Maximum Entropy Sampling and Optimal Bayesian Experimental Design

Sebastiani, Paola; Wynn, Henry P.

doi:10.1111/1467-9868.00225

Cited by 192 publications

(126 citation statements)

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“…Our method is related to the framework of "optimal experimental design" in which experiments are designed so as to optimally elicit information about the process under investigation (Sebastiani and Wynn 2000;Atkinson et al 2007). Normative statistical principles from Bayesian inference can, in some cases, be used to select an experimental design that will best resolve the details of participants' underlying cognitive processes (e.g., set the free parameters of a model of the process under scrutiny; Rafferty et al 2012).…”

Section: Resultsmentioning

confidence: 99%

“…Indeed, work in machine learning and information theory has established how information in any given task might be optimally selected so as to maximally discriminate between competing hypotheses and accelerate learning (optimal experimental design; Sebastiani and Wynn 2000). Although human learning does not always mirror these optimal strategies, judicious choice of information has been shown to improve learning, for instance of category boundaries (Gureckis and Markant 2012) or speech motor learning (Knock et al 2000).…”

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confidence: 99%

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Causal Model Comparison Shows That Human Representation Learning Is Not Bayesian

Geana

Niv

2014

Cold Spring Harb Symp Quant Biol

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How do we learn what features of our multidimensional environment are relevant in a given task? To study the computational process underlying this type of "representation learning," we propose a novel method of causal model comparison. Participants played a probabilistic learning task that required them to identify one relevant feature among several irrelevant ones. To compare between two models of this learning process, we ran each model alongside the participant during task performance, making predictions regarding the values underlying the participant's choices in real time. To test the validity of each model's predictions, we used the predicted values to try to perturb the participant's learning process: We crafted stimuli to either facilitate or hinder comparison between the most highly valued features. A model whose predictions coincide with the learned values in the participant's mind is expected to be effective in perturbing learning in this way, whereas a model whose predictions stray from the true learning process should not. Indeed, we show that in our task a reinforcement-learning model could help or hurt participants' learning, whereas a Bayesian ideal observer model could not. Beyond informing us about the notably suboptimal (but computationally more tractable) substrates of human representation learning, our manipulation suggests a sensitive method for model comparison, which allows us to change the course of people's learning in real time.We live in a rich, complex environment, in which we are constantly bombarded with a wide variety of sensory input. Even an action as simple as walking down the street carries with it a large volume of low-quality information in the form of people we see, places we walk by, cars, colors, voices, noises, emotional content, etc. Intuitively, one would imagine that given sufficient resources, it is best to always represent every aspect of the environment so that any detail can potentially be acted upon. However, the "curse of dimensionality" (Bellman 1957) posits that task representations that involve unnecessary stimulus dimensions will not afford efficient learning and decision-making, where efficiency is measured in the number of examples needed to learn the task. In particular, an increase in the number of dimensions of the problem (in our case, the dimensions of the environment that the brain may represent) implies that the learner needs to collect exponentially larger quantities of data to learn to solve the problem. If we want learning to be feasible it is therefore both computationally optimal and a practical imperative to represent tasks with as compact a representation as possible.What are the computational strategies that humans use to learn a representation for a given task? To address this question, we tested participants on a multidimensional trial-and-error choice task, in which only one dimension was relevant to predicting reward (Wilson and Niv 2012;Niv et al. 2015). To test the explanatory power of different models of learning dynamics, we develope...

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Causal Model Comparison Shows That Human Representation Learning Is Not Bayesian

Geana

Niv

2014

Cold Spring Harb Symp Quant Biol

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“…During the design phase, the optimal manoeuvre is selected, which is expected to Preprints of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 yield the most information for the next inference cycle. The optimal manoeuvre is determined using the idea of maximum entropy sampling, where it is believed the most is learnt by sampling from where the least is known, (Sebastiani and Wynn (2000)). In the following section, the steps used are described in more detail.…”

Section: Fig 1 Adaptive Bayesian Motion Planning Algorithm Flowchartmentioning

confidence: 99%

“…In order to choose the most informative manoeuvre using (6), we need to maximise (12). This means that the best move is to go toward the location whose predictive distribution has maximum entropy (equivalently, the least information); it is called as the principle of maximum entropy sampling (Sebastiani and Wynn (2000)). In other words, the most informative manoeuvre is where the predictive distribution has the most spread and uninformative.…”

Section: Designmentioning

confidence: 99%

Adaptive Bayesian Sensor Motion Planning for Hazardous Source Term Reconstruction

Hutchinson

Wen-hua

2017

IFAC-PapersOnLine

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There has been a strong interest in emergency planning in response to an attack or accidental release of harmful chemical, biological, radiological or nuclear substances. Under such circumstances, it is of paramount importance to determine the location and release rate of the hazardous source to forecast the future harm it may cause and employ methods to minimize the disturbance. In this paper, a sensor data collection strategy is proposed whereby an autonomous mobile sensor is guided to address such a problem with a high degree of accuracy and in a short amount of time. First, the parameters of the release source are estimated using the Markov chain Monte Carlo sampling approach. The most informative manoeuvre from the set of possible choices is then selected using the concept of maximum entropy sampling. Numerical simulations demonstrate the superior performance of the proposed algorithm compared to traditional approaches in terms of estimation accuracy and the number of measurements required.

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“…Since 2000 alone, they have been adopted in mixture hazard models (Louzada-Neto et al 2002), spatio-temporal models (Stroud et al 2001), structural equation models (Zhu and Lee 2001), disease mapping (Green and Richardson 2002), analysis of proportions (Brooks 2001), correlated data and clustered models (Chib and Hamilton 2000, Dunson 2000, Chen and Dey 2000, classification and discrimination (Wruck et al 2001), experimental design and analysis (Nobile andGreen 2000, Sebastiani andWynn 2000), random effects generalised linear models (Lenk and DeSarbo 2000) and binary data (Basu and Mukhopadhyay 2000). Mixtures of Weibulls (Tsionas 2002) and Gammas (Wiper et al 2001) have been considered, along with computational issues associated with MCMC methods (Liang and Wong 2001), issues of convergence (Liang and Wong 2001), the display…”

Section: Extensions To the Mixture Frameworkmentioning

confidence: 99%

Bayesian Modelling and Inference on Mixtures of Distributions

Marin¹,

Mengersen²,

Robert³

2005

Handbook of Statistics

330

364

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'But, as you have already pointed out, we do not need any more disjointed clues,' said Bartholomew. 'That has been our problem all along: we have a mass of small facts and small scraps of information, but we are unable to make any sense out of them. The last thing we need is more.' Susanna Gregory, A Summer of Discontent IntroductionToday's data analysts and modellers are in the luxurious position of being able to more closely describe, estimate, predict and infer about complex systems of interest, thanks to ever more powerful computational methods but also wider ranges of modelling distributions. Mixture models constitute a fascinating illustration of these aspects: while within a parametric family, they offer malleable approximations in non-parametric settings; although based on standard distributions, they pose highly complex computational challenges; and they are both easy to constrain to meet identifiability requirements and fall within the class of ill-posed problems. They also provide an endless benchmark for assessing new techniques, from the EM algorithm to reversible jump methodology. In particular, they exemplify the

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Maximum Entropy Sampling and Optimal Bayesian Experimental Design

Cited by 192 publications

References 20 publications

Causal Model Comparison Shows That Human Representation Learning Is Not Bayesian

Causal Model Comparison Shows That Human Representation Learning Is Not Bayesian

Adaptive Bayesian Sensor Motion Planning for Hazardous Source Term Reconstruction

Bayesian Modelling and Inference on Mixtures of Distributions

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