knitr::opts_chunk$set(collapse = FALSE, comment = "#>", prompt = FALSE, tidy = FALSE, echo = TRUE, message = FALSE, warning = FALSE, # Default figure options: dpi = 100, fig.align = 'center', fig.height = 6.0, fig.width = 6.5, out.width = "580px")
library(FFTrees)
The FFTrees package makes it very easy to visualize and evaluate fast-and-frugal trees (FFTs):
Use the main FFTrees()
function to create a set of FFTs (e.g., as an R object\ x
of type FFTrees
).
Visualize a tree in\ x
by evaluating plot(x)
.
The two key arguments for plotting are what
and tree
:
Whereas the tree
argument allows selecting between different trees in\ x
(using tree = 1
by default),
the what
argument distinguishes between five main types of plots:
plot(x, what = 'all')
visualizes a tree and corresponding performance statistics.
This is also the default when evaluating plot(x)
.
plot(x, what = 'tree')
visualizes only the tree diagram of the selected tree (without performance statistics).
plot(x, what = 'icontree')
visualizes the tree diagram of the selected tree with icon arrays on exit nodes
(with additional options for show.iconguide
and n.per.icon
.
plot(x, what = 'cues')
visualizes the current cue accuracies in ROC\ space (by calling the showcues()
function).
plot(x, what = 'roc')
visualizes a performance comparison of FFTs and competing algorithms in ROC\ space.
The other arguments of the plot.FFTrees()
function allow further customization of the plot
(e.g., by defining labels and parameters, or selectively hiding or showing elements).
In the following, we illustrate both ways by creating FFTs based on the titanic
data (included in the FFTrees package).
knitr::include_graphics("../inst/titanic.jpg")
The titanic
dataset contains basic survival statistics of Titanic passengers.
For each passenger, we know in which class s/he traveled, as well as binary categories specifying age, sex, and survival information.
To get a first impression, we inspect a random sample of cases:
set.seed(12) # reproducible randomness rcases <- sort(sample(1:nrow(titanic), 10)) # Sample of data: knitr::kable(titanic[rcases, ], caption = "A sample of 10 observations from the `titanic` data.")
Our current goal is to fit FFTs to this dataset. This essentially asks:
class
, age
and sex
to decide whether a passenger survived
?First, let's create an FFTrees
object (called titanic.fft
) from the titanic
dataset:
# Create FFTs for the titanic data: titanic.fft <- FFTrees(formula = survived ~., data = titanic, main = "Surviving the Titanic", decision.labels = c("Died", "Survived"))
Note that we used the entire titanic
data (i.e., all r nrow(titanic)
\ cases) to train titanic.fft
, rather than specifying train.p
to set aside some proportion of it or specifying a dedicated data.test
set for predictive purposes.
This implies that our present goal is to fit FFTs to the historic data, rather than on create and use FFTs to predict new cases.
We can visualize individual cue accuracies (specifically their sensitivities and specificities) by including the what = 'cues'
argument within the plot()
function.
Let's apply the function to the titanic.fft
object to see how accurate each of the cues were on their own in predicting survival:
plot(titanic.fft, what = "cues", main = "Cues predicting Titanic survival")
Given the axes of this plot, good performing cues should be near the top left corner of the graph (i.e., exhibit both a low false alarm rate and a high hit rate).
For the titanic
data, this implies that none of the cues predicts very well on its own.
The best individual cue appears to be sex
(indicated as\ 1), followed by class
\ (2).
By contrast, age
\ (3) seems a pretty poor cue for predicting survival on its own (despite its specificity of\ 97%).
Inspecting cue accuracies can provide valuable information for constructing FFTs. While they provide lower bounds on the performance of trees (as combining cues is only worthwhile when this yields a benefit), even poor individual cues can shine in combination with other predictors.
To visualize the tree from an FFTrees
object, use plot()
.
Let's plot one of the trees (Tree\ #1, i.e., the best one, given our current goal):
plot(titanic.fft, tree = 1)
The resulting plot visualizes one out of r
titanic.fft$trees$n\ possible trees in the
titanic.fftobject.
As
tree = 1corresponds to the best tree given our current
goalfor selecting FFTs, we could have plotted the same tree by specifying
tree = 'best.train'`.
As Figure\ 2 contains a lot of information in three distinct panels, let's briefly consider their contents:
Basic dataset information: The top row of the plot shows basic information on the current dataset: Its population size\ (N) and the baseline frequencies of the two categories of the criterion variable.
FFT and classification performance: The middle row shows the tree (in the center) as well as how many cases (here: persons) were classified at each level in the tree (on either side). For example, the current tree (Tree\ #1 of\ 4) can be understood as:
Accuracy and performance information:
The bottom row shows general performance statistics of the\ FFT:
As our models in titanic.fft
were trained on the entire titanic
dataset, we fitted FFTs to its r nrow(titanic)
\ cases, rather than setting aside some data for predictive purposes.
The panel label reflects this important distinction:
If the results of fitting data (i.e., data used to build the tree) are displayed, we'll see a "Training" label.
If a testing dataset separate from the one used to build the tree is used, we'll see a "Prediction" label.
The bottom panel provides performance information and is structured into three subpanels:
a. The classification table (on the left) shows the relationship between the true criterion states (as columns) and predicted decisions (as rows). The abbreviations hi (hits) and cr (Correct rejections) denote correct decisions; mi (misses) and fa (false-alarms) denote incorrect decisions.
b. A range of vertical levels (in the middle) show the tree's cumulative performance in terms of two frugality measures (mcu
and pci
) and various accuracy measures (sensitivity, specificity, accuracy, and balanced accuracy (see Accuracy statistics for details).
c. Finally, the plot (on the right) shows an ROC\ curve comparing the performance of all trees in the FFTrees
object.
Additionally, the performance of logistic regression (blue) and CART (red) are shown.
The tree plotted in the middle panel is highlighted in a solid green color (i.e., Figure\ 2 shows Tree\ #1).
Specifying additional arguments of plot()
changes what and how various elements are being displayed.
what
should be visualized? The what
argument selects contents to be plotted:
When what = 'all'
(as by default), the plot shows both a tree diagram and a range of corresponding performance statistics.
Using one of the other what
options narrows the range of what is being shown:
To only visualize a bare tree diagram (without performance statistics), we specify what = "tree"
(formerly stats = FALSE
).
To visualize the tree diagram with icon arrays on exit nodes, we specify what = "icontree"
(with additional options for show.iconguide
and n.per.icon
).
To visualize the performance comparison (for different FFTs and competing algorithms) in ROC\ space, we specify what = "roc"
.
The following examples illustrate the wide range of corresponding plots:
# Plot tree diagram with icon arrays: plot(titanic.fft, what = "icontree", n.per.icon = 50, show.iconguide = TRUE)
# Plot only the performance comparison in ROC space: plot(titanic.fft, what = "roc")
what
do not suffice, various show.
arguments (i.e., show.header
, show.tree
, show.confusion
, show.levels
, show.roc
, show.icons
, and show.iconguide
) allow to selectively turn on or turn off specific elements of the overall plot. For example: # Hide some elements of the FFT plot: plot(titanic.fft, show.icons = FALSE, # hide icons show.iconguide = FALSE, # hide icon guide show.header = FALSE # hide header )
tree
: Which tree do we want to plot?
As FFTrees
objects typically contain multiple FFTs, we need to indicate which tree we want to visualize.
We usually specify the tree to show by an integer value, such as tree = 2
, which will plot the corresponding tree (i.e., Tree\ #2) of the FFTrees
object. Alternatively, we can specify tree = "best.train"
or tree = "best.test"
to visualize the best training or prediction tree, respectively. This selects and shows the tree with the highest goal value (e.g., weighted accuracy\ wacc
) when fitting or testing data.
data
: Which data do we want to apply the tree to?
We can specify data = "train"
or data = "test"
to distinguish between a training and testing dataset (if available) in the FFTrees
object. As not all FFTrees
objects contain test data, data
is set to data = "train"
by default.
As the data
and tree
arguments can both refer to datasets used for training or fitting (i.e., the "train" or "test" sets), they should be specified consistently. For instance, the following command would visualize the best training tree in titanic.fft
:
plot(titanic.fft, tree = "best.train")
as data = "train"
by default. However, the following analog expression would fail:
plot(titanic.fft, tree = "best.test")
for two distinct reasons:
When data
remains unspecified, its default is data = "train"
.
Thus, asking for tree = "best.test"
would require switching to data = "test"
.
More crucially, titanic.fft
was created without any test data.
Hence, asking for the best test tree does not make sense --- which is why plot()
will show the best training tree (with a warning).
Shifting our emphasis from fitting to prediction, we primarily need to specify some test data that was not used to train the FFTrees
object.
When predicting performance for a new dataset (e.g.; data = test.data
), the plotting and printing functions will automatically apply an existing FFTrees
object to the new data and compute corresponding performance statistics (using the fftrees_apply()
function).
However, when applying existing FFTs to new data, the changes to the FFTrees
object are not stored in the input object, unless the (invisible) output of plot.FFTrees()
or print.FFTrees()
is re-assigned to that object.
The best way to fit FFTs to training data and evaluate them to test data is to explicitly include both datasets in the original FFTrees()
command by either using its data.test
or its train.p
argument.
For example, we can repeat the previous analysis, but now let's create separate training and test datasets by including the train.p = .50
argument.
This will split the dataset into a 50%\ training set, and a distinct 50%\ testing set.
(Alternatively, we could specify a dedicated test data set by using the data.test
argument.)
set.seed(100) # for replicability of the training/test split titanic.pred.fft <- FFTrees(formula = survived ~., data = titanic, train.p = .50, # use 50% to train, 50% to test main = "Titanic", decision.labels = c("Died", "Survived") )
Here is the best training tree applied to the training data:
# print(titanic.pred.fft, tree = 1) plot(titanic.pred.fft, tree = 1)
Tree\ #1 is the best training tree --- and could also be visualized by plot(titanic.pred.fft, tree = "best.train")
.
This tree has a high specificity of\ 92%, but a much lower sensitivity of just\ 51%.
The overall accuracy of the tree's classifications is at\ 79%, which exceeds the baseline, but is far from perfect.
However, as we can see in the ROC\ table, a logistic regression\ (LR) would not perform much better, and CART performed even worse than Tree\ #1.
Now let's inspect the performance of the same tree on the test data:
# print(titanic.pred.fft, data = "test", tree = 1) plot(titanic.pred.fft, data = "test", tree = 1)
We could have visualized the same tree by asking for plot(titanic.pred.fft, data = "test", tree = "best.test")
.
Note that the label of the bottom panel has now switched from "Accuracy (Training)" to "Accuracy (Testing)".
Both the sensitivity and specificity values have decreased somewhat, which is typical when using a model (fitted on training data) for predicting new (test) data.
Let's visualize the prediction performance of Tree\ #2, the most liberal tree (i.e., with the highest sensitivity):
plot(titanic.pred.fft, data = "test", tree = 2)
This alternative tree has a better sensitivity (of\ 63%), but its overall accuracy decreased to about baseline level (of\ 67%).
Whereas comparing training with test performance illustrates the trade-offs between mere fitting and genuine predictive modeling, comparing the performance details of various FFTs illustrates the typical trade-offs that any model for solving binary classification problems engages in. Importantly, both types of trade-offs are rendered transparent when using FFTrees.
Here is a complete list of the vignettes available in the FFTrees package:
| | Vignette | Description |
|--:|:------------------------------|:-------------------------------------------------|
| | Main guide: FFTrees overview | An overview of the FFTrees package |
| 1 | Tutorial: FFTs for heart disease | An example of using FFTrees()
to model heart disease diagnosis |
| 2 | Accuracy statistics | Definitions of accuracy statistics used throughout the package |
| 3 | Creating FFTs with FFTrees() | Details on the main FFTrees()
function |
| 4 | Manually specifying FFTs | How to directly create FFTs without using the built-in algorithms |
| 5 | Visualizing FFTs | Plotting FFTrees
objects, from full trees to icon arrays |
| 6 | Examples of FFTs | Examples of FFTs from different datasets contained in the package |
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