Exemplar models as a mechanism for performing Bayesian inference

Shi, Lei; Griffiths, Thomas L.; Feldman, Naomi H.; Sanborn, Adam N.

doi:10.3758/pbr.17.4.443

Cited by 114 publications

(133 citation statements)

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“…One such model is Lacerda's (1995) model of categorical effects as emergent from exemplar-based categorization, which has a direct mathematical link to our model, as described by Feldman et al (2009). Shi et al (2010) also provide an implemention of our model in an exemplar-based framework, which is closely related to the neural model proposed by Guenther and Gjaja (1996). In that model, there are more exemplars, or a higher level of neural firing, at category centers than near category boundaries.…”

Section: Ockham's Razor and Levels Of Analysismentioning

confidence: 99%

A unified account of categorical effects in phonetic perception

2016

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Categorical effects are found across speech sound categories, with the degree of these effects ranging from extremely strong categorical perception in consonants to nearly continuous perception in vowels. We show that both strong and weak categorical effects can be captured by a unified model. We treat speech perception as a statistical inference problem, assuming that listeners use their knowledge of categories as well as the acoustics of the signal to infer the intended productions of the speaker. Simulations show that the model provides close fits to empirical data, unifying past findings of categorical effects in consonants and vowels and capturing differences in the degree of categorical effects through a single parameter.

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Section: Ockham's Razor and Levels Of Analysismentioning

confidence: 99%

A unified account of categorical effects in phonetic perception

2016

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“…These kinds of models are sometimes called rational process models, since they are models of rational learners that are concerned with implementing the process of approximating Bayesian inference. For example, Shi, Griffiths, Feldman, & Sanborn (2010) discuss how exemplar models may provide a possible mechanism for implementing Bayesian inference, since these models allow an approximation process called importance sampling. Other examples include the work of Bonawitz et al (2011), who discuss how a simple sequential algorithm can be used to approximate Bayesian inference in a basic causal learning task, and that of Pearl, Goldwater, and Steyvers (2011), who (as described in section 3) investigated various online algorithms for Bayesian models of word segmentation.…”

Section: Algorithmsmentioning

confidence: 99%

Statistical Learning, Inductive Bias, and Bayesian Inference in Language Acquisition

Pearl¹,

Goldwater²

2016

Oxford Handbooks Online

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Bayesian models of language acquisition are powerful tools for exploring how linguistic generalizations can be made. Notably, Bayesian models assume children leverage statistical information in sophisticated ways, and so it is important to demonstrate that children’s behavior is consistent with both the assumptions of the Bayesian framework and the predictions of specific models. We first provide a historical overview of behavioral evidence suggesting children utilize available statistical information to make useful generalizations in a variety of tasks. We then discuss the Bayesian modeling framework, including benefits of particular interest to both developmental and theoretical linguists. We conclude with a review of several case studies that demonstrate how Bayesian models can be applied to problems of interest in language acquisition.

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“…The computationally-justified message passing scheme we developed, FBL, uses the same class of approximations as Daw et al (2008) as categorization Shi et al, 2010), sentence parsing (Levy et al, 2009), prediction (Brown & Steyvers, 2009), perceptual bistability (Gershman et al, 2012, and even human and animal learning (Lu et al, 2008;Rojas, 2010) to explain trial order effects. Sampling algorithms tend to come with asymptotic guarantees: with enough samples any computation done with these algorithms will be indistinguishable from computation done with the full probability distribution.…”

Section: Kinds Of Approximationsmentioning

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“…A classic way to combine computational-and algorithmic-level insights is to begin with an algorithmic-level model developed to fit human behavior and then investigate its computational-level properties (Ashby & Alfonso-Reese, 1995;Gigerenzer & Todd, 1999). This is not the only possible direction, and recently researchers have begun at the computational level of analysis and then worked toward understanding the algorithm (Griffiths et al, 2012;Sanborn et al, 2010;Shi et al, 2010).Identifying the algorithm to associate with a computational-level model adds both psychological plausibility and explanatory power -computational-level models often are intractable, so the algorithm can provide a computationally tractable approximation while also explaining behavior that differs from predictions of the (Kalman, 1960), which is a generalization of standard associative learning models (Dayan et al, 2000;Dayan & Kakade, 2001;Kruschke, 2008;Sutton, 1992), and it is approximated using Assumed Density Filtering (ADF; Boyen & Koller, 1998), an algorithm for sequential updating of a probability distribution. ADF approximates the full joint posterior distribution, which can contain dependencies between variables, with a factorized distribution that assumes the variables are independent.…”

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Constraining bridges between levels of analysis: A computational justification for locally Bayesian learning

Sanborn

Silva

2013

Journal of Mathematical Psychology

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Different levels of analysis provide different insights into behavior: computationallevel analyses determine the problem an organism must solve and algorithmiclevel analyses determine the mechanisms that drive behavior. However, many attempts to model behavior are pitched at a single level of analysis. Research into human and animal learning provides a prime example, with some researchers using computational-level models to understand the sensitivity organisms display to environmental statistics but other researchers using algorithmic-level models to understand organisms' trial order effects, including effects of primacy and recency. Recently, attempts have been made to bridge these two levels of analysis.Locally Bayesian Learning (LBL) creates a bridge by taking a view inspired by evolutionary psychology: Our minds are composed of modules that are each individually Bayesian but communicate with restricted messages. A different inspiration comes from computer science and statistics: Our brains are implementing the algorithms developed for approximating complex probability distributions. We show that these different inspirations for how to bridge levels of analysis are not necessarily in conflict by developing a computational justification for LBL. We Preprint submitted to ElsevierApril 26, 2013 demonstrate that a scheme that maximizes computational fidelity while using a restricted factorized representation produces the trial order effects that motivated the development of LBL. This scheme uses the same modular motivation as LBL, passing messages about the attended cues between modules, but does not use the rapid shifts of attention considered key for the LBL approximation. This work illustrates a new way of tying together psychological and computational constraints.Keywords: rational approximations; locally Bayesian learning; trial order effectsOur goal when we model behavior depends on the level of analysis. If we analyze behavior at Marr (1982)'s computational level, then we aim to determine the problem that people are attempting to solve. Or, as more often found in psychology, we might be interested in the mechanism that drives behavior, placing us at Marr (1982)'s algorithmic level. In human and animal learning, both computational-level (Courville et al., 2005;Danks et al., 2003;Dayan et al., 2000) and algorithmic-level models (Rescorla & Wagner, 1972;Mackintosh, 1975;Pearce & Hall, 1980) have been developed. Models developed at different levels of analysis have different strengths and this can be seen in how these models of human and animal learning are applied: computational-level approaches are used to explain how organisms are sensitive to complex statistics of the environment (De Houwer & Beckers, 2002;Mitchell et al., 2005;Shanks & Darby, 1998) and algorithmiclevel models are used to explain how organisms are sensitive to the presentation order of trials (Chapman, 1991;Hershberger, 1986;Medin & Edelson, 1988).The computational and algorithmic levels provide different perspectives on model d...

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Exemplar models as a mechanism for performing Bayesian inference

Cited by 114 publications

References 44 publications

A unified account of categorical effects in phonetic perception

A unified account of categorical effects in phonetic perception

Statistical Learning, Inductive Bias, and Bayesian Inference in Language Acquisition

Constraining bridges between levels of analysis: A computational justification for locally Bayesian learning

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