Examples of FFTrees

Creating FFTs

Let’s create some trees using FFTrees()! We’ll use the train.p = .50 argument to split the original data into a \(50\)% training set and a \(50\)% testing set:

# Create FFTs from the mushrooms data: 
set.seed(1) # for replicability of the training / test data split

mushrooms_fft <- FFTrees(formula = poisonous ~.,
                         data = mushrooms,
                         train.p = .50,   # split data into 50:50 training/test subsets
                         main = "Mushrooms",
                         decision.labels = c("Safe", "Poison"),
                         do.comp = FALSE)

Setting the do.comp = FALSE argument prevents the evaluation of alternative algorithms (beyond those needed for FFTs). This can save time, but also avoid error messages stemming from alternative prediction methods (e.g., rank-deficient fits of linear models).

Here’s basic information about the best performing FFT (Tree #1):

# Print information about the best tree (during training):
print(mushrooms_fft)

#> Mushrooms
#> FFTrees 
#> - Trees: 6 fast-and-frugal trees predicting poisonous
#> - Cost of outcomes:  hi = 0,  fa = 1,  mi = 1,  cr = 0
#> 
#> FFT #1: Definition
#> [1] If odor != {f,s,y,p,c,m}, decide Safe.
#> [2] If sporepc = {h,w,r}, decide Poison, otherwise, decide Safe.
#> 
#> FFT #1: Training Accuracy
#> Training data: N = 4,062, Pos (+) = 1,958 (48%) 
#> 
#> |          | True +   | True -   |   Totals:
#> |----------|----------|----------|
#> | Decide + | hi 1,683 | fa     0 |     1,683
#> | Decide - | mi   275 | cr 2,104 |     2,379
#> |----------|----------|----------|
#>   Totals:       1,958      2,104   N = 4,062
#> 
#> acc  = 93.2%   ppv  = 100.0%   npv  = 88.4%
#> bacc = 93.0%   sens = 86.0%   spec = 100.0%
#> 
#> FFT #1: Training Speed, Frugality, and Cost
#> mcu = 1.47,  pci = 0.93,  cost_dec = 0.068

Cool beans.

Visualizing cue accuracies

Let’s look at the individual cue training accuracies with plot(fft, what = "cues"):

# Plot the cue accuracies of an FFTrees object:
plot(mushrooms_fft, what = "cues")

#> Plotting cue training statistics:
#> — Cue accuracies ranked by bacc

It looks like the cues oder and sporepc are the best predictors. In fact, the single cue odor has a hit rate of \(97\)% and a false alarm rate of nearly \(0\)%! Based on this, we should expect the final trees to use just these cues.

Visualizing FFT performance

Now let’s plot the performance of the best training tree when applied to the test data:

# Plot the best FFT (for test data): 
plot(mushrooms_fft, data = "test")

Indeed, it looks like the best tree only uses the odor and sporepc cues. In our test dataset, the tree had a false alarm rate of \(0\)% (\(1 -\) specificity), and a sensitivity (aka. hit rate) of \(85\)%.

Trading off prediction errors

When considering the implications of our predictions, the fact that our FFT incurs many misses, but no false alarms, is problematic: Given our current task, failing to detect poisonous mushrooms has usually more serious consequences than falsely classifying some as poisonous. To change the balance between both possible errors, we can select another tree from the set of FFTs. In this case, FFT #2 would use the same two cues, but alter their exit structure so that our prediction incurs false alarms, but no misses. Alternatively, we could re-generate a new set of FFTs with a higher sensitivity weight value (e.g., increase the default value of sens.w = .50 to sens.w = .67) and optimize the FFTs’ weighted accuracy wacc.

An alternative FFT

Let’s assume that a famous mushroom expert insists that our FFT is using the wrong cues. According to her, the best predictors for poisonous mushrooms are ringtype and ringnum. To test this, we build a set of FFTs from only these cues and check how they perform relative to our initial tree:

# Create trees using only the ringtype and ringnum cues: 
mushrooms_ring_fft <- FFTrees(formula = poisonous ~ ringtype + ringnum,
                              data = mushrooms,
                              train.p = .50,
                              main = "Mushrooms (ring cues)",
                              decision.labels = c("Safe", "Poison"),
                              do.comp = FALSE)

Again, we plot the best training tree, when predicting the cases in the test dataset:

# Plotting the best training FFT (for test data): 
plot(mushrooms_ring_fft, data = "test")

As we can see, this tree (in mushrooms_ring_fft) has both sensitivity and specificity values of around \(80\)%, but does not perform as well as our earlier one (in mushrooms_fft). This suggests that we should discard the expert’s advice and primarily rely on the odor and sporepc cues.

Visualizing cue accuracies

We can plot the training cue accuracies during training by specifying what = "cues":

# Plot cue values: 
plot(iris_fft, what = "cues")

#> Plotting cue training statistics:
#> — Cue accuracies ranked by bacc

It looks like the two cues pet.len and pet.wid are the best predictors for this dataset. Based on this insight, we should expect the final trees will likely use one or both of these cues.

Visualizing FFT performance

Now let’s visualize the best tree:

# Plot best FFT: 
plot(iris_fft)

Indeed, it turns out that the best tree only uses the pet.len and pet.wid cues (in that order). For this data, the fitted tree exhibits a performance with a sensitivity of 100% and a specificity of 94%.

Viewing alternative FFTs

Now, this tree did quite well, but what if someone wanted a tree with the lowest possible false alarm rate? If we inspect the ROC plot in the bottom right corner of the figure, we see that Tree #2 has a specificity close to 100%. Let’s plot this tree:

# Plot FFT #2: 
plot(iris_fft, tree = 2)

As we can see, this tree does indeed have a higher specificity (of 98%), but this increase comes at a cost of a lower sensitivity (of 90%). Such trade-offs between conflicting measures are inevitable when fitting and predicting real-world data. Importantly, using FFTs and the FFTrees package help us to render such trade-offs more transparent.