# ROC and PR Curves in R

Interpret the results of your classification using Receiver Operating Characteristics (ROC) and Precision-Recall (PR) Curves in R with Plotly.

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## ROC and PR Curves in R

Interpret the results of your classification using Receiver Operating Characteristics (ROC) and Precision-Recall (PR) Curves in R with Plotly.

## Preliminary plots

Before diving into the receiver operating characteristic (ROC) curve, we will look at two plots that will give some context to the thresholds mechanism behind the ROC and PR curves.

In the histogram, we observe that the score spread such that most of the positive labels are binned near 1, and a lot of the negative labels are close to 0. When we set a threshold on the score, all of the bins to its left will be classified as 0's, and everything to the right will be 1's. There are obviously a few outliers, such as negative samples that our model gave a high score, and positive samples with a low score. If we set a threshold right in the middle, those outliers will respectively become false positives and false negatives.

As we adjust thresholds, the number of false positives will increase or decrease, and at the same time the number of true positives will also change; this is shown in the second plot. As you can see, the model seems to perform fairly well, because the true positive rate and the false positive rate decreases sharply as we increase the threshold. Those two lines each represent a dimension of the ROC curve.

library(plotly)
library(tidymodels)
set.seed(0)
X <- matrix(rnorm(10000),nrow=500)
y <- sample(0:1, 500, replace=TRUE)
data <- data.frame(X,y)
data$y <- as.factor(data$y)
X <- subset(data,select = -c(y))
logistic_glm <-
logistic_reg() %>%
set_engine("glm") %>%
set_mode("classification") %>%
fit(y ~ ., data = data)

y_scores <- logistic_glm %>%
predict(X, type = 'prob')

y_score <- y_scores$.pred_1 db <- data.frame(data$y, y_score)

z <- roc_curve(data = db, 'data.y', 'y_score')
z$specificity <- 1 - z$specificity
colnames(z) <- c('threshold', 'tpr', 'fpr')

fig1 <- plot_ly(x= y_score, color = data$y, colors = c('blue', 'red'), type = 'histogram', alpha = 0.5, nbinsx = 50) %>% layout(barmode = "overlay") fig1  fig2 <- plot_ly(data = z, x = ~threshold) %>% add_trace(y = ~fpr, mode = 'lines', name = 'False Positive Rate', type = 'scatter')%>% add_trace(y = ~tpr, mode = 'lines', name = 'True Positive Rate', type = 'scatter')%>% layout(title = 'TPR and FPR at every threshold') fig2 <- fig2 %>% layout(legend=list(title=list(text='<b> Rate </b>'))) fig2  ## Basic binary ROC curve We display the area under the ROC curve (ROC AUC). While ROC shows how the TPR and FPR vary with the threshold, the ROC AUC is a measure of the classification model's ability to distinguish one class from the other. An ideal classifier will have ROC AUC = 1. In our example, we see that the ROC AUC is fairly high, thus consistent with our interpretation of the previous plots. library(dplyr) library(ggplot2) library(plotly) library(pROC) set.seed(0) X <- matrix(rnorm(10000),nrow=500) y <- sample(0:1, 500, replace=TRUE) db <- data.frame(X,y) db$y <- as.factor(db$y) test_data = db[1:20] model<- logistic_reg() %>% set_engine("glm") %>% set_mode("classification") %>% # Fit the model fit(y ~., data = db) ypred <- predict(model, new_data = test_data, type = "prob") yscore <- data.frame(ypred$.pred_0)
rdb <- cbind(db$y,yscore) colnames(rdb) = c('y','yscore') pdb <- roc_curve(rdb, y, yscore) pdb$specificity <- 1 - pdb$specificity auc = roc_auc(rdb, y, yscore) auc = auc$.estimate

tit = paste('ROC Curve (AUC = ',toString(round(auc,2)),')',sep = '')

fig <-  plot_ly(data = pdb ,x =  ~specificity, y = ~sensitivity, type = 'scatter', mode = 'lines', fill = 'tozeroy') %>%
layout(title = tit,xaxis = list(title = "False Positive Rate"), yaxis = list(title = "True Positive Rate")) %>%
add_segments(x = 0, xend = 1, y = 0, yend = 1, line = list(dash = "dash", color = 'black'),inherit = FALSE, showlegend = FALSE)
fig


## Multiclass ROC Curve

When you have more than 2 classes, you will need to plot the ROC curve for each class separately. Make sure that you use a one-versus-rest model, or make sure that your problem has a multi-label format; otherwise, your ROC curve might not return the expected results.

library(plotly)
library(tidymodels)
library(fastDummies)

data(iris)
ind <- sample.int(150, 50)
samples <- sample(x = iris$Species, size = 50) iris[ind,'Species'] = samples # Define the inputs and outputs X <- subset(iris, select = -c(Species)) iris$Species <- as.factor(iris$Species) # Fit the model logistic <- multinom_reg() %>% set_engine("nnet") %>% set_mode("classification") %>% fit(Species ~ ., data = iris) y_scores <- logistic %>% predict(X, type = 'prob') # One hot encode the labels in order to plot them y_onehot <- dummy_cols(iris$Species)
colnames(y_onehot) <- c('drop', 'setosa', 'versicolor', 'virginica')
y_onehot <- subset(y_onehot, select = -c(drop))

z = cbind(y_scores, y_onehot)

z$setosa <- as.factor(z$setosa)
roc_setosa <- roc_curve(data = z, setosa, .pred_setosa)
roc_setosa$specificity <- 1 - roc_setosa$specificity
colnames(roc_setosa) <- c('threshold', 'tpr', 'fpr')
auc_setosa <- roc_auc(data = z, setosa, .pred_setosa)
auc_setosa <- auc_setosa$.estimate setosa <- paste('setosa (AUC=',toString(round(1-auc_setosa,2)),')',sep = '') z$versicolor <- as.factor(z$versicolor) roc_versicolor <- roc_curve(data = z, versicolor, .pred_versicolor) roc_versicolor$specificity <- 1 - roc_versicolor$specificity colnames(roc_versicolor) <- c('threshold', 'tpr', 'fpr') auc_versicolor <- roc_auc(data = z, versicolor, .pred_versicolor) auc_versicolor <- auc_versicolor$.estimate
versicolor <- paste('versicolor (AUC=',toString(round(1-auc_versicolor,2)),')', sep = '')

z$virginica <- as.factor(z$virginica)
roc_virginica <- roc_curve(data = z, virginica, .pred_virginica)
roc_virginica$specificity <- 1 - roc_virginica$specificity
colnames(roc_virginica) <- c('threshold', 'tpr', 'fpr')
auc_virginica <- roc_auc(data = z, virginica, .pred_virginica)
auc_virginica <- auc_virginica$.estimate virginica <- paste('virginica (AUC=',toString(round(1-auc_virginica,2)),')',sep = '') # Create an empty figure, and iteratively add a line for each class fig <- plot_ly()%>% add_segments(x = 0, xend = 1, y = 0, yend = 1, line = list(dash = "dash", color = 'black'), showlegend = FALSE) %>% add_trace(data = roc_setosa,x = ~fpr, y = ~tpr, mode = 'lines', name = setosa, type = 'scatter')%>% add_trace(data = roc_versicolor,x = ~fpr, y = ~tpr, mode = 'lines', name = versicolor, type = 'scatter')%>% add_trace(data = roc_virginica,x = ~fpr, y = ~tpr, mode = 'lines', name = virginica, type = 'scatter')%>% layout(xaxis = list( title = "False Positive Rate" ), yaxis = list( title = "True Positive Rate" ),legend = list(x = 100, y = 0.5)) fig  ## Precision-Recall Curves Plotting the PR curve is very similar to plotting the ROC curve. The following examples are slightly modified from the previous examples: library(dplyr) library(ggplot2) library(plotly) library(pROC) set.seed(0) X <- matrix(rnorm(10000),nrow=500) y <- sample(0:1, 500, replace=TRUE) db <- data.frame(X,y) db$y <- as.factor(db$y) test_data = db[1:20] model<- logistic_reg() %>% set_engine("glm") %>% set_mode("classification") %>% # Fit the model fit(y ~., data = db) ypred <- predict(model, new_data = test_data, type = "prob") yscore <- data.frame(ypred$.pred_0)
rdb <- cbind(db$y,yscore) colnames(rdb) = c('y','yscore') pdb <- pr_curve(rdb, y, yscore) auc = roc_auc(rdb, y, yscore) auc = auc$.estimate

tit = paste('ROC Curve (AUC = ',toString(round(auc,2)),')',sep = '')

fig <-  plot_ly(data = pdb ,x =  ~recall, y = ~precision, type = 'scatter', mode = 'lines', fill = 'tozeroy') %>%
add_segments(x = 0, xend = 1, y = 1, yend = 0, line = list(dash = "dash", color = 'black'),inherit = FALSE, showlegend = FALSE) %>%
layout(title = tit, xaxis = list(title = "Recall"), yaxis = list(title = "Precision") )

fig


In this example, we use the average precision metric, which is an alternative scoring method to the area under the PR curve.

library(plotly)
library(tidymodels)
library(fastDummies)

data(iris)
ind <- sample.int(150, 50)
samples <- sample(x = iris$Species, size = 50) iris[ind,'Species'] = samples # Define the inputs and outputs X <- subset(iris, select = -c(Species)) iris$Species <- as.factor(iris$Species) # Fit the model logistic <- multinom_reg() %>% set_engine("nnet") %>% set_mode("classification") %>% fit(Species ~ ., data = iris) y_scores <- logistic %>% predict(X, type = 'prob') y_onehot <- dummy_cols(iris$Species)
colnames(y_onehot) <- c('drop', 'setosa', 'versicolor', 'virginica')
y_onehot <- subset(y_onehot, select = -c(drop))

z = cbind(y_scores, y_onehot)

z$setosa <- as.factor(z$setosa)
pr_setosa <- pr_curve(data = z, setosa, .pred_setosa)
aps_setosa <- mean(pr_setosa$precision) setosa <- paste('setosa (AP =',toString(round(aps_setosa,2)),')',sep = '') z$versicolor <- as.factor(z$versicolor) pr_versicolor <- pr_curve(data = z, versicolor, .pred_versicolor) aps_versicolor <- mean(pr_versicolor$precision)
versicolor <- paste('versicolor (AP = ',toString(round(aps_versicolor,2)),')',sep = '')

z$virginica <- as.factor(z$virginica)
pr_virginica <- pr_curve(data = z, virginica, .pred_virginica)
aps_virginica <- mean(pr_virginica$precision) virginica <- paste('virginica (AP = ',toString(round(aps_virginica,2)),')',sep = '') # Create an empty figure, and add a new line for each class fig <- plot_ly()%>% add_segments(x = 0, xend = 1, y = 1, yend = 0, line = list(dash = "dash", color = 'black'), showlegend = FALSE) %>% add_trace(data = pr_setosa,x = ~recall, y = ~precision, mode = 'lines', name = setosa, type = 'scatter')%>% add_trace(data = pr_versicolor,x = ~recall, y = ~precision, mode = 'lines', name = versicolor, type = 'scatter')%>% add_trace(data = pr_virginica,x = ~recall, y = ~precision, mode = 'lines', name = virginica, type = 'scatter')%>% layout(xaxis = list( title = "Recall" ), yaxis = list( title = "Precision" ),legend = list(x = 100, y = 0.5)) fig  ## References Learn more about histograms, filled area plots and line charts: • https://plot.ly/r/histograms/ • https://plot.ly/r/filled-area-plots/ • https://plot.ly/r/line-charts/ ### What About Dash? Dash for R is an open-source framework for building analytical applications, with no Javascript required, and it is tightly integrated with the Plotly graphing library. Learn about how to install Dash for R at https://dashr.plot.ly/installation. Everywhere in this page that you see fig, you can display the same figure in a Dash for R application by passing it to the figure argument of the Graph component from the built-in dashCoreComponents package like this: library(plotly) fig <- plot_ly() # fig <- fig %>% add_trace( ... ) # fig <- fig %>% layout( ... ) library(dash) library(dashCoreComponents) library(dashHtmlComponents) app <- Dash$new()
app$layout( htmlDiv( list( dccGraph(figure=fig) ) ) ) app$run_server(debug=TRUE, dev_tools_hot_reload=FALSE)