본고는 딥러닝의 이미지 인식 원리와 유아의 이미지 인식 원리를 종합하면서, 이미지-개념 학습을 위한 새로운 교수학습모델, 즉 “베이지안 구조구성주의 교수학습모델”(Bayesian Structure-constructivist Teaching-learning Model: BSTM)을 제안한다. 달리 말하면, 기계학습 원리와 인간학습 원리를 비교함으로써 얻게 되는 시너지 효과를 바탕으로, 유아들의 이미지-개념 학습을 위한 새로운 교수 모델을 구성하는 것을 목표로 한다. 이런 맥락에서 본고는 전체적으로 3가지 차원에서 논의된다. 첫째, 아동의 이미지 학습에 대한 역사적 중요 이론인 “대상 전체론적 가설”, “분류학적 가설”, “배타적 가설”, “기본 수준 범주 가설” 등을 역사 비판적 관점에서 검토한다. 둘째, (...) 컴퓨터 공학에서 전개된 머신러닝의 이미지 학습 원리 및 그 구조의 역사적 변형들에 대해서 비판적으로 분석하면서, 특히 딥러닝의 교육 인식론적 의미를 도출한다. 셋째, 선행하는 논의들을 토대로 이미지와 개념을 연결시키는 학습, 즉 단어학습을 위한 필자의 고유한 이론인 구조구성주의 개념교수모델을 제안한다. 이때 필자는 피아제의 명제논리학적 학습 가설, 즉 논리-수학적 구조를 중시하는 기존의 피아제 학파의 학습 가설과 최근의 베이지안 학습 이론에서 강조된 확률론적 추론 가설, 특히 “교육학적 추론 가설”을 동시에 포함할 수 있는 교수학습모델의 구조 및 주요 지향점들을 제안한다. (shrink)

This study presents a probabilistic model of melody perception, which infers the key of a melody and also judges the probability of the melody itself. The model uses Bayesian reasoning: For any “surface” pattern and underlying “structure,” we can infer the structure maximizing P(structure|surface) based on knowledge of P(surface, structure). The probability of the surface can then be calculated as ∑ P(surface, structure), summed over all structures. In this case, the surface is a pattern of notes; (...) the structure is a key. A generative model is proposed, based on three principles: (a) melodies tend to remain within a narrow pitch range; (b) note‐to‐note intervals within a melody tend to be small; and (c) notes tend to conform to a distribution (or key profile) that depends on the key. The model is tested in three ways. First, it is tested on its ability to identify the keys of a set of folksong melodies. Second, it is tested on a melodic expectation task in which it must judge the probability of different notes occurring given a prior context; these judgments are compared with perception data from a melodic expectation experiment. Finally, the model is tested on its ability to detect incorrect notes in melodies by assigning them lower probabilities than the original versions. (shrink)

In this paper, we present a probabilistic-based method to predict malaria disease at an early stage. Malaria is a very dangerous disease that creates a lot of health problems. Therefore, there is a need for a system that helps us to recognize this disease at early stages through the visual symptoms and from the environmental data. In this paper, we proposed a Bayesian network model to predict the occurrences of malaria disease. The proposed BN model is (...) built on different attributes of the patient’s symptoms and environmental data which are divided into training and testing parts. Our proposed BN model when evaluated on the collected dataset found promising results with an accuracy of 81%. One the other hand, F1 score is also a good evaluation of these probabilistic models because there is a huge variation in class data. The complexity of these models is very high due to the increase of parent nodes in the given influence diagram, and the conditional probability table also becomes more complex. (shrink)

My research program proposes that children have representations and learning mechanisms that can be characterized as causal models of the world Bayesian Fundamentalism.”.

In this paper, we describe a model that learns semantic representations from the distributional statistics of language. This model, however, goes beyond the common bag‐of‐words paradigm, and infers semantic representations by taking into account the inherent sequential nature of linguistic data. The model we describe, which we refer to as a Hidden Markov Topics model, is a natural extension of the current state of the art in Bayesian bag‐of‐words models, that is, the Topics model (...) of Griffiths, Steyvers, and Tenenbaum (2007), preserving its strengths while extending its scope to incorporate more fine‐grained linguistic information. (shrink)

As is clear to any user of software, quality control of software has not reached the same levels of sophistication as it has with traditional manufacturing. In this paper we argue that this is because insufficient thought is being given to the methods of reasoning under uncertainty that are appropriate to this domain. We then describe how we have built a large-scale Bayesian network to overcome the difficulties that have so far been met in software quality control. This exploits (...) a number of recent advances in tool support for constructing large networks. We end the paper by describing how the network was validated and illustrate the range of reasoning styles that can be modelled with this tool. (shrink)

'The Probabilistic Mind' is a follow-up to the influential and highly cited 'Rational Models of Cognition'. It brings together developments in understanding how, and how far, high-level cognitive processes can be understood in rational terms, and particularly using probabilistic Bayesian methods.

Our scientific theories, like our cognitive structures in general, consist of propositions linked by evidential, explanatory, probabilistic, and logical connections. Those theoretical webs ‘impinge on the world at their edges,’ subject to a continuing barrage of incoming evidence. Our credences in the various elements of those structures change in response to that continuing barrage of evidence, as do the perceived connections between them. Here we model scientific theories as Bayesian nets, with credences at nodes and conditional links (...) between them modelled as conditional probabilities. We update those networks, in terms of both credences at nodes and conditional probabilities at links, through a temporal barrage of random incoming evidence. Robust patterns of punctuated equilibrium, suggestive of ‘normal science’ alternating with ‘paradigm shifts,’ emerge prominently in that change dynamics. The suggestion is that at least some of the phenomena at the core of the Kuhnian tradition are predictable in the typical dynamics of scientific theory change captured as Bayesian nets under even a random evidence barrage. (shrink)

Mathematical developments in probabilistic inference have led to optimism over the prospects for Bayesian models of cognition. Our target article calls for better differentiation of these technical developments from theoretical contributions. It distinguishes between Bayesian Fundamentalism, which is theoretically limited because of its neglect of psychological mechanism, and Bayesian Enlightenment, which integrates rational and mechanistic considerations and is thus better positioned to advance psychological theory. The commentaries almost uniformly agree that mechanistic grounding is critical to the (...) success of the Bayesian program. Some commentaries raise additional challenges, which we address here. Other commentaries claim that all Bayesian models are mechanistically grounded, while at the same time holding that they should be evaluated only on a computational level. We argue this contradictory stance makes it difficult to evaluate a model's scientific contribution, and that the psychological commitments of Bayesian models need to be made more explicit. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality (...) assumptions. Through these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition (...) but leaves one’s conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’. (shrink)

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature (...) of the information sources. Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for (...) discrete datasets. The full Bayesian significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

Bayesian paradigm has been widely acknowledged as a coherent approach to learning putative probability model structures from a finite class of candidate models. Bayesian learning is based on measuring the predictive ability of a model in terms of the corresponding marginal data distribution, which equals the expectation of the likelihood with respect to a prior distribution for model parameters. The main controversy related to this learning method stems from the necessity of specifying proper prior distributions (...) for all unknown parameters of a model, which ensures a complete determination of the marginal data distribution. Even for commonly used models, subjective priors may be difficult to specify precisely, and therefore, several automated learning procedures have been suggested in the literature. Here we introduce a novel Bayesian learning method based on the predictive entropy of a probability model, that can combine both subjective and objective probabilistic assessment of uncertain quantities in putative models. It is shown that our approach can avoid some of the limitations of the earlier suggested objective Bayesian methods. (shrink)

We derive a probabilistic account of the vagueness and context-sensitivity of scalar adjectives from a Bayesian approach to communication and interpretation. We describe an iterated-reasoning architecture for pragmatic interpretation and illustrate it with a simple scalar implicature example. We then show how to enrich the apparatus to handle pragmatic reasoning about the values of free variables, explore its predictions about the interpretation of scalar adjectives, and show how this model implements Edgington’s Vagueness: a reader, 1997) account of (...) the sorites paradox, with variations. The Bayesian approach has a number of explanatory virtues: in particular, it does not require any special-purpose machinery for handling vagueness, and it is integrated with a promising new approach to pragmatics and other areas of cognitive science. (shrink)

Natural language is full of patterns that appear to fit with general linguistic rules but are ungrammatical. There has been much debate over how children acquire these “linguistic restrictions,” and whether innate language knowledge is needed. Recently, it has been shown that restrictions in language can be learned asymptotically via probabilistic inference using the minimum description length (MDL) principle. Here, we extend the MDL approach to give a simple and practical methodology for estimating how much linguistic data are required (...) to learn a particular linguistic restriction. Our method provides a new research tool, allowing arguments about natural language learnability to be made explicit and quantified for the first time. We apply this method to a range of classic puzzles in language acquisition. We find some linguistic rules appear easily statistically learnable from language experience only, whereas others appear to require additional learning mechanisms (e.g., additional cues or innate constraints). (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly (...) pragmatic in character and are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

In the literature there are at least two models for probabilistic belief revision: Bayesian updating and imaging [Lewis, D. K. (1973), Counterfactuals, Blackwell, Oxford; Gärdenfors, P. (1988), Knowledge in flux: modeling the dynamics of epistemic states, MIT Press, Cambridge, MA]. In this paper we focus on imaging rules that can be described by the following procedure: (1) Identify every state with some real valued vector of characteristics, and accordingly identify every probabilistic belief with an expected vector of (...) characteristics; (2) For every initial belief and every piece of information, choose the revised belief which is compatible with this information and for which the expected vector of characteristics has minimal Euclidean distance to the expected vector of characteristics of the initial belief. This class of rules thus satisfies an intuitive notion of minimal belief revision. The main result in this paper is to provide an axiomatic characterization of this class of imaging rules. (shrink)

The "myside bias'' in evaluating arguments is an empirically well-confirmed phenomenon that consists of overweighting arguments that endorse one's beliefs or attack alternative beliefs while underweighting arguments that attack one's beliefs or defend alternative beliefs. This paper makes two contributions: First, it proposes a probabilistic model that adequately captures three salient features of myside bias in argument evaluation. Second, it provides a Bayesian justification of this model, thus showing that myside bias has a rational Bayesian (...) explanation under certain conditions. (shrink)

15년 전부터 등장한 베이지안 확률론적 추론 모형은 통계학, 과학철학, 심리학, 인지과학, 컴퓨터과학, 신경과학 등에서 학계의 연구를 지배하는 강력한 핵심논제가 된 후로 이젠 교육학과 심지어는 논리학 분야에까지 큰 반향을 일으키고 있다. 이러한 다양화로 인해, 굿에 따르면, 베이즈주의 유형은 46,656 가지로 분류된다. 이러한 다양한 모형들 중에서 베이지안 확률모형을 학습이론에 적용하려는 학자들은 학습자의 학습 과정이 정확히 베이지안 확률추론 과정을 항상 따른다고 주장한다. 그런데 이러한 확률론적 모형은 피아제의 구성주의적 전망을 계승한 것은 분명하다. 왜냐하면, 이 모델을 지지하는 학자들 자신이 자신들의 학적 운동을 “새로운 합리적 구성주의”라고 (...) 명시적으로 명명하기 때문이다. 그럼에도 불구하고, 이러한 확률론적 학습모형은 “지식은 인과성을 중심으로 구조화된다.”라는 가설을 확고하게 지지하면서, 피아제의 명제 논리적 모형에 의한 학습이론을 강하게 비판한다. 그러나 베이지안 학습 이론가들은 경험을 통한 새로운 항들의 연결로서의 학습, 그리고 학습에서 모순 및 인과성의 역할 등에 대한 피아제의 세부적인 연구 성과들을 놓치고 있다. 다른 한편으로 베이지안 학습이론은 여러 가지 점에서 온전한 발달 이론을 제공하기에는 아직 미흡하다. 이런 점에서, 필자는 현상 없이는 구조를 이해할 수 없듯이, 구조 없이는 현상을 이해할 수 없다는 사실을 강조하면서, 인과성 추론을 핵심으로 하는 베이지안 학습 모델과 인과적 물리적 인식뿐만 아니라, 동시에 논리-수학적 인식 모델을 강조하는 피아제의 학습 모델은 새로이 종합되어야 한다는 것을 논증하고자 한다. (shrink)

Lexical ambiguity can be syntactic if it involves more than one grammatical category for a single word, or semantic if more than one meaning can be associated with a word. In this article we discuss the application of a Bayesian‐network model in the resolution of lexical ambiguities of both types. The network we propose comprises a parsing subnetwork, which can be constructed automatically for any context‐free grammar, and a subnetwork for semantic analysis, which, in the spirit of Fillmore's (...) (1968) case grammars, seeks to fulfill the required cases of all candidates for verb of the sentence. Solving for the highest joint probability of the variables conditioned upon the evidences to the network yields the most likely candidate with its meaning, along with its cases and respective meanings. This is achieved by fixing the values of all evidence nodes concurrently, and then performing a stochastic simulation in which the remaining nodes are updated probabilistically with a high degree of parallelism. The process of disambiguation is directed neither by the syntax nor the semantics, but rather by the interrelation between the two subnetworks. The use of a Bayesian‐network model allows us to express this interrelation between the two subnetworks and among their constituents in a rather direct and rigorous way that, in connection with the convergence properties of the stochastic simulation, reveals a very robust model. (shrink)

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent, (...) whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave. (shrink)

The basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in (...) class='Hi'>Bayesian cognitive science, where probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

The coherentist theory of justification provides a response to the sceptical challenge: even though the independent processes by which we gather information about the world may be of dubious quality, the internal coherence of the information provides the justification for our empirical beliefs. This central canon of the coherence theory of justification is tested within the framework of Bayesian networks, which is a theory of probabilistic reasoning in artificial intelligence. We interpret the independence of the information gathering processes (...) (IGPs) in terms of conditional independences, construct a minimal sufficient condition for a coherence ranking of information sets and assess whether the confidence boost that results from receiving information through independent IGPs is indeed a positive function of the coherence of the information set. There are multiple interpretations of what constitute IGPs of dubious quality. Do we know our IGPs to be no better than randomization processes? Or, do we know them to be better than randomization processes but not quite fully reliable, and if so, what is the nature of this lack of full reliability? Or, do we not know whether they are fully reliable or not? Within the latter interpretation, does learning something about the quality of some IGPs teach us anything about the quality of the other IGPs? The Bayesian-network models demonstrate that the success of the coherentist canon is contingent on what interpretation one endorses of the claim that our IGPs are of dubious quality. (shrink)

When we perceive the external world, our brain has to deal with the incompleteness and uncertainty associated with sensory inputs, memory and prior knowledge. In theoretical neuroscience probabilistic approaches have received a growing interest recently, as they account for the ability to reason with incomplete knowledge and to efficiently describe perceptive and behavioral tasks. How can the probability distributions that need to be estimated in these models be represented and processed in the brain, in particular at the single cell (...) level? We consider the basic function carried out by photoreceptor cells which consists in detecting the presence or absence of light. We give a system-level understanding of the process of phototransduction based on a bayesian formalism: we show that the process of phototransduction is equivalent to a temporal probabilistic inference in a Hidden Markov Model (HMM), for estimating the presence or absence of light. Thus, the biochemical mechanisms of phototransduction underlie the estimation of the current state probability distribution of the presence of light. A classical descriptive model describes the interactions between the different molecular messengers, ions, enzymes and channel proteins occurring within the photoreceptor by a set of nonlinear coupled differential equations. In contrast, the probabilistic HMM model is described by a discrete recurrence equation. It appears that the binary HMM has a general solution in the case of constant input. This allows a detailed analysis of the dynamics of the system. The biochemical system and the HMM behave similarly under steady-state conditions. Consequently a formal equivalence can be found between the biochemical system and the HMM. Numerical simulations further extend the results to the dynamic case and to noisy input. All in all, we have derived a probabilistic model equivalent to a classical descriptive model of phototransduction, which has the additional advantage of assigning a function to phototransduction. The example of phototransduction shows how simple biochemical interactions underlie simple probabilistic inferences. (shrink)

This paper addresses a data integration problem: given several mutually consistent datasets each of which measures a subset of the variables of interest, how can one construct a probabilistic model that fits the data and gives reasonable answers to questions which are under-determined by the data? Here we show how to obtain a Bayesian network model which represents the unique probability function that agrees with the probability distributions measured by the datasets and otherwise has maximum entropy. (...) We provide a general algorithm, OBN-cDS, which offers substantial efficiency savings over the standard brute-force approach to determining the maximum entropy probability function. Furthermore, we develop modifications to the general algorithm which enable further efficiency savings but which are only applicable in particular situations. We show that there are circumstances in which one can obtain the model directly from the data; by solving algebraic problems; and by solving relatively simple independent optimisation problems. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that utilizes a new class of Bayesian learning methods that are better suited to modelling (...) dynamic and conditional inferences than standard Bayesian conditionalization, is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (shrink)

The causal view of categories assumes that categories are represented by features and their causal relations. To study the effect of causal knowledge on categorization, researchers have used Bayesian causal models. Within that framework, categorization may be viewed as dependent on a likelihood computation (i.e., the likelihood of an exemplar with a certain combination of features, given the category's causal model) or as a posterior computation (i.e., the probability that the exemplar belongs to the category, given its features). (...) Across three experiments, in combination with computational modeling, we offer evidence that categorization is better accounted for by assuming that people compute posteriors and not likelihoods, though both probabilities are closely related. This result contrasts with existing analyses of causal-based categorization, which assume that likelihood computations give a good approximation of human judgments. We also find that people are able to compute likelihoods in a closely related task that elicits judgments of consistency rather than category membership judgments. Our analyses show that people do use causal probabilistic information as prescribed by a Bayesian model but that they flexibly compute likelihoods or posteriors depending on the task. We discuss our results in relation to the relevant literature on the topic. (shrink)

Models of category learning have been extensively studied in cognitive science and primarily tested on perceptual abstractions or artificial stimuli. In this paper, we focus on categories acquired from natural language stimuli, that is, words. We present a Bayesian model that, unlike previous work, learns both categories and their features in a single process. We model category induction as two interrelated subproblems: the acquisition of features that discriminate among categories, and the grouping of concepts into categories based (...) on those features. Our model learns categories incrementally using particle filters, a sequential Monte Carlo method commonly used for approximate probabilistic inference that sequentially integrates newly observed data and can be viewed as a plausible mechanism for human learning. Experimental results show that our incremental learner obtains meaningful categories which yield a closer fit to behavioral data compared to related models while at the same time acquiring features which characterize the learned categories. (shrink)

Bayesian cognitive science is a research programme that relies on modelling resources from Bayesian statistics for studying and understanding mind, brain, and behaviour. Conceiving of mental capacities as computing solutions to inductive problems, Bayesian cognitive scientists develop probabilistic models of mental capacities and evaluate their adequacy based on behavioural and neural data generated by humans (or other cognitive agents) performing a pertinent task. The overarching goal is to identify the mathematical principles, algorithmic procedures, and causal mechanisms (...) that enable cognitive agents to take uncertainty into account and weigh it appropriately in producing adaptive behaviour. -/- The appeal of Bayesian cognitive science derives from its transparency, normativity, and unifying power. Resources from Bayesian statistics allow cognitive scientists to characterise transparently, in terms of random variables and probabilistic dependencies between them, the inductive problems that many mental capacities are presumed to solve. Given this characterisation, researchers can define an upper bound on one’s performance on that problem and use it as a benchmark for interpreting experimental results, formulating hypotheses about why and when deviations from optimal performance should be expected, and seeking explanations of mental capacities within one encompassing theoretical framework. -/- Although critics question the testability, explanatory power, and plausibility of Bayesian models of mental capacities, Bayesian cognitive science has proved itself to be an incredibly fruitful research programme. Fuelled by empirical and theoretical results from psychology, neuroscience, philosophy, computer science, artificial intelligence, and evolution, Bayesian cognitive science has: advanced our understanding of why cognitive systems should keep track of uncertainty and use it to facilitate adaptive behaviour; clarified how the brain might encode information about the uncertainty of its stimuli and perform computations with probability distributions; and crystallised the insight that cognitive agents’ management of uncertainty might be grounded in predictive processes aimed at avoiding surprising exchanges with the environment. (shrink)

BackgroundDistorted gambling-related cognitions are tightly related to gambling problems, and are one of the main targets of treatment for disordered gambling, but their etiology remains uncertain. Although folk wisdom and some theoretical approaches have linked them to lower domain-general reasoning abilities, evidence regarding that relationship remains unconvincing.MethodIn the present cross-sectional study, the relationship between probabilistic/abstract reasoning, as measured by the Berlin Numeracy Test, and the Matrices Test, respectively, and the five dimensions of the Gambling-Related Cognitions Scale, was tested in (...) a sample of 77 patients with gambling disorder and 58 individuals without gambling problems.Results and interpretationNeither BNT nor matrices scores were significantly related to gambling-related cognitions, according to frequentist analyses, performed both considering and disregarding group in the models. Correlation Bayesian analyses largely supported the null hypothesis, i.e., the absence of relationships between the measures of interest. This pattern or results reinforces the idea that distorted cognitions do not originate in a general lack of understanding of probability or low fluid intelligence, but probably result from motivated reasoning. (shrink)

This paper studies a fundamental mechanism by which conflicts between arguments are drawn from sentiments regarding acceptability of the arguments. Given sets of arguments, an inverse abstract argumentation problem seeks attack relations between arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in each of the attack relations. It is an inverse problem of the traditional problem we refer to as the forward abstract argumentation problem. Given an attack relation, the forward abstract argumentation (...) problem seeks sets of arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in the attack relation. We give a probabilistic model of argumentation-theoretic inference. It is a generative model formalising the process by which acceptability semantics interprets acceptability of arguments in a given attack relation. We show that it gives a broad view of solutions to the forward and inverse abstract argumentation problems. Specifically, solutions to the inverse and forward abstract argumentation problems are shown to be equivalent to a maximum likelihood estimate and maximum likelihood prediction, respectively, which are both available with the generative model. In addition, they are shown to be special cases of the posterior distribution and the evidence, respectively, which are both obtained by probabilistic inference on the generative model. We report an experiment result and application example of the generative model in the inverse problems. (shrink)

In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and (...) van Fraassen’s erotetic account are incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (shrink)

While Conviction Narrative Theory correctly criticizes utility-based accounts of decision-making, it unfairly reduces probabilistic models to point estimates and treats affect and narrative as mechanistically opaque yet explanatorily sufficient modules. Hierarchically nested Bayesian accounts offer a mechanistically explicit and parsimonious alternative incorporating affect into a single biologically plausible precision-weighted mechanism that tunes decision-making toward narrative versus sensory dependence under varying uncertainty levels.

Using Bayesian network causal models, we provide a simple general account of probabilistic causal interaction. We also detail problems in the leading accounts by Ellery Eells, and any others which require valence reversals, contextual unanimity, or average effects.

Bayesian epistemologists support the norms of probabilism and conditionalization using Dutch book and accuracy arguments. These arguments assume that rationality requires agents to maximize practical or epistemic value in every doxastic state, which is evaluated from a subjective point of view (e.g., the agent’s expectancy of value). The accuracy arguments also presuppose that agents are opinionated. The goal of this paper is to discuss the assumptions of these arguments, including the measure of epistemic value. I have designed AI agents (...) based on the Bayesian model and a nonmonotonic framework and tested how they achieve practical and epistemic value in conditions in which an alternative set of assumptions holds. In one of the tested conditions, the nonmonotonic agent, which is not opinionated and fulfills neither probabilism nor conditionalization, outperforms the Bayesian in the measure of epistemic value that I argue for in the paper (α-value). I discuss the consequences of these results for the epistemology of rationality. (shrink)

This paper provides a model of belief representation in which ambiguity and unambiguity are endogenously distinguished in a purely subjective setting where objects of choices are, as usual, maps from states to consequences. Specifically, I first extend the maxmin expected utility theory and get a representation of beliefs such that the probabilistic beliefs over each ambiguous event are represented by a non-degenerate interval, while the ones over each unambiguous event are represented by a number. I then consider a (...) class of the biseparable preferences. Two representation results are achieved and can be used to identify the unambiguity in the context of the biseparable preferences. Finally a subjective definition of ambiguity is suggested. It provides a choice theoretic foundation for the Knightian distinction between ambiguity and unambiguity. (shrink)

There has been a probabilistic turn in contemporary cognitive science. Far and away, most of the work in this vein is Bayesian, at least in name. Coinciding with this development, philosophers have increasingly promoted Bayesianism as the best normative account of how humans ought to reason. In this paper, we make a push for exploring the probabilistic terrain outside of Bayesianism. Non-Bayesian, but still probabilistic, theories provide plausible competitors both to descriptive and normative Bayesian (...) accounts. We argue for this general idea via recent work on explanationist models of updating, which are fundamentally probabilistic but assign a substantial, non-Bayesian role to explanatory considerations. (shrink)

Genetic Programming is a powerful optimization algorithm, which employs the crossover for genetic operation. Because the crossover operator in GP randomly selects sub-trees, the building blocks may be destroyed by the crossover. Recently, algorithms called PMBGPs based on probabilistic techniques have been proposed in order to improve the problem mentioned above. We propose a new PMBGP employing Bayesian network for generating new individuals with a special chromosome called expanded parse tree, which much reduces a number of possible symbols (...) at each node. Although the large number of symbols gives rise to the large conditional probability table and requires a lot of samples to estimate the interactions among nodes, a use of the expanded parse tree overcomes these problems. Computational experiments on two subjects demonstrate that our new PMBGP is much superior to prior probabilistic models. (shrink)

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the (...) evidence calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen (...) and Winkler Risk Analysis, 19, 187–203, [7]; Dietrich and List [14]; Herzberg Theory and Decision, 1–19, [28]). We argue that this assumption is not always in order. We show how to extend the canonical mathematical framework for pooling to cover pooling with imprecise probabilities by employing set-valued pooling functions and generalizing common pooling axioms accordingly. As a proof of concept, we then show that one IP construction satisfies a number of central pooling axioms that are not jointly satisfied by any of the standard pooling recipes on pain of triviality. Following Levi, 3–11, [39]), we also argue that IP models admit of a much better philosophical motivation as a model of rational consensus. (shrink)

In the Bayesian framework, a language learner should seek a grammar that explains observed data well and is also a priori probable. This paper proposes such a measure of prior probability. Indeed it develops a full statistical framework for lexicalized syntax. The learner's job is to discover the system of probabilistic transformations (often called lexical redundancy rules) that underlies the patterns of regular and irregular syntactic constructions listed in the lexicon. Specifically, the learner discovers what transformations apply in (...) the language, how often they apply, and in what contexts. It considers simpler systems of transformations to be more probable a priori. Experiments show that the learned transformations are more effective than previous statistical models at predicting the probabilities of lexical entries, especially those for which the learner had no direct evidence. (shrink)

On a widely held view, episodes of inner speech provide at least one way in which we become conscious of our thoughts. However, it can be argued, on the one hand, that consciousness of thoughts in virtue of inner speech presupposes interpretation of the simulated speech. On the other hand, the need for such self-interpretation seems to clash with distinctive first-personal characteristics that we would normally ascribe to consciousness of one’s own thoughts: a special reliability; a lack of conscious ambiguity (...) and incomprehensibility; and a sense of causal agency. I try to resolve this puzzle by proposing an account for the requisite self-interpretation of inner speech in terms of Bayesian probabilistic inference. Drawing on “perceptual loop” accounts of speech control, I argue that such interpretive probabilistic inferences are used for the control of inner speech, and that as a consequence of this function, they are biased toward the correct interpretations. I conclude by showing how this model can explain the first-personal characteristics of consciousness of one’s own thoughts. In the case of the sense of causal agency, the resulting explanation yields novel accounts for “audible thoughts” and thought insertion. (shrink)

A consistent finding in research on conditional reasoning is that individuals are more likely to endorse the valid modus ponens (MP) inference than the equally valid modus tollens (MT) inference. This pattern holds for both abstract task and probabilistic task. The existing explanation for this phenomenon within a Bayesian framework (e.g., Oaksford & Chater, 2008) accounts for this asymmetry by assuming separate probability distributions for both MP and MT. We propose a novel explanation within a computational-level Bayesian (...) account of reasoning according to which “argumentation is learning”. We show that the asymmetry must appear for certain prior probability distributions, under the assumption that the conditional inference provides the agent with new information that is integrated into the existing knowledge by minimizing the Kullback-Leibler divergence between the posterior and prior probability distribution. We also show under which conditions we would expect the opposite pattern, an MT-MP asymmetry. (shrink)

This work provides a conceptual foundation for a Bayesian approach to artificial inference and learning. I argue that Bayesian confirmation theory provides a general normative theory of inductive learning and therefore should have a role in any artificially intelligent system that is to learn inductively about its world. I modify the usual Bayesian theory in three ways directly pertinent to an eventual research program in artificial intelligence. First, I construe Bayesian inference rules as defeasible, allowing them (...) to be overridden in certain contexts and therefore allowing them to play a part in a hybrid system, coexisting with non-Bayesian modes of inference. I take seriously the need to find meaningful prior probabilities for hypotheses, and elaborate means for supplying an artificial intelligence with such. And I address the computational complexity of Bayesian inference by reference to simplifications using causal networks and by allowing the probabilistic acceptance of hypotheses and subsequent qualitative inference to supplement Bayesian reasoning. The result is a Pragmatic Bayesian model of induction. (shrink)

Experimental studies of speech production involving compensations for auditory and somatosensory perturbations and adaptation after training suggest that both types of sensory information are considered to plan and monitor speech production. Interestingly, individual sensory preferences have been observed in this context: subjects who compensate less for somatosensory perturbations compensate more for auditory perturbations, and \textit{vice versa}. We propose to integrate this sensory preference phenomenon in a model of speech motor planning using a probabilistic model in which speech (...) units are characterized both in auditory and somatosensory terms. Sensory preference is implemented in the model according to two approaches. In the first approach, which is often used in motor control models accounting for sensory integration, sensory preference is attributed to the relative precision (i.e., inverse of the variance) of the sensory characterization of the speech motor goals associated with phonological units (which are phonemes in the context of this paper). In the second, ``more original’’ variant, sensory preference is implemented by modulating the sensitivity of the comparison between the predicted sensory consequences of motor commands and the sensory characterizations of the phonemes. We present simulation results using these two variants, in the context of the adaptation to an auditory perturbation, implemented in a 2-dimensional biomechanical model of the tongue. Simulation results show that both variants lead to qualitatively similar results. Distinguishing them experimentally would require precise analyses of partial compensation patterns. However, the second proposed variant implements sensory preference without changing the sensory characterizations of the phonemes. This dissociates sensory preference and sensory characterizations of the phonemes, and makes the account of sensory preference more flexible. Indeed, in the second variant the sensory characterizations of the phonemes can remain stable, when sensory preference varies as a response to cognitive or attentional control. This opens new perspectives for capturing speech production variability associated with aging, disorders and speaking conditions. (shrink)

On a widely held view, episodes of inner speech provide at least one way in which we become conscious of our thoughts. However, it can be argued, on the one hand, that consciousness of thoughts in virtue of inner speech presupposes interpretation of the simulated speech. On the other hand, the need for such self-interpretation seems to clash with distinctive first-personal characteristics that we would normally ascribe to consciousness of one’s own thoughts: a special reliability; a lack of conscious ambiguity (...) and incomprehensibility; and a sense of causal agency. I try to resolve this puzzle by proposing an account for the requisite self-interpretation of inner speech in terms of Bayesian probabilistic inference. Drawing on “perceptual loop” accounts of speech control, I argue that such interpretive probabilistic inferences are used for the control of inner speech, and that as a consequence of this function, they are biased toward the correct interpretations. I conclude by showing how this model can explain the first-personal characteristics of consciousness of one’s own thoughts. In the case of the sense of causal agency, the resulting explanation yields novel accounts for “audible thoughts” and thought insertion. (shrink)

Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, (...) e.g., the cosmological constant on the number of observers it allows for. However, uniform probability distributions usually appealed to in such arguments are an inadequate representation of indifference, and lead to unfounded predictions. It has been argued that this inability to represent ignorance is a fundamental flaw of any inductive framework using additive measures. In the first paper, I examine how imprecise probabilities fare as an inductive framework and avoid such unwarranted inferences. In the second paper, I detail how this framework allows us to successfully avoid the conclusions of Doomsday arguments in a way no Bayesian approach that represents credal states by single credence functions could. -/- There are in the cosmology literature several kinds of arguments referring to self- locating uncertainty. In the multiverse framework, different "pocket-universes" may have different fundamental physical parameters. We don’t know if we are typical observers and if we can safely assume that the physical laws we draw from our observations hold elsewhere. The third paper examines the validity of the appeal to the "Sleeping Beauty problem" and assesses the nature and role of typicality assumptions often endorsed to handle such questions. -/- A more general issue for the use of probabilities in cosmology concerns the inadequacy of Bayesian and statistical model selection criteria in the absence of well-motivated measures for different cosmological models. The criteria for model selection commonly used tend to focus on optimizing the number of free parameters, but they can select physically implausible models. The fourth paper examines the possibility for Bayesian model selection to circumvent the lack of well-motivated priors. (shrink)

In criminal trials, evidence often involves a degree of uncertainty and decision-making includes moving from the initial presumption of innocence to inference about guilt based on that evidence. The jurors’ ability to combine evidence and make accurate intuitive probabilistic judgments underpins this process. Previous research has shown that errors in probabilistic reasoning can be explained by a misalignment of the evidence presented with the intuitive causal models that people construct. This has been explored in abstract and context-free situations. (...) However, less is known about how people interpret evidence in context-rich situations such as legal cases. The present study examined participants’ intuitive probabilistic reasoning in legal contexts and assessed how people’s causal models underlie the process of belief updating in the light of new evidence. The study assessed whether participants update beliefs in line with Bayesian norms and if errors in belief updating can be explained by the causal structures underpinning the evidence integration process. The study was based on a recent case in England where a couple was accused of intentionally harming their baby but was eventually exonerated because the child’s symptoms were found to be caused by a rare blood disorder. Participants were presented with a range of evidence, one piece at a time, including physical evidence and reports from experts. Participants made probability judgments about the abuse and disorder as causes of the child’s symptoms. Subjective probability judgments were compared against Bayesian norms. The causal models constructed by participants were also elicited. Results showed that overall participants revised their beliefs appropriately in the right direction based on evidence. However, this revision was done without exact Bayesian computation and errors were observed in estimating the weight of evidence. Errors in probabilistic judgments were partly accounted for, by differences in the causal models representing the evidence. Our findings suggest that understanding causal models that guide people’s judgments may help shed light on errors made in evidence integration and potentially identify ways to address accuracy in judgment. (shrink)

Definitions of syncopation share two characteristics: the presence of a meter or analogous hierarchical rhythmic structure and a displacement or contradiction of that structure. These attributes are translated in terms of a Bayesian theory of syncopation, where the syncopation of a rhythm is inferred based on a hierarchical structure that is, in turn, learned from the ongoing musical stimulus. Several experiments tested its simplest possible implementation, with equally weighted priors associated with different meters and independence of auditory events, which (...) can be decomposed into two terms representing note density and deviation from a metric hierarchy. A computational simulation demonstrated that extant measures of syncopation fall into two distinct factors analogous to the terms in the simple Bayesian model. Next, a series of behavioral experiments found that perceived syncopation is significantly related to both terms, offering support for the general Bayesian construction of syncopation. However, we also found that the prior expectations associated with different metric structures are not equal across meters and that there is an interaction between density and hierarchical deviation, implying that auditory events are not independent from each other. Together, these findings provide evidence that syncopation is a manifestation of a form of temporal expectation that can be directly represented in Bayesian terms and offer a complementary, feature‐driven approach to recent Bayesian models of temporal prediction. (shrink)