In the study of
decision-making
In psychology, decision-making (also spelled decision making and decisionmaking) is regarded as the Cognition, cognitive process resulting in the selection of a belief or a course of action among several possible alternative options. It could be ...
, a fast-and-frugal tree is a simple graphical structure that categorizes objects by asking one question at a time. These
decision trees
A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains condit ...
are used in a range of fields:
psychology
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betwe ...
,
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
, and
management science
Management science (or managerial science) is a wide and interdisciplinary study of solving complex problems and making strategic decisions as it pertains to institutions, corporations, governments and other types of organizational entities. It is ...
. Unlike other decision or
classification Classification is a process related to categorization, the process in which ideas and objects are recognized, differentiated and understood.
Classification is the grouping of related facts into classes.
It may also refer to:
Business, organizat ...
trees
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are u ...
, such as
Leo Breiman
Leo Breiman (January 27, 1928 – July 5, 2005) was a distinguished statistician at the University of California, Berkeley. He was the recipient of numerous honors and awards, and was a member of the United States National Academy of Sciences.
...
's CART, fast-and-frugal trees are intentionally simple, both in their construction as well as their execution, and operate speedily with little information. For this reason, fast-and-frugal-trees are potentially attractive when designing resource-constrained tasks
Laura Martignon, Vitouch, Takezawa and Forster first introduced both the concept and the term in 2003;
[Martignon, Laura; Vitouch, Oliver; Takezawa, Masanori; Forster, Malcolm]
"Naive and Yet Enlightened: From Natural Frequencies to Fast and Frugal Decision Trees"
published in ''Thinking : Psychological perspectives on reasoning, judgement and decision making'' (David Hardman and Laura Macchi; editors), Chichester: John Wiley & Sons, 2003. similar
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
s for other tasks had been used before, building on the formal models created by
Gerd Gigerenzer
Gerd Gigerenzer (born 3 September 1947) is a German psychologist who has studied the use of bounded rationality and heuristics in decision making. Gigerenzer is director emeritus of the Center for Adaptive Behavior and Cognition (ABC) at the Max ...
and
Herbert A. Simon
Herbert Alexander Simon (June 15, 1916 – February 9, 2001) was an American political scientist, with a Ph.D. in political science, whose work also influenced the fields of computer science, economics, and cognitive psychology. His primary ...
.
In categorization tasks with two options and ''m'' cues—also known as features or attributes—available for making such a decision, an FFT is defined as follows:
''A fast-and-frugal tree is a classification or a decision tree that has m+1 exits, with one exit for each of the first m -1 cues and two exits for the last cue.''
Mathematically, fast-and-frugal trees can be viewed as
lexicographic
Lexicography is the study of lexicons, and is divided into two separate academic disciplines. It is the art of compiling dictionaries.
* Practical lexicography is the art or craft of compiling, writing and editing dictionaries.
* Theoretica ...
heuristics or as linear classification models with non-compensatory weights and a threshold . Their formal properties and construction have also been analyzed using signal detection theory by Luan, Schooler and Gigerenzer in 2011 .
Basic Organization
Construction
The basic elements are the cues. The cues are ranked, with one cue at each level of the tree and an exit node at each level (except for two exit nodes for the last cue at the last level of the tree). Whenever a cue is used, a question is asked about the value of the cue. The answers to the questions might immediately lead to an exit, or they might lead to a further question (and eventually to an exit). A characteristic property of fast-and-frugal trees is that, for each question, there is at least one possible answer that leads to an exit.
In the literature on fast-and-frugal trees, many different algorithms have been proposed
for (1) ordering cues and (2) deciding which possible answer to a question about a cue leads immediately to an exit. A fast-and-frugal tree is fully defined if both the following conditions are met. Often, in order to keep construction simple and intuitive, the algorithms use (1) simple measures of cue "goodness" (e.g., correlation between cue and category, considering each cue independently of the other cues) and (2) make simple choices about exits (e.g., decide on each exit independently of the other exits), but more complex algorithms have been proposed as well.
Execution
To use a fast-and-frugal tree, begin at the root and check one cue at a time. At each step, one of the possible outcomes is an exit node which allows for a decision (or action) -- if an exit is reached, stop; otherwise, continue until an exit is reached. you take an exit, stop; otherwise, continue and ask more questions until an exit is reached.
![FFT-FIG01](https://upload.wikimedia.org/wikipedia/commons/3/3e/FFT-FIG01.png)
Figure 1 illustrates a fast-and-frugal tree for classifying a patient as “high risk” of having a heart stroke and thus having to be sent to the “coronary care unit” or as "low risk” and thus having to be sent to a “regular nursing bed" (Green& Mehr, 1997).
Consider three patients, John, Mary, and Jack:
* John has
ST segment
In electrocardiography, the ST segment connects the QRS complex and the T wave and has a duration of 0.005 to 0.150 sec (5 to 150 ms).
It starts at the J point (junction between the QRS complex and ST segment) and ends at the beginning of the T ...
changes thus is classified as "high risk" and sent to the coronary care unit-- without considering other cues.
* Mary has no
ST segment
In electrocardiography, the ST segment connects the QRS complex and the T wave and has a duration of 0.005 to 0.150 sec (5 to 150 ms).
It starts at the J point (junction between the QRS complex and ST segment) and ends at the beginning of the T ...
changes, does have chest pain as her chief complaint, but does not have any of the remaining five factors, thus is classified as "low risk" and sent to a regular nursing bed, after all three cues are checked.
* Jack has no
ST segment
In electrocardiography, the ST segment connects the QRS complex and the T wave and has a duration of 0.005 to 0.150 sec (5 to 150 ms).
It starts at the J point (junction between the QRS complex and ST segment) and ends at the beginning of the T ...
change and does not have chest pain as his chief complaint, thus is classified as "low risk" and sent to a regular nursing bed, by considering these two cues.
Performance
The accuracy and
robustness
Robustness is the property of being strong and healthy in constitution. When it is transposed into a system, it refers to the ability of tolerating perturbations that might affect the system’s functional body. In the same line ''robustness'' ca ...
of fast-and-frugal trees has been shown to be comparable to that of Bayesian benchmarks in studies by Laskey and Martignon (2014). 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 .
A signal detection analysis of fast-and-frugal trees
Fast-and-frugal trees are used to perform binary classifications or decisions. In psychology, medicine, and other fields, signal detection theory (or
detection theory
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (ca ...
) has been the classic theory under which such tasks are analyzed.
The theory assumes that there are two categories of events or people (e.g., people with and without heart problems), of which the category more relevant to us is referred as “signal” while the other is referred to as “noise.” The two differ in their distribution on an observation scale that we may call “evidence,” with the signal distribution having a higher mean. One can make two possible classifications, namely “signal” or “noise,” upon gathering the evidence. This leads to four possible outcomes: hit (classify as “signal” when it is indeed a signal), correct rejection (classify as “noise” when it is indeed a noise), miss (classify as “noise” when it is actually a signal), and false alarm (classify as “signal” when it is actually a noise). To maximize overall accuracy or the expected value of a classification, the theory posits that we need to carefully select the classification criterion on the evidence scale, above which we make a “signal” decision and below which “noise.” 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.
![FIGURE2-FFT-ByCesare](https://upload.wikimedia.org/wikipedia/commons/9/95/FIGURE2-FFT-ByCesare.png)
In 2011, Luan, Schooler, and Gigerenzer analyzed characteristics of fast-and-frugal trees from the perspective of signal detection theory. There are several key findings from this analysis. First, the choice of the exit structure of a fast-and-frugal tree corresponds to the setting of the decision criterion in signal detection. In a nutshell, the earlier a "signal exit" appears in a fast-and-frugal tree, the more liberally biased is the tree. The relative biases of two fast-and-frugal trees are determined by the first exit in which the two differ, with the one having the “signal exit” - denoted by "s" - always being more liberal as the one having the "noise exit" - denoted by "n" (Figure 2). For example, an FFTsnnn ( here again s = "Signal exit", n = "noise exit") is more liberally biased than an FFTnsss. This principle is referred to as the “lexicographic decision bias” of fast-and-frugal trees.
Second, a series of simulations show that fast-and-frugal trees with different exit structures will lead to different—sometimes drastically different—expected value of a decision when the consequences of a miss and a false alarm differ. Therefore, when constructing and applying a fast-and-frugal tree, one needs to choose an exit structure that matches well the decision payoff structure of a task.
Third, the overall sensitivity of a fast-and-frugal tree—that is, how well the tree can discriminate a signal from a noise and which can be measured by d’ or A’ from
signal detection
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called Stimulus (psychology), stimulus in living organisms, Signal (electronics), signal in machines) and random pa ...
theory—is affected by properties of the cues that make up the tree, such as the mean and variance of the cues’ sensitivities and the inter-cue correlations among the cues, but not much by the exit structure of the tree.
And finally, the performance of fast-and-frugal trees is robust and comparable to much more sophisticated decision algorithms developed in signal detection theory, including the
ideal observer analysis
Ideal observer analysis is a method for investigating how information is processed in a perceptual system. It is also a basic principle that guides modern research in perception.
The ''ideal observer'' is a theoretical system that performs a spec ...
model and the optimal sequential sampling model. In the context of out-of-sample predictions, fast-and-frugal trees perform the best relative to other models when the learning sample size is relatively small (e.g., less than 80 trials).
Computing support
In 2017, Phillips, Neth, Woike and Gaissmaier introduced the R packag
FFTrees hosted on CRAN (with a
accompanying app, which constructs, depicts graphically, and evaluates quantitatively fast and frugal trees in user-friendly ways.
More examples of fast-and-frugal trees
There have been many applications of fast-and-frugal trees in both prescribing how a decision should be made and describing how people actually make decisions. 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
[Keller, N., & Katsikopoulos, K. V. (2016) ]
On the role of psychological heuristics in operational research; and a demonstration in military stability operations. European Journal of Operational Research, 249, 1063–1073.
/ref> ; the tree is illustrated in Figure 3. Two examples of fast-and-frugal trees’ descriptive uses are shown in Figure 4. The trees on the left and right describe, respectively, how a person decides whether to forgive another person for an offense the latter committed during social interactions and how British judges make a bail-or-jail decision . In general, fast-and-frugal trees can be applied to help or model any binary decision-making processes that involve multiple cues.
Related articles and other sources
References
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Cybernetics
Decision trees
Heuristics