Understanding the Kalman Filter

Meinhold, Richard J.; Singpurwalla, Nozer D.

doi:10.2307/2685871

Cited by 281 publications

(186 citation statements)

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“…The Kalman filter was originally developed in the context of least-squares estimation for dynamic systems (Kalman, 1960), and a Bayesian formulation and tutorial was presented by Meinhold and Singpurwalla (1983). The Kalman filter was introduced to associative learning theorists by Sutton (1992).…”

Section: Examples: One Traditional and Two Bayesian Modelsmentioning

confidence: 99%

Bayesian approaches to associative learning: From passive to active learning

Kruschke

2008

Learning & Behavior

128

132

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210Bayesian formalizations of learning are a revolutionary advance over traditional approaches. Bayesian models assume that the learner maintains multiple candidate hypotheses with differing degrees of belief, unlike traditional models that assume the learner has a punctate state of mind. Bayesian models can account for some associative learning phenomena that are very challenging for traditional approaches. Perhaps more important, but even less prominent in the associative learning literature, is the fact that Bayesian models provide a foundation for models of active learning. Because Bayesian models represent degrees of belief across multiple hypotheses, the active learner can assess which possible probing of the environment is most likely to achieve beliefs that reduce uncertainty or make some hypotheses highly probable. Traditional models, by contrast, typically treat the learner as a passive recipient of information, and such models offer no predictions for how a real learner would actively probe its environment.This article is divided into two main parts. The first is a selective review of Bayesian models of associative learning. Two different Bayesian models are described in detail and compared with the traditional Rescorla-Wagner (1972) model. The behavior of the models is illustrated by applications to some well-known phenomena, such as backward blocking. The review also indicates how the specific models are situated in the larger space of all possible Bayesian models, which offers a remarkably liberating cornucopia of representational options for models of learning.The second part of the article focuses on active learning. Two different goals for active learning are reviewed, and the predictions of the two Bayesian models are presented. This article is the first application of active-learning formalisms to models of associative learning. The derivations and simulations demonstrate that different combinations of knowledge representations and active-learning goals generate different predictions, some of which are already informed by results in the literature. The broad framework that combines Bayesian models of passive learning with various goals for active learning is a gold mine for new research. TRADITIONAL AND BAYESIAN THEORIESIn traditional cognitive models, the learner's knowledge at any given moment is represented as a specific state. For example, the learner may have an associative weight of 0.413 between "tone" and "shock," or the learner may know that the concept "cat" has a value of 0.289 on the scale of ferocity. When new information is delivered by the world, the values may change. For example, if another instance of shock preceded by a tone occurs, the associative weight might then increase to 0.582. On the other hand, if a cat snuggles up and purrs, that concept's ferocity value might decrease to 0.116. The punctate values comprise the totality of the learner's knowledge.Bayesian approaches assume a radically different mental ontology, in which the learner entertains an entire spectrum of ...

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Section: Examples: One Traditional and Two Bayesian Modelsmentioning

confidence: 99%

Bayesian approaches to associative learning: From passive to active learning

Kruschke

2008

Learning & Behavior

128

132

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“…The weights have prior belief distributions defined as multivariate normal. The Kalman filter uses Bayesian updating to adjust the probability distribution on the weights (Meinhold & Singpurwalla, 1983). Because the model is linear, the posterior distributions on the weights are also multivariate normal, and the Kalman filter equations elegantly express the posterior mean and covariance as a simple function of the prior mean and covariance.…”

Section: Trial-order Invariancementioning

confidence: 99%

Locally Bayesian learning with applications to retrospective revaluation and highlighting.

Kruschke¹

2006

Psychological Review

106

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A scheme is described for locally Bayesian parameter updating in models structured as successions of component functions. The essential idea is to back-propagate the target data to interior modules, such that an interior component's target is the input to the next component that maximizes the probability of the next component's target. Each layer then does locally Bayesian learning. The approach assumes online trial-by-trial learning. The resulting parameter updating is not globally Bayesian but can better capture human behavior. The approach is implemented for an associative learning model that first maps inputs to attentionally filtered inputs and then maps attentionally filtered inputs to outputs. The Bayesian updating allows the associative model to exhibit retrospective revaluation effects such as backward blocking and unovershadowing, which have been challenging for associative learning models. The back-propagation of target values to attention allows the model to show trial-order effects, including highlighting and differences in magnitude of forward and backward blocking, which have been challenging for Bayesian learning models.

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“…This algorithm uses the Kalman filter principle [65] to estimate the separation between correctly and incorrectly recognized samples. The Kalman filter is a linear quadratic estimation algorithm that produces statistically optimal estimates of unknown variables from noisy data.…”

Section: Kalman Filter Based Algorithmmentioning

confidence: 99%

Online active supervision of an evolving classifier for customized-gesture-command learning

Bouillon

Anquetil

2017

Neurocomputing

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To cite this version:Manuel Bouillon, Eric Anquetil.Online active supervision of an evolving classifier for customized-gesture-command learning.Neurocomputing AbstractTouch sensitive interfaces enable new interaction methods, like gesture commands. For users to easily memorize more than a dozen of gesture commands, it is important to enable gesture set customization. The classifier used to recognize drawn symbols must hence be customizable -able to learn from very few data -and evolving -able to learn new classes on-the-fly and improve during its use. The objective of this work is to obtain a gesture command system that cooperates as best as possible with the user: that learns from its mistakes without soliciting the user too often. This paper presents a novel approach for the online active learning of gesture commands, with three contributions. The IntuiSup supervisor monitors the learning process and user interactions. The Evolving Sampling by Uncertainty (ESU) algorithm enables to maintain the error/interaction compromise over time. The Boosted-ESU (B-ESU) method optimizes interaction impact to fasten system learning speed. The efficiency of our approach is evaluated on the publicly available ILG Data Base of gesture commands. Experimentation shows the effectiveness of the supervision strategy and improvements both in term of accuracy and learning speed.

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Understanding the Kalman Filter

Cited by 281 publications

References 0 publications

Bayesian approaches to associative learning: From passive to active learning

Bayesian approaches to associative learning: From passive to active learning

Locally Bayesian learning with applications to retrospective revaluation and highlighting.

Online active supervision of an evolving classifier for customized-gesture-command learning

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