The perception of probability.

Gallistel, C. R.; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E.

doi:10.1037/a0035232

Cited by 89 publications

(315 citation statements)

References 75 publications

(144 reference statements)

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“…|| statistic is gamma(.5,1) regardless of the sample size, n. This is proved to be the case for the Bernoulli distribution in Gallistel et al (2014). Because the exponential when discretized becomes the Bernoulli, this result also holds for the exponential.…”

Section: Assessing Model Viabilitymentioning

confidence: 54%

“…Despite the local variations in relative frequency inherent in a random sequence, they keep a constant estimate, sometimes for hundreds of successive trials-an example of behavioral stasis. However, when the hidden parameter does change, subjects respond quickly and abruptly (Gallistel, Krishan et al 2014). …”

Section: Assessing Model Viabilitymentioning

confidence: 99%

“…The stasis-vs-abruptness paradox led Gallistel et al (2014) to formulate a principle informally termed "if it ain't broke, don't fix it," where 'it' refers to the current stochastic model. The reasoning behind the principle is that it is easier to determine whether the current stochastic model does justice to the data so far accumulated than to determine why it has failed and what needs to be done to fix or replace it.…”

Section: Assessing Model Viabilitymentioning

confidence: 99%

“…The model-viability test proposed Gallistel et al (2014) relies on the surprisingly simple distributional properties of an easily computed information-theoretic statistic, D !" || , the product of the number of data encoded (n) and a Kullback-Leibler divergence, D !"…”

Section: Assessing Model Viabilitymentioning

confidence: 99%

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Information Theory, Memory, Prediction, and Timing in Associative Learning

Wilkes

Gallistel

2017

Computational Models of Brain and Behavior

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Section: Assessing Model Viabilitymentioning

confidence: 54%

Section: Assessing Model Viabilitymentioning

confidence: 99%

Section: Assessing Model Viabilitymentioning

confidence: 99%

Section: Assessing Model Viabilitymentioning

confidence: 99%

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Information Theory, Memory, Prediction, and Timing in Associative Learning

Wilkes

Gallistel

2017

Computational Models of Brain and Behavior

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“…However, the present paper kept volatility constant and capitalized on a different effect: confidence should also decrease whenever an environmental change is suspected, even if the frequency of such change (i.e., volatility) is kept constant (19,20). Accordingly, several studies have shown that a drop in confidence boosts learning (15,20) and may even reset the learning process altogether (43,44). The present study presents a detailed analysis of the brain mechanisms underlying this rational behavior, and leads to the conclusion that the human brain closely approximates the confidence-weighted hierarchical learning algorithm, which is optimal in the present circumstances.…”

Section: Discussionmentioning

confidence: 99%

Brain networks for confidence weighting and hierarchical inference during probabilistic learning

Meyniel

Dehaene

2017

Proc. Natl. Acad. Sci. U.S.A.

108

146

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Learning is difficult when the world fluctuates randomly and ceaselessly. Classical learning algorithms, such as the delta rule with constant learning rate, are not optimal. Mathematically, the optimal learning rule requires weighting prior knowledge and incoming evidence according to their respective reliabilities. This "confidence weighting" implies the maintenance of an accurate estimate of the reliability of what has been learned. Here, using fMRI and an idealobserver analysis, we demonstrate that the brain's learning algorithm relies on confidence weighting. While in the fMRI scanner, human adults attempted to learn the transition probabilities underlying an auditory or visual sequence, and reported their confidence in those estimates. They knew that these transition probabilities could change simultaneously at unpredicted moments, and therefore that the learning problem was inherently hierarchical. Subjective confidence reports tightly followed the predictions derived from the ideal observer. In particular, subjects managed to attach distinct levels of confidence to each learned transition probability, as required by Bayes-optimal inference. Distinct brain areas tracked the likelihood of new observations given current predictions, and the confidence in those predictions. Both signals were combined in the right inferior frontal gyrus, where they operated in agreement with the confidenceweighting model. This brain region also presented signatures of a hierarchical process that disentangles distinct sources of uncertainty. Together, our results provide evidence that the sense of confidence is an essential ingredient of probabilistic learning in the human brain, and that the right inferior frontal gyrus hosts a confidence-based statistical learning algorithm for auditory and visual sequences.T he sensory data that we receive from our environment are often captured by temporal regularities-for instance the colors of traffic lights change according to a predictable greenyellow-red pattern; thunder is often followed by rain, etc. Knowledge of those hidden regularities is often acquired through learning, by aggregating successive observations into summary estimates (e.g., the probability of the light turning red when it is currently yellow). When sensory data are received sequentially, learning can be described as an iterative process that updates the internal estimates each time a new observation is received. Learners must therefore constantly balance two sources of information: their current estimates and the new incoming observations. Any learning algorithm must find a solution to this balancing act. Finding the correct balance is especially critical in a world that is both stochastic and changing (1), i.e., where observations are governed by probabilities that can change over time (a situation called volatility). An excessive reliance on incoming observations will make the learned estimates dominated by fluctuations instead of converging to the true underlying probabilities. Conversely, an excessive reliance o...

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Theoretical implications of quantitative properties of interval timing and probability estimation in mouse and rat

Kheifets

Freestone

Gallistel

2017

J Exper Analysis Behavior

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In three experiments with mice (Mus musculus) and rats (Rattus norvigicus), we used a switch paradigm to measure quantitative properties of the interval-timing mechanism. We found that: 1) Rodents adjusted the precision of their timed switches in response to changes in the interval between the short and long feed latencies (the temporal goalposts). 2) The variability in the timing of the switch response was reduced or unchanged in the face of large trial-to-trial random variability in the short and long feed latencies. 3) The adjustment in the distribution of switch latencies in response to changes in the relative frequency of short and long trials was sensitive to the asymmetry in the Kullback-Leibler divergence. The three results suggest that durations are represented with adjustable precision, that they are timed by multiple timers, and that there is a trial-by-trial (episodic) record of feed latencies in memory.

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The perception of probability.

Cited by 89 publications

References 75 publications

Information Theory, Memory, Prediction, and Timing in Associative Learning

Information Theory, Memory, Prediction, and Timing in Associative Learning

Brain networks for confidence weighting and hierarchical inference during probabilistic learning

Theoretical implications of quantitative properties of interval timing and probability estimation in mouse and rat

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