Naive and yet Enlightened: From Natural Frequencies to Fast and Frugal Decision Trees

Martignon, Laura; Vitouch, Oliver; Takezawa, Masanori; Forster, Malcolm R.

doi:10.1093/acprof:oso/9780199744282.003.0006

Cited by 40 publications

(79 citation statements)

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“…negative. Because the test result is causally affected by the state of the criterion, this tree is often referred to as a causal tree (Martignon et al, 2003;Waldmann & Martignon, 1998).…”

Section: Natural Sampling and Natural Frequencies: Three Casesmentioning

confidence: 99%

“…A much simpler alternative is offered by fast-and-frugal heuristics (Gigerenzer, Todd, & the ABC Research Group, 1999), specifically, fast-and-frugal trees (Martignon, Katsikopoulos, & Woike, 2008Martignon, Vitouch, Takezawa, & Forster, 2003). The fast-and-frugal trees we analyze in this article can be conceptualized as pruned and simplified natural frequency trees.…”

Section: Introductionmentioning

confidence: 99%

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Integrating and testing natural frequencies, naïve Bayes, and fast-and-frugal trees.

Woike¹,

Hoffrage²,

Martignon³

2017

Decision

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This article relates natural frequency representations of cue-criterion relationships to fast-and-frugal heuristics for inferences based on multiple cues. In the conceptual part of this work, three approaches to classification are compared to one another: The first uses a natural Bayesian classification scheme, based on profile memorization and natural frequencies. The second is based on Naïve Bayes, a heuristic that assumes conditional independence between cues (given the criterion). The third approach is to construct fast-and-frugal classification trees, which can be conceived as pruned versions of diagnostic natural frequency trees. Fastand-frugal trees can be described as lexicographic classifiers but can also be related to another fundamental class of models, namely linear models. Linear classifiers with fixed thresholds and noncompensatory weights coincide with fast-and-frugal trees-not as processes but in their output. Various heuristic principles for tree construction are proposed. In the second, empirical part of this article, the classification performance of the three approaches when making inferences under uncertainty (i.e., out of sample) is evaluated in 11 medical data sets in terms of Receiver Operating Characteristics (ROC) diagrams and predictive accuracy. Results show that the two heuristic approaches, Naïve Bayes and fast-and-frugal trees, generally outperformed the model that is normative when fitting known data, namely classification based on natural frequencies (or, equivalently, profile memorization). The success of fast-and-frugal trees is grounded in their ecological rationality: their construction principles can exploit the structure of information in the data sets. Finally, implications, applications, limitations, and possible extensions of this work are discussed.

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“…negative. Because the test result is causally affected by the state of the criterion, this tree is often referred to as a causal tree (Martignon et al, 2003;Waldmann & Martignon, 1998).…”

Section: Natural Sampling and Natural Frequencies: Three Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integrating and testing natural frequencies, naïve Bayes, and fast-and-frugal trees.

Woike¹,

Hoffrage²,

Martignon³

2017

Decision

Self Cite

View full text Add to dashboard Cite

show abstract

“…Martignon et al, 2011). For binary predictors, a fast-and-frugal tree has n + 1 exists, while a full tree has 2 n exits.…”

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confidence: 99%

Cognitive Processes in Decisions Under Risk are not the Same as in Decisions Under Uncertainty

Volz¹,

Martignon²

2012

Front. Neurosci.

124

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We deal with risk versus uncertainty, a distinction that is of fundamental importance for cognitive neuroscience yet largely neglected. In a world of risk (“small world”), all alternatives, consequences, and probabilities are known. In uncertain (“large”) worlds, some of this information is unknown or unknowable. Most of cognitive neuroscience studies exclusively study the neural correlates for decisions under risk (e.g., lotteries), with the tacit implication that understanding these would lead to an understanding of decision making in general. First, we show that normative strategies for decisions under risk do not generalize to uncertain worlds, where simple heuristics are often the more accurate strategies. Second, we argue that the cognitive processes for making decisions in a world of risk are not the same as those for dealing with uncertainty. Because situations with known risks are the exception rather than the rule in human evolution, it is unlikely that our brains are adapted to them. We therefore suggest a paradigm shift toward studying decision processes in uncertain worlds and provide first examples.

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“…Additive prototype models compute a representative (average) member of each class and compare how far away each feature combination is from this prototype. Fast and Frugal trees reach between 39% and 61% classification accuracy if constructed by the max(val+,valÀ) and zigzag(val+,valÀ) tree construction methods (Martignon, Vitouch, Takezawa, & Forster, 2003), respectively, while in our task 100% accuracy is achievable.…”

Section: Environment 1: Deterministic Taskmentioning

confidence: 80%

Naïve and Robust: Class‐Conditional Independence in Human Classification Learning

2017

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Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model (the dependence-independence structure and category learning model, DISC-LM) that incorporates varying degrees of prior belief in class-conditional independence, learns whether or not independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments-designed using optimal experimental design principles-were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks.

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Naive and yet Enlightened: From Natural Frequencies to Fast and Frugal Decision Trees

Cited by 40 publications

References 0 publications

Integrating and testing natural frequencies, naïve Bayes, and fast-and-frugal trees.

Integrating and testing natural frequencies, naïve Bayes, and fast-and-frugal trees.

Cognitive Processes in Decisions Under Risk are not the Same as in Decisions Under Uncertainty

Naïve and Robust: Class‐Conditional Independence in Human Classification Learning

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