Why people underestimate y when extrapolating in linear functions.

Kwantes, Peter J.; Neal, Alan C.

doi:10.1037/0278-7393.32.5.1019

Cited by 23 publications

(59 citation statements)

References 14 publications

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“…First, people largely anchor their responses at either zero or one. This is consistent with other observations in function learning (Kwantes & Neal, 2006), but in the present experiment, the choice of anchor was not consistent. The inconsistency of the anchor is mirrored by the second feature, which is the tendency of participants to make extreme quasi-periodic responses.…”

Section: Discussionsupporting

confidence: 82%

Learning and extrapolating a periodic function

Kalish

2013

Mem Cogn

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How people learn continuous functional relationships remains a poorly understood capacity. In this article, I argue that the mere presence of nonmonotonic extrapolation of periodic functions neither threatens existing theories of function learning nor distinguishes between them. However, I show that merely learning periodic functions is extremely difficult. It is only when stimuli are presented numerically, rather than as numberless quantities, that participants learn anything like a periodic function. In addition, I show that even then, people do not regularly extrapolate periodically. The lesson is that careful methodologies will be required to understand a psychological capacity that is as idiosyncratic as the learning of complex functions appears to be. Keywords Function learning . Individual differencesFunctions, like categories, are an essential aspect of our environment and our relationship to it. We must know how much force to use to lift a bucket as a function of how much water it holds, how long to water the lawn as a function of the day's temperature, and how slowly to drink our wine to enable our safe drive home given how long we intend to stay at the party and how much we have been eating. We all must be able to quickly learn how hard to press the gas pedal to get a given amount of acceleration each time we get into a rental car, while plumbers may learn over time to estimate how far from a junction a leak is by the sound of the turbulent water.

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Section: Discussionsupporting

confidence: 82%

Learning and extrapolating a periodic function

Kalish

2013

Mem Cogn

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“…More generally, our demonstration shows that an established and classic theory for memory that has previously been applied to understand a suite of behaviors including (a) recognition memory (Hintzman 1984), (b) frequency judgment (Hintzman 1988), (c) cued recall (Hintzman 1986), (d) classification (Hintzman 1986), (e) function learning (Kwantes and Neal 2006), (f) judgment and decision (Dougherty et al 1999;Thomas et al 2008), (g) speech normalization (Goldinger 1998), (h) confidence/accuracy inversions in eyewitness identification (Clark 1997), (i) language processing (Rosch and Mervis 1975), (j) false memory (Arndt and Hirshman 1998), (k) memory dissociations in aging (Benjamin 2010), (l) implicit learning (Jamieson and Mewhort 2009a, 2010, (m) speeded choice (Jamieson and Mewhort 2009b), (n) associative learning (Jamieson et al 2010b, (o) the production effect in recognition memory (Jamieson et al 2016a), and (p) selective memory impairment in amnesia (Jamieson et al 2010a;Curtis and Jamieson 2018) can also be used to understand semantics. The cross-lab and cross-domain effort represents the way that science ought to progress-by developing a general account of memory and its processes in a working computational system to produce a common explanation of behavior rather than a set of labspecific and domain-specific theories for different behaviors (Newell 1973).…”

Section: Discussionmentioning

confidence: 99%

An Instance Theory of Semantic Memory

et al. 2018

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Distributional semantic models (DSMs) specify learning mechanisms with which humans construct a deep representation of word meaning from statistical regularities in language. Despite their remarkable success at fitting human semantic data, virtually all DSMs may be classified as prototype models in that they try to construct a single representation for a word's meaning aggregated across contexts. This prototype representation conflates multiple meanings and senses of words into a center of tendency, often losing the subordinate senses of a word in favor of more frequent ones. We present an alternative instance-based DSM based on the classic MINERVA 2 multiple-trace model of episodic memory. The model stores a representation of each language instance in a corpus, and a word's meaning is constructed on-the-fly when presented with a retrieval cue. Across two experiments with homonyms in both an artificial and natural language corpus, we show how the instance-based model can naturally account for the subordinate meanings of words in appropriate context due to nonlinear activation over stored instances, but classic prototype DSMs cannot. The instance-based account suggests that meaning may not be something that is created during learning or stored per se, but may rather be an artifact of retrieval from an episodic memory store.

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“…To date, extrapolation-based studies of function learning are comparatively sparse, but have revealed several biases in human learners. For example, people's extrapolation judgments follow linear patterns , but see Kalish et al (2004)), and more specifically tend toward functions with a positive slope and an intercept of zero (Kwantes and Neal 2006). In one instance of this bias, when people are trained using data from a quadratic function, their average predictions fall between the true function and straight lines fitted to the closest training points.…”

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confidence: 99%

A rational model of function learning

et al. 2015

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Theories of how people learn relationships between continuous variables have tended to focus on two possibilities: one, that people are estimating explicit functions, or two that they are performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian linear regression and Gaussian processes, which provide a probabilistic basis for similarity-based function learning, we show that learning explicit rules and using similarity can be seen as two views of one solution to this problem. We use this insight to define a rational model of human function learning that combines the strengths of both approaches and accounts for a wide variety of experimental results. Keywords A rational model of function learningEvery time we get into a rental car, we have to learn how hard to press the gas pedal for a given amount of acceleration. Solving this problem-which is an important part of driving safely-requires learning a relationship between two continuous variables. Over the past 50 years, several studies of function learning have shed light on how people come to understand continuous relationships (Carroll 1963;Brehmer 1971;1974;Koh and Meyer 1991;Busemeyer et al. 1997;DeLosh et al. 1997;Kalish et al. 2004;McDaniel and Busemeyer 2005). It has become clear that people can learn and recall a wide variety of relationships, but demonstrate certain systematic biases that tell us about the mental representations and implicit assumptions that humans employ when solving function learning problems. For example, people tend to expect that relationships will be linear when extrapolating to novel examples , and find it more difficult to learn relationships that change direction than those that do not (Brehmer 1974;Byun 1995).Several models have been developed to understand the cognitive mechanisms behind function learning. These models tend to fall into two different theoretical camps. The first includes rule-based theories (e.g., Carroll, 1963, Brehmer, 1974, Koh and Meyer, 1991, which suggest that people learn an explicit function from a given family, such as polynomials (Carroll 1963;McDaniel and Busemeyer 2005) or power-law functions (Koh and Meyer 1991). This approach attributes rich representations to human learners, but has traditionally given limited treatment to how such representations could be acquired. A second approach includes similarity-based theories (e.g., DeLosh et al., 1997, which focus on the idea that 1194 Psychon Bull Rev (2015) 22:1193-1215 people learn by forming associations: if x is used to predict y, observations with similar x values should also have similar y values. This approach can be straightforwardly implemented in a connectionist architecture and thus gives an account of the underlying learning mechanisms, but faces challenges in explaining how people generalize so broadly beyond their experience. Most recently, hybrids of these two approaches have ...

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Why people underestimate y when extrapolating in linear functions.

Cited by 23 publications

References 14 publications

Learning and extrapolating a periodic function

Learning and extrapolating a periodic function

An Instance Theory of Semantic Memory

A rational model of function learning

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