Fast-and-frugal trees

Fast-and-frugal tree or matching heuristic[1](in the study of decision-making) is a simple graphical structure that categorizes objects by asking one question at a time.

[3] Laura Martignon, Vitouch, Takezawa and Forster first introduced both the concept and the term in 2003;[4] similar heuristics for other tasks had been used before, building on the formal models created by Gerd Gigerenzer and Herbert A. Simon.

Mathematically, fast-and-frugal trees can be viewed as lexicographic heuristics or as linear classification models with non-compensatory weights and a threshold.

[GM] Consider three patients, John, Mary, and Jack: The accuracy and robustness of fast-and-frugal trees has been shown to be comparable to that of Bayesian benchmarks in studies by Laskey and Martignon (2014).

[LM] Extensive studies comparing the performance of fast-and-frugal trees to that of classification algorithms used in statistics and machine learning, such as naive Bayes, CART, random forests, and logistic regression, have also been carried out by using dozens of real-world datasets.

Specially, when the cost of a miss is very high (i.e., classifying a patient with heart problem as normal), a lower, more "liberal" criterion (i.e., toward the left in the evidence scale) needs to be selected, whereas when the cost of a false alarm is very high (e.g., classifying an innocent person as guilty of a murder), a higher, more "conservative" criterion will be better.

This implies that a good decision-maker needs to be properly biased in most real-world situations; this is the most critical and relevant insight from signal detection theory on classification and decision making.

In 2017, Phillips, Neth, Woike and Gaissmaier[PNWG] introduced the R package FFTrees,[7] hosted on CRAN (with an accompanying app[8]), which constructs, depicts graphically, and evaluates quantitatively fast and frugal trees in user-friendly ways.

Beyond the medical field, an example of their prescriptive applications is instructing soldiers stationed in Afghanistan how to distinguish whether a car approaching a check-point is driven by civilians or potential suicide bombers;[9][KK] the tree is illustrated in Figure 3.

Example of Fast-and-Frugal Tree
Figure 1. A fast-and-frugal tree that helps emergency room doctors decide whether to send a patient to a regular nursing bed or the coronary care unit (Green & Mehr, 1997). [GM]
Example 2 of Fast-and-Frugal Tree
Figure 2. The higher section of the figure illustrates the assumptions of signal-detection theory in a binary decision task. The three vertical lines represent three decision criteria the agent and the decision-maker may adopt. The lower section illustrates the four possible FFTs that can be constructed when three features are consulted in a fixed order. Based on the classifications pointed to by the first two exits, the trees are named from left to right FFTss, FFTsn, FFTns, and FFTnn. The arrows connecting the figure parts indicate roughly the locations of the four FFTs' decision criteria when they are used to make a binary s/n (for signal and noise, respectively) classification or decision. Among the four, FFTss has the most liberal decision criterion and FFTnn the most conservative one. The decision criteria of FFTsn and FFTns are less extreme than the other two, with FFTsn being more liberal than FFTns.
Example 3 of Fast-and-Frugal Tree
Figure 3. A fast-and-frugal tree that can help soldiers stationed in Afghanistan distinguish whether a car approaching a check-point is driven by civilians or potential suicide bombers (Keller & Katsikopoulos, 2016). [KK]
Example 4 of Fast-and-Frugal Tree
Figure 4. Fast-and-frugal trees that describe how a person decides whether to forgive another person for an offense the latter committed during social interactions (left; Tan, Luan, & Katsikopoulos, 2017) [TLK] and how British judges decide whether to make a punitive bail decision (right. Dhami, 2003). [D]