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Threshold Selection for Classifiers

Nina Zumel

WVPlots has a variety of visualizations that help modelers to design classifiers best suited to their goals. In particular, ThresholdPlot is a tool to select classifier thresholds that give the best tradeoffs among relevant performance metrics. This note demonstrates an example of using WVPlots to evaluate and design classifiers.

Example Data

Here we create an example synthetic data set, where score is the score produced by a trained model, and y is the actual outcome in the evaluation data set (TRUE or FALSE).

library(WVPlots)
## Loading required package: wrapr

set.seed(1452225)

# data with two different regimes of behavior
d <- rbind(
  data.frame(
    score = rnorm(1000),
    y = sample(c(TRUE, FALSE), prob = c(0.02, 0.98), size = 1000, replace = TRUE)),
  data.frame(
    score = rnorm(200) + 5,
    y = sample(c(TRUE, FALSE), size = 200, replace = TRUE))
)

One can create different classifiers from this single model, with different performance metrics, by varying the decision threshold. Datums that score higher than the threshold are predicted to be in the class of interest (TRUE).

The ROC plot gives this model an AUC of 0.91, which seems pretty high.

ROCPlot(d, "score", "y", truthTarget=TRUE, title="Model ROC")

The double density plot shows that in general, true instances score higher than most false instances. It further suggests that a threshold in the “valley” of the plot, say around a value of 2.5, would achieve good separation between true and false instances. But is that separation good enough to achieve project goals?

DoubleDensityPlot(d, "score", "y", title="Distribution of scores as a function of outcome")

A big disadvantage of both the ROC and double density plots is that they hide the fact that the classes are unbalanced; this is more obvious when the TRUE and FALSE distributions are separated. We can show the actual class prevalences with ShadowHist:

ShadowHist(d, "score", "y", title="Distribution of scores as a function of outcome")

Notice that from the ShadowHist we can see that datums that score above a threshold of 2.5 may not be majority true instances. So while this model may look pretty good initially, we still aren’t sure if we can pick a threshold that produces a classification rule that meets project goals.

PRTPlot: Plotting Precision vs Recall

For a given model, PRTPlot plots the precision and recall for different choices of threshold. As is expected, higher thresholds give higher precision, at the cost of lower recall.

PRTPlot(d, "score", "y",  truthTarget=TRUE, title="precision and recall as a function of threshold")

The plot suggests that a threshold of 2.5 produces a classifier with about 87% recall, but only 50% precision. Depending on the project goals, this may or may not be good enough. Unfortunately this model can’t achieve higher precision without drastically impairing recall, so if higher simultaneous precision and recall are needed, it may be time to go back to the drawing board.

ThresholdPlot: Plotting Other Metrics by Threshold

If precision/recall aren’t the performance metrics for your application, ThresholdPlot produces similar plots for a variety of classifier metrics. See the documentation for all the metrics that can be plotted; here are a few examples.

# replicate PRTPlot. Looks a little different because ThresholdPlot does different smoothing
ThresholdPlot(d, "score", "y", title="Reproduce PRTPlot",
              truth_target=TRUE, # default
              metrics = c("precision", "recall"))
## Warning: Removed 1 row(s) containing missing values (geom_path).


# default: sensitivity/specificity
ThresholdPlot(d, "score", "y", title="Sensitivity and Specificity as a Function of Threshold")

“Unrolling” the ROC

One useful application of ThresholdPlot is to “unroll” an ROC plot: if the ROC shows that your model can meet an acceptable trade-off of true positive rate and false positive rate, then ThresholdPlot can tell you which threshold achieves that goal.

ThresholdPlot(d, "score", "y", title="ROC 'unrolled'",
              metrics = c("true_positive_rate", "false_positive_rate"))

Our example model with a threshold of 2.5 achieves a true positive rate (or recall) of about 87%, with a false positive rate of about 12%.

Diagnostics on Data Distribution

ThresholdPlot can also be used to show some possibly useful diagnostics on score distribution. fraction measures how much of the data scores above a given threshold value. cdf is 1 - fraction, or the CDF of the scores (how much of the data is below a given threshold value).

ThresholdPlot(d, "score", "y", title="Score distribution",
              metrics = c("fraction", "cdf"))

MetricPairPlot

MetricPairPlot provides another way of visualizing the tradeoffs between a pair of complementary performance metrics, by plotting them against each other. For instance, plotting true_positive_rate vs false_positive_rate gives you the equivalent of the ROC.

MetricPairPlot(d, 'score', 'y', title='ROC equivalent',
                 x_metric = "false_positive_rate", # default
                 y_metric = "true_positive_rate")  # default

The above plot is just an ad-hoc version of ROCPlot.

# Plot ROCPlot for comparison
ROCPlot(d, 'score', 'y', truthTarget=TRUE, title='ROC example')

You can plot other pairs as well, for instance precision vs. recall:

MetricPairPlot(d, 'score', 'y', title='recall/precision', x_metric = 'recall', y_metric = 'precision')
## Warning: Removed 2 row(s) containing missing values (geom_path).

MetricPairPlot takes the same metrics as ThresholdPlot. See the documentation for details.