
\tikzstyle{block} = [rectangle, draw, fill=vert!20, draw= vert!80, text = marronfonce,
text width=3.5em, text centered, rounded corners, minimum height=2em,line width=1pt]
\tikzstyle{block3} = [rectangle, draw, fill=vert!10, draw= vert!90, text = marronfonce,
text width=3em, text centered, rounded corners, minimum height=1.1em,line width=0.7pt]
\tikzstyle{inp} = [rectangle, draw, text = marronfonce,
text width=4.4em, text centered, rounded corners, minimum height=1em,line width=1pt]
\begin{tikzpicture}[node distance = 2cm, auto]
% nodes
\node(DC){\includegraphics[width= 0.22\textwidth]{cellule_dend}};
\nodeleft of = DC, node distance = 3 cm, color = pert{\includegraphics[width= 0.17\textwidth]{romain.png}};
\noderight of = DC, node distance = 4 cm{\includegraphics[width= 0.17\textwidth]{ast_ob}};
\noderight of = TL, node distance = 3 cm{\includegraphics[width= 0.17\textwidth]{paf-asterix}};
\node[below of = DC, node distance =2.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{ Dendritic cells};
\node[below of = Pert, node distance =2.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbators};
\node[below of = TL, node distance =2.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ \;\;\;\; Th \;\; \;\; lymphocytes};
\node[above of = TL, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{ Th responses};
\node[above of =DC, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{ DC signals};
\path [line,color = dc] ([yshift=-0.8 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.8 cm]TL.west);
\path [line,color = dc] ([yshift=-0.4 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.4 cm]TL.west);
\path [line,color = dc] ([xshift=- 0.1 cm]DC.east) -- (TL.west);
\path [line,color = dc] ([yshift=0.4 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.4 cm]TL.west);
\path [line,color = dc] ([yshift=0.8 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.8 cm]TL.west);
\path line, color = gray -- (DC.west);
\path line,color = lt -- ([yshift = -0.7cm]L.west);
\path line,color = lt -- ([yshift = -0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm]TL.east) -- (L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.35cm]TL.east) -- ([yshift = 0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.7cm]TL.east) -- ([yshift = 0.7cm]L.west);
\end{tikzpicture}
\tiny{ Grandclaudon, M., Perrot-Dockès, M, Trichot, C et al. \textit{ A Quantitative Multivariate Model of Human Dendritic Cell-T Helper Cell Communication (March 15, 2019)}. Available at \url{http://dx.doi.org/10.2139/ssrn.3353217} }
<!-- \node[below of = DC, node distance =3.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{Sentinnelles}; -->
<!-- \node[below of = Pert, node distance =3.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbation}; -->
<!-- \node[below of = TL, node distance =3.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ Warriors}; -->
<!-- \node[below of = TL, node distance =3.2 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{Actions}; -->
<!-- \node[above of =DC, node distance =3.2 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{Warnings}; -->
# Experimental set up :
\framesubtitle{Ordralphabetix and Cétautomatix are two!}
```{tikz, tikz-ex2b, fig.cap = "DC Th dialogue", fig.ext = 'pdf', echo =FALSE, fig.num=1}
\definecolor{vert}{RGB}{ 109,205,89}
\definecolor{bleu}{RGB}{93,139,172}
\definecolor{marron}{RGB}{172,126,93}
\definecolor{marronfonce}{RGB}{120,88,65}
\definecolor{i1}{RGB}{122,181,168}
\definecolor{i2}{RGB}{122,165,181}
\definecolor{i3}{RGB}{122,181,139}
\definecolor{dc}{RGB}{173,220,153}
\definecolor{dc2}{RGB}{123, 87, 229}
\definecolor{lt}{RGB}{153,173,220}
\definecolor{pert}{RGB}{220,153,173}
\tikzstyle{line} = [draw, -latex, color = marron, line width=1pt]
\tikzstyle{block} = [rectangle, draw, fill=vert!20, draw= vert!80, text = marronfonce,
text width=3.5em, text centered, rounded corners, minimum height=2em,line width=1pt]
\tikzstyle{block3} = [rectangle, draw, fill=vert!10, draw= vert!90, text = marronfonce,
text width=3em, text centered, rounded corners, minimum height=1.1em,line width=0.7pt]
\tikzstyle{inp} = [rectangle, draw, text = marronfonce,
text width=4.4em, text centered, rounded corners, minimum height=1em,line width=1pt]
\begin{tikzpicture}[node distance = 2cm, auto]
\node(DC){\includegraphics[width= 0.19\textwidth]{cellule_dend1}};
\node[left of = DC, node distance = 3 cm, color = pert](Pert){\includegraphics[width= 0.17\textwidth]{romain.png}};
\node[right of = DC, node distance = 4 cm](TL){\includegraphics[width= 0.17\textwidth]{ast_ob}};
\node[right of = TL, node distance = 3 cm](L){\includegraphics[width= 0.17\textwidth]{paf-asterix}};
\node[below of = DC, node distance =2.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{ \textbf{Ordra}};
\node[below of = Pert, node distance =2.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbators};
\node[below of = TL, node distance =2.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ \;\;\;\; Th \;\; \;\; lymphocytes};
\node[above of = TL, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{ Th responses};
\node[above of =DC, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{ DC signals};
\path [line,color = dc] ([yshift=-0.8 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.8 cm]TL.west);
\path [line,color = dc] ([yshift=-0.4 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.4 cm]TL.west);
\path [line,color = dc] ([xshift=- 0.1 cm]DC.east) -- (TL.west);
\path [line,color = dc] ([yshift=0.4 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.4 cm]TL.west);
\path [line,color = dc] ([yshift=0.8 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.8 cm]TL.west);
\path [line, color = gray](Pert) -- (DC.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.7cm]TL.east) -- ([yshift = -0.7cm]L.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.35cm]TL.east) -- ([yshift = -0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm]TL.east) -- (L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.35cm]TL.east) -- ([yshift = 0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.7cm]TL.east) -- ([yshift = 0.7cm]L.west);
\end{tikzpicture}
\begin{tikzpicture}[node distance = 2cm, auto]
\node(DC){\includegraphics[width= 0.19\textwidth]{cellule_dend2}};
\node[left of = DC, node distance = 3 cm, color = pert](Pert){\includegraphics[width= 0.17\textwidth]{romain.png}};
\node[right of = DC, node distance = 4 cm](TL){\includegraphics[width= 0.17\textwidth]{ast_ob}};
\node[right of = TL, node distance = 3 cm](L){\includegraphics[width= 0.17\textwidth]{paf-asterix}};
\node[below of = DC, node distance =2.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{ \textbf{Cetau}};
\node[below of = Pert, node distance =2.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbators};
\node[below of = TL, node distance =2.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ \;\;\;\; Th \;\; \;\; lymphocytes};
\node[above of = TL, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{ Th responses};
\node[above of =DC, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{ DC signals};
\path [line,color = dc] ([yshift=-0.8 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.8 cm]TL.west);
\path [line,color = dc] ([yshift=-0.4 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.4 cm]TL.west);
\path [line,color = dc] ([xshift=- 0.1 cm]DC.east) -- (TL.west);
\path [line,color = dc] ([yshift=0.4 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.4 cm]TL.west);
\path [line,color = dc] ([yshift=0.8 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.8 cm]TL.west);
\path [line, color = gray](Pert) -- (DC.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.7cm]TL.east) -- ([yshift = -0.7cm]L.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.35cm]TL.east) -- ([yshift = -0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm]TL.east) -- (L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.35cm]TL.east) -- ([yshift = 0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.7cm]TL.east) -- ([yshift = 0.7cm]L.west);
\end{tikzpicture}
Statistical modelling
\framesubtitle{Understand the Gallic language}
\begin{itemize}
\item \textbf{Dataset description:}
\begin{itemize}
\item \textcolor{dc!70!black}{$\boldsymbol{X}$}: $n\times p$ design matrix : the DC signals \includegraphics[width =0.12\textwidth]{cellule_dend}
\item \textcolor{lt!70!black}{$\boldsymbol{Y}$}: $n\times q$ response matrix : the Th responses \includegraphics[width =0.12\textwidth]{ast_ob}
\end{itemize}
\item \textbf{Question:} Which variables influence the responses?
\item \textbf{Approach:}
\begin{itemize}
\item Variable selection in
$$
\boldsymbol{Y}=\boldsymbol{XB}+\boldsymbol{E},
$$
where \begin{itemize}
\item $\boldsymbol{B}$: $p\times q$ \textbf{sparse} coefficients matrix
\item $\boldsymbol{E}$: $n\times q$ error matrix with $$\forall i\in{1,\dots, n}, \; (E_{i,1},\dots,E_{i,q})\stackrel{iid}{\sim}~\mathcal{N}(0,\boldsymbol{\Sigma}_q)$$
\end{itemize}
\item We take the dependence into account by estimating $\boldsymbol{\Sigma}_q$.
\end{itemize}
\end{itemize}
Statistical modelling
\framesubtitle{Understand the Gallic language}
\begin{itemize}
\item \textbf{Dataset description:}
\begin{itemize}
\item \textcolor{dc!70!black}{$\boldsymbol{X}$}: $n\times p$ design matrix : the DC signals \includegraphics[width =0.12\textwidth]{cellule_dend}
\item \textcolor{lt!70!black}{$\boldsymbol{Y}$}: $n\times q$ response matrix : the Th responses \includegraphics[width =0.12\textwidth]{ast_ob}
\end{itemize}
\item \textbf{Question:} Which variables influence the responses?
\item \textbf{Approach:}
\begin{itemize}
\item Variable selection in
$$
\boldsymbol{Y}=\boldsymbol{XB}+\boldsymbol{E},
$$
where \begin{itemize}
\item $\boldsymbol{B}$: $p\times q$ \textbf{sparse} coefficients matrix
\item $\boldsymbol{E}$: $n\times q$ error matrix with $$\forall i\in{1,\dots, n}, \; (E_{i,1},\dots,E_{i,q})\stackrel{iid}{\sim}~\mathcal{N}(0,\boldsymbol{\Sigma}_q)$$
\end{itemize}
\item We take the dependence into account by estimating $\boldsymbol{\Sigma}_q$.
\end{itemize}
\end{itemize}
Differents penalties : for different point of view
\begin{itemize}
\item \textcolor{outcome}{\textbf{Lasso}} : \textit{select variables without taking into account potential links.}
\begin{equation} \label{grouplasso}
\widehat{b}L = \Am{b} \left\lbrace||y-\bX b||_2^2 + \lambda ||b||_1 \right\rbrace,
\end{equation}
\item \textcolor{outcome}{\textbf{Group-Lasso}} : \textit{select a group of variables.}
\begin{equation} \label{grouplasso}
\widehat{b}G = \Am{b_1, \dots, b_L} \left\lbrace||y-\sum_{1 \leq \ell \leq L}\bX_{(\ell)} b_{(\ell)}||2^2 + \lambda\sum{1 \leq \ell \leq L}\sqrt{p_\ell} ||b_\ell||_2\right\rbrace,
\end{equation}
\item \textcolor{outcome}{\textbf{Fused-Lasso}} : \textit{influence a group of variables to have the same coefficient.}
\begin{equation}\label{fuselasso}
\widehat{b}F =\Am{b}||y-\bX b||2^2 + \left\lbrace\lambda_1\sum{(i,j) \in \mathcal{G}} |b_i - b_j|+ \lambda_2 ||b||_1\right\rbrace,
\end{equation}
\end{itemize}
Differents penalties : for different point of view
\begin{itemize}
\item \textcolor{outcome}{\textbf{Lasso}} : \textit{select variables without taking into account potential links.}
\begin{equation} \label{grouplasso}
\widehat{b}L = \Am{b} \left\lbrace||y-\bX b||_2^2 + \lambda ||b||_1 \right\rbrace,
\end{equation}
\item \textcolor{outcome}{\textbf{Group-Lasso}} : \textit{select a group of variables.}
\begin{equation} \label{grouplasso}
\widehat{b}G = \Am{b_1, \dots, b_L} \left\lbrace||y-\sum_{1 \leq \ell \leq L}\bX_{(\ell)} b_{(\ell)}||2^2 + \lambda\sum{1 \leq \ell \leq L}\sqrt{p_\ell} ||b_\ell||_2\right\rbrace,
\end{equation}
\item \textcolor{outcome}{\textbf{Fused-Lasso}} : \textit{influence a group of variables to have the same coefficient.}
\begin{equation}\label{fuselasso}
\widehat{b}F =\Am{b}||y-\bX b||2^2 + \left\lbrace\lambda_1\sum{(i,j) \in \mathcal{G}} |b_i - b_j|+ \lambda_2 ||b||_1\right\rbrace,
\end{equation}
\end{itemize}
VariSel for one model type
set.seed(4)
load("raw_data.RData")
load("data_Tmod_sspdc.RData")
X <- Xbrt %>% as.data.frame() %>%
mutate(pert_dc= pert_dc, dc= dc) %>%
group_by(pert_dc, dc) %>%
summarize_if(is.numeric, mean) %>% ungroup() %>%
as.data.frame()
#
# Y <- Y_bxcx %>% as.data.frame() %>%
# mutate(pert_dc= pert_dc, dc= dc) %>%
# group_by(pert_dc, dc) %>%
# summarize_if(is.numeric, mean) %>%
# ungroup() %>% as.data.frame()
DC_sign <- X_bxcx[,c(36,37, 40)]
T_resp <- Y_bxcx[,c(2,10)]
# DC_sign <- X %>% select(-dc,-pert_dc) %>%
# as.matrix() %>% scale()
#
# T_resp <- Y %>% select(IFNg, IL3) %>%
# as.matrix() %>% scale()
# dc <- Y %>% pull(dc)
dc <- as.character(dc)
dc[dc == "bDC "] <- "Ordra"
dc[dc == "MoDC"] <- "Cetau"
mod <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="group_multi_regr")
X <- model.matrix(~DC_sign:dc -1)
mod <- train_VariSel( Y = T_resp,
X = X,
sepx = ":",
type ="group_multi_regr")
VariSel for one model type
mod <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="group_multi_regr")
X <- model.matrix(~DC_sign:dc -1)
mod <- train_VariSel( Y = T_resp,
X = X,
sepx = ":",
type ="group_multi_regr")
VariSel for one model type : Outcome
plot(mod)
Different modelling strategy
col <- pal_uchicago()(6)
mod <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="group_multi_regr")
m2 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="group_multi_both")
m3 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="fused_multi_both")
m4 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="fused_multi_regr")
m5 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="lasso_multi")
compar_path(mods = list(mod,m2,m3,m4))
Different modelling strategy
col <- pal_uchicago()(6)
mod <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="group_multi_regr")
m2 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="group_multi_both")
m3 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="fused_multi_both")
m4 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="fused_multi_regr")
m5 <- train_VariSel( Y = T_resp,
regressors = DC_sign,
group = dc,
type ="lasso_multi")
compar_path(mods = list(mod,m2,m3,m4))
Models selection
ct <- compar_type( Y = T_resp, regressors = DC_sign,
group = dc,
types = c("group_multi_regr" , "group_multi_both" ,
"fused_multi_regr", "fused_multi_both",
"lasso_multi" ), times = 10)
plot_ct(ct) + labs(title ='')
Best models representation
bm <- get_best_models(ct,criterion = "MSE_boot")
plot_md(bm)
Conclusion
This is an R package to perform variable selection in multivariate linear models.
It can
\begin{itemize}
\item Associate explicative variables
\item Associate responses
\item Associate both explicative variables and responses
\item Let all variables 'free', without assoiciating any of them
\end{itemize}
Come and see the vignette!
\textcolor{outcome}{https://github.com/Marie-PerrotDockes/VariSel}
Marie-PerrotDockes/VariSel documentation built on May 7, 2020, 1:09 a.m.
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knitr::opts_chunk$set(dev = "cairo_pdf", message = 'hide', warning = FALSE, cache = TRUE) library(VariSel) library(tidyverse) library(extrafont) library(ggsci) require(tidymodels) require(furrr) require(rlang) require(patchwork) loadfonts() theme_set(theme_bw() + theme_bw() + theme(strip.background = element_rect(fill = "white"), text = element_text(face="bold", family="LM Roman 10", size=16) )) scale_colour_discrete <- function(...)scale_color_uchicago() scale_fill_discrete <- function(...)scale_fill_uchicago()
A simple vision of the immune system :
\framesubtitle{Or how Astérix and Obélix can kick-off the Romans}
```{tikz, tikz-ex2, fig.cap = "DC Th dialogue", fig.ext = 'pdf', echo =FALSE} \definecolor{vert}{RGB}{ 109,205,89} \definecolor{bleu}{RGB}{93,139,172} \definecolor{marron}{RGB}{172,126,93} \definecolor{marronfonce}{RGB}{120,88,65} \definecolor{i1}{RGB}{122,181,168} \definecolor{i2}{RGB}{122,165,181} \definecolor{i3}{RGB}{122,181,139} \definecolor{dc}{RGB}{173,220,153} \definecolor{dc2}{RGB}{123, 87, 229} \definecolor{lt}{RGB}{153,173,220} \definecolor{pert}{RGB}{220,153,173} \tikzstyle{line} = [draw, -latex, color = marron, line width=1pt] \tikzstyle{block} = [rectangle, draw, fill=vert!20, draw= vert!80, text = marronfonce, text width=3.5em, text centered, rounded corners, minimum height=2em,line width=1pt] \tikzstyle{block3} = [rectangle, draw, fill=vert!10, draw= vert!90, text = marronfonce, text width=3em, text centered, rounded corners, minimum height=1.1em,line width=0.7pt] \tikzstyle{inp} = [rectangle, draw, text = marronfonce, text width=4.4em, text centered, rounded corners, minimum height=1em,line width=1pt] \begin{tikzpicture}[node distance = 2cm, auto] % nodes \node(DC){\includegraphics[width= 0.22\textwidth]{cellule_dend}}; \nodeleft of = DC, node distance = 3 cm, color = pert{\includegraphics[width= 0.17\textwidth]{romain.png}}; \noderight of = DC, node distance = 4 cm{\includegraphics[width= 0.17\textwidth]{ast_ob}}; \noderight of = TL, node distance = 3 cm{\includegraphics[width= 0.17\textwidth]{paf-asterix}}; \node[below of = DC, node distance =2.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{ Dendritic cells}; \node[below of = Pert, node distance =2.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbators}; \node[below of = TL, node distance =2.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ \;\;\;\; Th \;\; \;\; lymphocytes}; \node[above of = TL, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{ Th responses}; \node[above of =DC, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{ DC signals};
\path [line,color = dc] ([yshift=-0.8 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.8 cm]TL.west);
\path [line,color = dc] ([yshift=-0.4 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.4 cm]TL.west);
\path [line,color = dc] ([xshift=- 0.1 cm]DC.east) -- (TL.west);
\path [line,color = dc] ([yshift=0.4 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.4 cm]TL.west);
\path [line,color = dc] ([yshift=0.8 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.8 cm]TL.west);
\path line, color = gray -- (DC.west); \path line,color = lt -- ([yshift = -0.7cm]L.west); \path line,color = lt -- ([yshift = -0.35cm]L.west); \path [line,color = lt] ([xshift= -0.4cm]TL.east) -- (L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.35cm]TL.east) -- ([yshift = 0.35cm]L.west); \path [line,color = lt] ([xshift= -0.4cm, yshift = 0.7cm]TL.east) -- ([yshift = 0.7cm]L.west); \end{tikzpicture}
\tiny{ Grandclaudon, M., Perrot-Dockès, M, Trichot, C et al. \textit{ A Quantitative Multivariate Model of Human Dendritic Cell-T Helper Cell Communication (March 15, 2019)}. Available at \url{http://dx.doi.org/10.2139/ssrn.3353217} }
<!-- \node[below of = DC, node distance =3.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{Sentinnelles}; -->
<!-- \node[below of = Pert, node distance =3.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbation}; -->
<!-- \node[below of = TL, node distance =3.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ Warriors}; -->
<!-- \node[below of = TL, node distance =3.2 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{Actions}; -->
<!-- \node[above of =DC, node distance =3.2 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{Warnings}; -->
# Experimental set up :
\framesubtitle{Ordralphabetix and Cétautomatix are two!}
```{tikz, tikz-ex2b, fig.cap = "DC Th dialogue", fig.ext = 'pdf', echo =FALSE, fig.num=1}
\definecolor{vert}{RGB}{ 109,205,89}
\definecolor{bleu}{RGB}{93,139,172}
\definecolor{marron}{RGB}{172,126,93}
\definecolor{marronfonce}{RGB}{120,88,65}
\definecolor{i1}{RGB}{122,181,168}
\definecolor{i2}{RGB}{122,165,181}
\definecolor{i3}{RGB}{122,181,139}
\definecolor{dc}{RGB}{173,220,153}
\definecolor{dc2}{RGB}{123, 87, 229}
\definecolor{lt}{RGB}{153,173,220}
\definecolor{pert}{RGB}{220,153,173}
\tikzstyle{line} = [draw, -latex, color = marron, line width=1pt]
\tikzstyle{block} = [rectangle, draw, fill=vert!20, draw= vert!80, text = marronfonce,
text width=3.5em, text centered, rounded corners, minimum height=2em,line width=1pt]
\tikzstyle{block3} = [rectangle, draw, fill=vert!10, draw= vert!90, text = marronfonce,
text width=3em, text centered, rounded corners, minimum height=1.1em,line width=0.7pt]
\tikzstyle{inp} = [rectangle, draw, text = marronfonce,
text width=4.4em, text centered, rounded corners, minimum height=1em,line width=1pt]
\begin{tikzpicture}[node distance = 2cm, auto]
\node(DC){\includegraphics[width= 0.19\textwidth]{cellule_dend1}};
\node[left of = DC, node distance = 3 cm, color = pert](Pert){\includegraphics[width= 0.17\textwidth]{romain.png}};
\node[right of = DC, node distance = 4 cm](TL){\includegraphics[width= 0.17\textwidth]{ast_ob}};
\node[right of = TL, node distance = 3 cm](L){\includegraphics[width= 0.17\textwidth]{paf-asterix}};
\node[below of = DC, node distance =2.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{ \textbf{Ordra}};
\node[below of = Pert, node distance =2.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbators};
\node[below of = TL, node distance =2.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ \;\;\;\; Th \;\; \;\; lymphocytes};
\node[above of = TL, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{ Th responses};
\node[above of =DC, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{ DC signals};
\path [line,color = dc] ([yshift=-0.8 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.8 cm]TL.west);
\path [line,color = dc] ([yshift=-0.4 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.4 cm]TL.west);
\path [line,color = dc] ([xshift=- 0.1 cm]DC.east) -- (TL.west);
\path [line,color = dc] ([yshift=0.4 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.4 cm]TL.west);
\path [line,color = dc] ([yshift=0.8 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.8 cm]TL.west);
\path [line, color = gray](Pert) -- (DC.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.7cm]TL.east) -- ([yshift = -0.7cm]L.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.35cm]TL.east) -- ([yshift = -0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm]TL.east) -- (L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.35cm]TL.east) -- ([yshift = 0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.7cm]TL.east) -- ([yshift = 0.7cm]L.west);
\end{tikzpicture}
\begin{tikzpicture}[node distance = 2cm, auto]
\node(DC){\includegraphics[width= 0.19\textwidth]{cellule_dend2}};
\node[left of = DC, node distance = 3 cm, color = pert](Pert){\includegraphics[width= 0.17\textwidth]{romain.png}};
\node[right of = DC, node distance = 4 cm](TL){\includegraphics[width= 0.17\textwidth]{ast_ob}};
\node[right of = TL, node distance = 3 cm](L){\includegraphics[width= 0.17\textwidth]{paf-asterix}};
\node[below of = DC, node distance =2.2 cm,text width= 0.17\textwidth,text centered,color =dc!70!black]{ \textbf{Cetau}};
\node[below of = Pert, node distance =2.2 cm,text width= 0.22\textwidth,text centered,color =pert!70!black]{ Perturbators};
\node[below of = TL, node distance =2.2 cm,text width= 0.22\textwidth, text centered,color =lt!70!black]{ \;\;\;\; Th \;\; \;\; lymphocytes};
\node[above of = TL, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 1.2 cm, color =lt!90!black]{ Th responses};
\node[above of =DC, node distance =1.5 cm,text width= 0.15\textwidth, text centered, xshift = 2 cm, color =dc!90!black]{ DC signals};
\path [line,color = dc] ([yshift=-0.8 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.8 cm]TL.west);
\path [line,color = dc] ([yshift=-0.4 cm,xshift=- 0.1 cm]DC.east) -- ([yshift=-0.4 cm]TL.west);
\path [line,color = dc] ([xshift=- 0.1 cm]DC.east) -- (TL.west);
\path [line,color = dc] ([yshift=0.4 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.4 cm]TL.west);
\path [line,color = dc] ([yshift=0.8 cm, xshift=- 0.1 cm]DC.east) -- ([yshift=0.8 cm]TL.west);
\path [line, color = gray](Pert) -- (DC.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.7cm]TL.east) -- ([yshift = -0.7cm]L.west);
\path [line,color = lt]([xshift= -0.4cm, yshift = -0.35cm]TL.east) -- ([yshift = -0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm]TL.east) -- (L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.35cm]TL.east) -- ([yshift = 0.35cm]L.west);
\path [line,color = lt] ([xshift= -0.4cm, yshift = 0.7cm]TL.east) -- ([yshift = 0.7cm]L.west);
\end{tikzpicture}
Statistical modelling
\framesubtitle{Understand the Gallic language}
\begin{itemize} \item \textbf{Dataset description:}
\begin{itemize} \item \textcolor{dc!70!black}{$\boldsymbol{X}$}: $n\times p$ design matrix : the DC signals \includegraphics[width =0.12\textwidth]{cellule_dend} \item \textcolor{lt!70!black}{$\boldsymbol{Y}$}: $n\times q$ response matrix : the Th responses \includegraphics[width =0.12\textwidth]{ast_ob} \end{itemize}
\item \textbf{Question:} Which variables influence the responses?
\item \textbf{Approach:} \begin{itemize} \item Variable selection in $$ \boldsymbol{Y}=\boldsymbol{XB}+\boldsymbol{E}, $$ where \begin{itemize} \item $\boldsymbol{B}$: $p\times q$ \textbf{sparse} coefficients matrix \item $\boldsymbol{E}$: $n\times q$ error matrix with $$\forall i\in{1,\dots, n}, \; (E_{i,1},\dots,E_{i,q})\stackrel{iid}{\sim}~\mathcal{N}(0,\boldsymbol{\Sigma}_q)$$
\end{itemize} \item We take the dependence into account by estimating $\boldsymbol{\Sigma}_q$. \end{itemize} \end{itemize}
Statistical modelling
\framesubtitle{Understand the Gallic language}
\begin{itemize} \item \textbf{Dataset description:}
\begin{itemize} \item \textcolor{dc!70!black}{$\boldsymbol{X}$}: $n\times p$ design matrix : the DC signals \includegraphics[width =0.12\textwidth]{cellule_dend} \item \textcolor{lt!70!black}{$\boldsymbol{Y}$}: $n\times q$ response matrix : the Th responses \includegraphics[width =0.12\textwidth]{ast_ob} \end{itemize}
\item \textbf{Question:} Which variables influence the responses?
\item \textbf{Approach:} \begin{itemize} \item Variable selection in $$ \boldsymbol{Y}=\boldsymbol{XB}+\boldsymbol{E}, $$ where \begin{itemize} \item $\boldsymbol{B}$: $p\times q$ \textbf{sparse} coefficients matrix \item $\boldsymbol{E}$: $n\times q$ error matrix with $$\forall i\in{1,\dots, n}, \; (E_{i,1},\dots,E_{i,q})\stackrel{iid}{\sim}~\mathcal{N}(0,\boldsymbol{\Sigma}_q)$$
\end{itemize} \item We take the dependence into account by estimating $\boldsymbol{\Sigma}_q$. \end{itemize} \end{itemize}
Differents penalties : for different point of view
\begin{itemize} \item \textcolor{outcome}{\textbf{Lasso}} : \textit{select variables without taking into account potential links.} \begin{equation} \label{grouplasso} \widehat{b}L = \Am{b} \left\lbrace||y-\bX b||_2^2 + \lambda ||b||_1 \right\rbrace, \end{equation} \item \textcolor{outcome}{\textbf{Group-Lasso}} : \textit{select a group of variables.} \begin{equation} \label{grouplasso} \widehat{b}G = \Am{b_1, \dots, b_L} \left\lbrace||y-\sum_{1 \leq \ell \leq L}\bX_{(\ell)} b_{(\ell)}||2^2 + \lambda\sum{1 \leq \ell \leq L}\sqrt{p_\ell} ||b_\ell||_2\right\rbrace, \end{equation} \item \textcolor{outcome}{\textbf{Fused-Lasso}} : \textit{influence a group of variables to have the same coefficient.} \begin{equation}\label{fuselasso} \widehat{b}F =\Am{b}||y-\bX b||2^2 + \left\lbrace\lambda_1\sum{(i,j) \in \mathcal{G}} |b_i - b_j|+ \lambda_2 ||b||_1\right\rbrace, \end{equation} \end{itemize}
Differents penalties : for different point of view
\begin{itemize} \item \textcolor{outcome}{\textbf{Lasso}} : \textit{select variables without taking into account potential links.} \begin{equation} \label{grouplasso} \widehat{b}L = \Am{b} \left\lbrace||y-\bX b||_2^2 + \lambda ||b||_1 \right\rbrace, \end{equation} \item \textcolor{outcome}{\textbf{Group-Lasso}} : \textit{select a group of variables.} \begin{equation} \label{grouplasso} \widehat{b}G = \Am{b_1, \dots, b_L} \left\lbrace||y-\sum_{1 \leq \ell \leq L}\bX_{(\ell)} b_{(\ell)}||2^2 + \lambda\sum{1 \leq \ell \leq L}\sqrt{p_\ell} ||b_\ell||_2\right\rbrace, \end{equation} \item \textcolor{outcome}{\textbf{Fused-Lasso}} : \textit{influence a group of variables to have the same coefficient.} \begin{equation}\label{fuselasso} \widehat{b}F =\Am{b}||y-\bX b||2^2 + \left\lbrace\lambda_1\sum{(i,j) \in \mathcal{G}} |b_i - b_j|+ \lambda_2 ||b||_1\right\rbrace, \end{equation} \end{itemize}
VariSel for one model type
set.seed(4) load("raw_data.RData") load("data_Tmod_sspdc.RData") X <- Xbrt %>% as.data.frame() %>% mutate(pert_dc= pert_dc, dc= dc) %>% group_by(pert_dc, dc) %>% summarize_if(is.numeric, mean) %>% ungroup() %>% as.data.frame() # # Y <- Y_bxcx %>% as.data.frame() %>% # mutate(pert_dc= pert_dc, dc= dc) %>% # group_by(pert_dc, dc) %>% # summarize_if(is.numeric, mean) %>% # ungroup() %>% as.data.frame() DC_sign <- X_bxcx[,c(36,37, 40)] T_resp <- Y_bxcx[,c(2,10)] # DC_sign <- X %>% select(-dc,-pert_dc) %>% # as.matrix() %>% scale() # # T_resp <- Y %>% select(IFNg, IL3) %>% # as.matrix() %>% scale() # dc <- Y %>% pull(dc) dc <- as.character(dc) dc[dc == "bDC "] <- "Ordra" dc[dc == "MoDC"] <- "Cetau"
mod <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="group_multi_regr")
X <- model.matrix(~DC_sign:dc -1) mod <- train_VariSel( Y = T_resp, X = X, sepx = ":", type ="group_multi_regr")
VariSel for one model type
mod <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="group_multi_regr")
X <- model.matrix(~DC_sign:dc -1) mod <- train_VariSel( Y = T_resp, X = X, sepx = ":", type ="group_multi_regr")
VariSel for one model type : Outcome
plot(mod)
Different modelling strategy
col <- pal_uchicago()(6) mod <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="group_multi_regr") m2 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="group_multi_both") m3 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="fused_multi_both") m4 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="fused_multi_regr") m5 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="lasso_multi")
compar_path(mods = list(mod,m2,m3,m4))
Different modelling strategy
col <- pal_uchicago()(6) mod <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="group_multi_regr") m2 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="group_multi_both") m3 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="fused_multi_both") m4 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="fused_multi_regr") m5 <- train_VariSel( Y = T_resp, regressors = DC_sign, group = dc, type ="lasso_multi")
compar_path(mods = list(mod,m2,m3,m4))
Models selection
ct <- compar_type( Y = T_resp, regressors = DC_sign, group = dc, types = c("group_multi_regr" , "group_multi_both" , "fused_multi_regr", "fused_multi_both", "lasso_multi" ), times = 10)
plot_ct(ct) + labs(title ='')
Best models representation
bm <- get_best_models(ct,criterion = "MSE_boot") plot_md(bm)
Conclusion
This is an R package to perform variable selection in multivariate linear models. It can \begin{itemize} \item Associate explicative variables \item Associate responses \item Associate both explicative variables and responses \item Let all variables 'free', without assoiciating any of them \end{itemize}
Come and see the vignette! \textcolor{outcome}{https://github.com/Marie-PerrotDockes/VariSel}
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