Inverse Bayesian inference in swarming behaviour of soldier crabs

Gunji, Yukio Pegio; Murakami, Hisashi; Tomaru, Takenori; Basios, Vasileios

doi:10.1098/rsta.2017.0370

Cited by 23 publications

(26 citation statements)

References 51 publications

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“…This 392 coincides with the maximum likelihood estimation. In contrast, when , the present formula coincides = 0 393 with the Bayesian inference expressed in formula (5) 20. 394A comparison of formula (5) with formula (24) reveals that their difference lies in the presence or 395 absence of on the right side, because can be regarded as a constant.…”

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confidence: 56%

“…Here, we can see that the denominator on the right side is the weighted average of and , At this step, formula (20) for inverse Bayesian inference can also be rewritten as follows.…”

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confidence: 99%

“…= 0 ( | ) 381 These considerations suggest that becomes larger according to increase of updates to the model. 382 In this sense, we can say that formula (20) for inverse Bayesian inference during the steady period represents 383 a process of learning, and corresponds to the rate of learning. 384 With respect to the portion that corresponds to Bayesian inference, suppose in the formula m = -1 385 (7), then we can rewrite it as:…”

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Extended Bayesian inference incorporating symmetry bias

Shinohara

Manome

Suzuki

et al. 2019

Preprint

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2In this study, we start by proposing a causal induction model that incorporates symmetry bias. This 3 model is important in two aspects. First, it can reproduce causal induction of human judgment with higher 4 accuracy than conventional models. Second, it allows us to estimate the level of symmetry bias of subjects 5 from experimental data. We further propose an inference method that incorporates the aforementioned causal 6 induction model into Bayesian inference. In this method, the component of Bayesian inference, which 7 updates the degree of confidence for each hypothesis, and the component of inverse Bayesian inference that 8 modifies the model of the hypothesis coexist. Our study demonstrates that inverse Bayesian inference enables 9 us to deal flexibly with unstable situations where the object of inference changes from time to time. 10 11 Author summary 12 We acquire knowledge through learning and make various inferences based on such knowledge and 13 observational data (evidence). If the evidence is insufficient, then the certainty of the conclusion will decline. 14 Moreover, even if the evidence is sufficient, the conclusion may be wrong if the knowledge is incomplete in 15 the first place. In order to model such inference based on incomplete knowledge, we proposed an inference 16 system that performs learning and inference simultaneously and seamlessly. Prepare two coins A and B with 17 different probabilities of landing heads, and repeat the coin toss using either of them. However, the coin that 18 is being tossed is also replaced repeatedly. The system observes only the result of coin toss each time, and 19 estimates the probability of landing heads of coin tossed at the moment. In this task, it is necessary not only 20 to estimate the probabilities of the landing heads of coin A and B, but also to estimate which coin is being 21 used at the moment. In this paper, we show that the proposed system handles such tasks very efficiently by 22 simultaneously performing inference and learning. 23 24 25As a cognitive bias observed in humans, the disposition to infer from 'if P then Q' to 'if Q then P' 26 or to 'if not P, then not Q' is well documented [1, 2, 3, 4, 5, 6, 7, 8]. The former is termed symmetry bias [9] 27 and the latter is termed mutual exclusivity bias [4]. 28 Consider a simple example. We tend to infer from 'if you clean the room, then I will take you out' 29 to 'I will take you out if and only if you clean the room' or 'if you don't clean the room, then I will not take 30 you out'. Although these inferences are invalid according to classical logic, various people are inclined to 31 make them regardless of age. 32 In contrast, among non-human animals, the symmetry bias has been reported in behaviour of only 33 some California sea lions [10] and chimpanzees [11]. Although the symmetry bias produces wrong inferences 34 from the classical logic point of view, humans do show some positive features apparently stemming from the 35 symmetry bias. For instance, once you are able to respond to th...

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mentioning

confidence: 56%

“…Here, we can see that the denominator on the right side is the weighted average of and , At this step, formula (20) for inverse Bayesian inference can also be rewritten as follows.…”

mentioning

confidence: 99%

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confidence: 99%

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Extended Bayesian inference incorporating symmetry bias

Shinohara

Manome

Suzuki

et al. 2019

Preprint

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“…as inverse Bayesian 257 inference [21][22][23][24]. If the former process of updating the confidences for hypotheses is referred to as 258 inference, inverse Bayesian inference can be called "learning" because it forms a model for a hypothetical 259 instead of an inference.…”

Section: Extended Bayesian Inferencementioning

confidence: 99%

“…Taking the logarithm of both sides of formula (23) in the EBI, the following transformation can be made.…”

Section: Extended Bayesian Inferencementioning

confidence: 99%

A new method of Bayesian causal inference in non-stationary environments

Shinohara

Manome

Suzuki

et al. 2019

Preprint

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15 16 AUTHOR CONTRIBUTIONS STATEMENT 17 S. S. conceived the extended confidence model and the extended Bayesian inference, conducted the 18 meta-analysis and the simulation, wrote the manuscript. U. C., T. T., and H. O revised it. N. M., K. S., U. 19 C., T. T., H. O., P.Y.G., Y. N., and S. M. contributed to the interpretation of the study findings. All authors 20 participated in the editing and revision of the final version of the manuscript.21 22 23Bayesian inference is the process of narrowing down the hypotheses (causes) to the one that best explains 24 the observational data (effects). To accurately estimate a cause, a considerable amount of data is required to 25 be observed for as long as possible. However, the object of inference is not always constant. In this case, a 26 method such as exponential moving average (EMA) with a discounting rate is used to improve the ability to 27 respond to a sudden change; it is also necessary to increase the discounting rate. That is, a trade-off is 28 established in which the followability is improved by increasing the discounting rate, but the accuracy is 29 reduced. Here, we propose an extended Bayesian inference (EBI), wherein human-like causal inference is 30 incorporated. We show that both the learning and forgetting effects are introduced into Bayesian inference 31 by incorporating the causal inference. We evaluate the estimation performance of the EBI through the 32 learning task of a dynamically changing Gaussian mixture model. In the evaluation, the EBI performance is 33 compared with those of the EMA and a sequential discounting expectation-maximization algorithm. The 34 EBI was shown to modify the trade-off observed in the EMA. 35 36 42 down hypotheses (causal candidates) to one that best explains the observational data (the effects). 43 As an example, consider a situation in which one attempts to read another's emotions. Because one 44 cannot directly view another's emotions, they can only be inferred from external cues (observation data), 45 such as facial expressions and voice tones. The unknown emotions correspond to the hypotheses in 46 Bayesian inference; i.e., it is the inferred target. In addition, a probability distribution representing what 47 "smile," the emotion of "joy" is presumed as the cause of the "smile." 52Attention should be paid to the following two points. First, to infer someone's emotions more accurately, 53 it is better to have as much observation data as possible, but only if it is ensured that the emotion will not 54 change during the estimation. Emotions change from moment to moment. In such an unsteady situation, it 55 is necessary to consider whether the observation data are derived from the same emotion throughout the 56 period being observed for the estimation. This may be a problem with online clustering of non-stationary 57 data. The second point is that because a model for a stranger cannot be given in advance, it is necessary to 58 learn and construct it from observed data. If this model is wrong, one cannot obtain the...

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