Bayesian Learners Research Articles

Play in Cognitive Development: From Rational Constructivism to Predictive Processing.

It is widely believed that play and curiosity are key ingredients as children develop models of the world. There is also an emerging consensus that children are Bayesian learners who combine their structured prior beliefs with estimations of the likelihood of new evidence to infer the most probable model of the world. An influential school of thought within developmental psychology, rational constructivism, combines these two ideas to propose that children learn intuitive theories of how the world works in part by engaging in play activities that allow them to gather new information for testing their theories. There are still, however, at least two pieces missing from rational constructivist theories of development. First, rational constructivism has so far devoted little attention to explaining why children's preferred form of learning, play, feels so fun, enjoyable, and rewarding. Rational constructivism may suggest that children are curious and like to play because reducing uncertainty and learning better theories of the causal workings of the world is enjoyable. What remains unclear, however, is why reducing uncertainty in play is interesting, fun, and joyful, while doing so in other forms of learning can be frustrating or boring. Second, rational constructivism may have overlooked how children, during play, will take control of and manipulate their environment, sometimes in an effort to create ideal niches for surprise-extraction, sometimes for developing strategies for making the world fit with their predictions. These missing elements from rational constructivism can be provided by understanding the contribution of play to development in terms of predictive processing, an influential framework in cognitive neuroscience that models many of the brain's cognitive functions as processes of model-based, probabilistic prediction.

Discerning media bias within a network of political allies and opponents: Disruption by partisans

An individual’s opinions about media bias derive from their own independent assessment of media outputs combined with peer pressure from networked political allies and opponents. Here we generalize previous idealized, probabilistic models of the perception formation process, based on a network of Bayesian learners inferring the bias of a coin, by introducing obdurate agents (partisans), whose opinions stay fixed. It is found that even one partisan destabilizes an allies-only network, stopping it from achieving asymptotic learning and forcing persuadable agents to vacillate indefinitely (turbulent nonconvergence) between the true coin bias θ0 and the partisan’s belief θp. The dwell time td at the partisan’s belief increases, as the partisan fraction f increases, and decreases, when multiple partisans disagree amongst themselves. In opponents-only networks, asymptotic learning occurs, whether or not partisans are present. However, the counterintuitive tendency to reach wrong conclusions first, identified in previous work with zero partisans, does not persist in general for θ0≠θp in complete networks; it is a property of sparsely connected systems (e.g. Barabási–Albert networks with attachment parameter ≲10). In mixed networks containing allies and opponents, partisans drive counterintuitive outcomes, which depend sensitively, on where they reside. A strongly balanced triad exhibits intermittency with a partisan (sudden transitions between long intervals of static beliefs and turbulent nonconvergence) and asymptotic learning without a partisan. Counterintuitively, in an unbalanced triad, one of the persuadable agents achieves asymptotic learning at θ0, when the partisan is located favorably, but is driven away from θ0, when there is no partisan. The above results are interpreted briefly in terms of the social science theory of structural balance.

Learning rules of engagement for social exchange within and between groups

Globalizing economies and long-distance trade rely on individuals from different cultural groups to negotiate agreement on what to give and take. In such settings, individuals often lack insight into what interaction partners deem fair and appropriate, potentially seeding misunderstandings, frustration, and conflict. Here, we examine how individuals decipher distinct rules of engagement and adapt their behavior to reach agreements with partners from other cultural groups. Modeling individuals as Bayesian learners with inequality aversion reveals that individuals, in repeated ultimatum bargaining with responders sampled from different groups, can be more generous than needed. While this allows them to reach agreements, it also gives rise to biased beliefs about what is required to reach agreement with members from distinct groups. Preregistered behavioral (N = 420) and neuroimaging experiments (N = 49) support model predictions: Seeking equitable agreements can lead to overly generous behavior toward partners from different groups alongside incorrect beliefs about prevailing norms of what is appropriate in groups and cultures other than one's own.

Play in predictive minds: A cognitive theory of play.

In this article, we argue that a predictive processing framework (PP) may provide elements for a proximate model of play in children and adults. We propose that play is a behavior in which the agent, in contexts of freedom from the demands of certain competing cognitive systems, deliberately seeks out or creates surprising situations that gravitate toward sweet-spots of relative complexity with the goal of resolving surprise. We further propose that play is experientially associated with a feel-good quality because the agent is reducing significant levels of prediction error (i.e., surprise) faster than expected. We argue that this framework can unify a range of well-established findings in play and developmental research that highlights the role of play in learning, and that casts children as Bayesian learners. The theory integrates the role of positive valence in play (i.e., explaining why play is fun); and what it is to be in a playful mood. Central to the account is the idea that playful agents may create and establish an environment tailored to the generation and further resolution of surprise and uncertainty. Play emerges here as a variety of niche construction where the organism modulates its physical and social environment in order to maximize the productive potential of surprise. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Bayesian learners in gradient boosting for linear mixed models.

Selection of relevant fixed and random effects without prior choices made from possibly insufficient theory is important in mixed models. Inference with current boosting techniques suffers from biased estimates of random effects and the inflexibility of random effects selection. This paper proposes a new inference method "BayesBoost" that integrates a Bayesian learner into gradient boosting with simultaneous estimation and selection of fixed and random effects in linear mixed models. The method introduces a novel selection strategy for random effects, which allows for computationally fast selection of random slopes even in high-dimensional data structures. Additionally, the new method not only overcomes the shortcomings of Bayesian inference in giving precise and unambiguous guidelines for the selection of covariates by benefiting from boosting techniques, but also provides Bayesian ways to construct estimators for the precision of parameters such as variance components or credible intervals, which are not available in conventional boosting frameworks. The effectiveness of the new approach can be observed via simulation and in a real-world application.

Sparse bayesian learning for genomic selection in yeast.

Genomic selection, which predicts phenotypes such as yield and drought resistance in crops from high-density markers positioned throughout the genome of the varieties, is moving towards machine learning techniques to make predictions on complex traits that are controlled by several genes. In this paper, we consider sparse Bayesian learning and ensemble learning as a technique for genomic selection and ranking markers based on their relevance to a trait. We define and explore two different forms of the sparse Bayesian learning for predicting phenotypes and identifying the most influential markers of a trait, respectively. We apply our methods on a Saccharomyces cerevisiae dataset, and analyse our results with respect to existing related works, trait heritability, as well as the accuracies obtained from linear and Gaussian kernel functions. We find that sparse Bayesian methods are not only competitive with other machine learning methods in predicting yeast growth in different environments, but are also capable of identifying the most important markers, including both positive and negative effects on the growth, from which biologists can get insight. This attribute can make our proposed ensemble of sparse Bayesian learners favourable in ranking markers based on their relevance to a trait.

Vacillating about media bias: Changing one’s mind intermittently within a network of political allies and opponents

One form of long-term behavior revealed by opinion dynamics simulations is intermittency, where an individual cycles between eras of stable, constant beliefs and turbulent, fluctuating beliefs, for example when inferring the political bias of a media organization. We explore this phenomenon by building an idealized network of Bayesian learners, who infer the bias of a coin from observations of coin tosses and peer pressure from political allies and opponents. Numerical simulations reveal that three types of network structure lead to three different types of intermittency, which are caused by agents “locking out” opponents from sure beliefs in specific ways. The probability density functions of the dwell times, over which the learners sustain stable or turbulent beliefs, differ across the three types of intermittency. Hence, one can observe the dwell times of a learner to infer the underlying network structure, at least in principle.

On Bayesian integration in sensorimotor learning: Another look at Kording and Wolpert (2004)

Kording and Wolpert (2004), hereafter referred to as KW, describe an experiment where subjects strove for accuracy in a stochastic environment and, on some trials, received mid-trial and post-trial feedback. KW claims that subjects learned the underlying stochastic distribution from the post-trial feedback of previous trials. KW also claims that subjects regarded mid-trial feedback that had a smaller visual size as more precise and they were therefore more sensitive to such mid-trial feedback. KW concludes that the observations are consistent with optimal Bayesian learning. KW has become an extremely influential paper in the large literature arguing that subjects are optimal Bayesian learners in stochastic environments. It is therefore crucial that the KW conclusions follow from their dataset. We note that KW analyzes data that have been both averaged across trials and averaged across other important trial-specific details. We also note that KW mischaracterizes the accuracy of the mid-trial feedback and the relative sizes of the mid-trial feedback. When we analyze the trial-level KW data, we do not find that subjects were more sensitive to mid-trial feedback when it had a smaller visual size. Our trial-level analysis also suggests a recency bias, rather than evidence that the subjects learned the stochastic distribution. In other words, we do not find that the observations are consistent with optimal Bayesian learning. In the KW dataset, it seems that evidence for optimal Bayesian learning is a statistical artifact of analyzing averaged data. Our results from the KW dataset would seem to have important implications for the literature on Bayesian judgments.

Discerning media bias within a network of political allies and opponents: The idealized example of a biased coin

Perceptions of political bias in the media are formed directly, through the independent consumption of the published outputs of a media organization, and indirectly, through observing the collective responses of political allies and opponents to the same published outputs. A network of Bayesian learners is constructed to model this system, in which the bias perceived by each agent obeys a probability density function, which is updated according to Bayes’s theorem given data about the published outputs and the beliefs of the agent’s political allies and opponents. The Bayesian framework allows for uncertain beliefs, multimodal probability distribution functions, and antagonistic interactions with opponents, not just cooperation with allies. Numerical simulations are performed to test the idealized example of inferring the bias of a coin. It is found that some agents converge on the wrong conclusion faster than others converge on the right conclusion under a surprisingly broad range of conditions, when antagonistic interactions are present which “lock out” some agents from the truth, e.g. in Barabási–Albert networks. It is also found that structurally unbalanced networks routinely experience turbulent nonconvergence, where some agents fail to achieve a steady-state belief, e.g. when they are allies of two agents who are opponents themselves. The subtle phenomenon of long-term intermittency is also explored.

The Aggregate Impact of Consumer Reviews on Market Outcome in Differentiated Products Market

We investigate the aggregate impact of consumer reviews on market outcome in a differentiated product category. We model consumers as Bayesian learners who use online consumer reviews to learn and update their beliefs on product quality before their choice. For our empirical analysis, we use aggregate-level, longitudinal data from Amazon.com in the digital camcorder category and estimate the demand parameters. Using model estimates, we conduct two simulation studies and quantify the impact of consumer reviews on the market outcome. We report that the products experience heterogenous market share changes: the standard deviation of market share changes across products and time is 16.7%, ranging from -40% to 20%. In addition, consistent with the previous findings in experience goods, the marginal effect of low consumer ratings is greater than that of high consumer ratings. We discuss model limitations and offer directions for further research.

Alleviating the independence assumptions of averaged one-dependence estimators by model weighting

Of numerous proposals to refine naive Bayes by weakening its attribute independence assumption, averaged one-dependence estimators (AODE) has been shown to be able to achieve significantly higher classification accuracy at a moderate cost in classification efficiency. However, all one-dependence estimators (ODEs) in AODE have the same weights and are treated equally. To address this issue, model weighting, which assigns discriminate weights to ODEs and then linearly combine their probability estimates, has been proved to be an efficient and effective approach. Most information-theoretic weighting metrics, including mutual information, Kullback-Leibler measure and the information gain, place more emphasis on the correlation between root attribute (value) and class variable. We argue that the topology of each ODE can be divided into a set of local directed acyclic graphs (DAGs) based on the independence assumption, and multivariate mutual information is introduced to measure the extent to which the DAGs fit data. Based on this premise, in this study we propose a novel weighted AODE algorithm, called AWODE, that adaptively selects weights to alleviate the independence assumption and make the learned probability distribution fit the instance. The proposed approach is validated on 40 benchmark datasets from UCI machine learning repository. The experimental results reveal that, AWODE achieves bias-variance trade-off and is a competitive alternative to single-model Bayesian learners (such as TAN and KDB) and other weighted AODEs (such as WAODE).

The influence of sample size on preferences from experience.

People often learn from experience about the distribution of outcomes of risky options. Typically, people draw small samples, when they can actively sample information from risky gambles to make decisions. We examine how the size of the sample that people experience in decision from experience affects their preferences between risky options. In two studies (N = 40 each), we manipulated the size of samples that people could experience from risky gambles and measured subjective selling prices and the confidence in selling price judgements after sampling. The results show that, on average, sample size influenced neither the selling prices nor confidence. However, cognitive modelling of individual-level learning showed that around half of the participants could be classified as Bayesian learners, whereas the other half adhered to a frequentist learning strategy and that if learning was cognitively simpler more participants adhered to the latter. The observed selling prices of Bayesian learners changed with sample size as predicted by Bayesian principles, whereas sample size affected the judgements of frequentist learners much less. These results illustrate the variability in how people learn from sampled information and provide an explanation for why sample size often does not affect judgements.

Asymptotic behavior of Bayesian learners with misspecified models

We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This framework has become increasingly popular in economics to study behavior driven by incorrect or biased beliefs. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a differential inclusion that describes the evolution of the frequency of actions. We then present a series of implications that can be readily applied to economic applications, thus providing off-the-shelf tools that can be used to characterize behavior under misspecified learning.

A novel technology adoption in an OLG framework: examining the cross-generational effects of promotional policies

We posit and analyse an inter-temporal decision-making problem associated with adopting a novel environmental-friendly (green) technology to replace a conventional one. Our analysis uses an overlapping generations model that incorporates credit market imperfections and adoptees’ bequest levels. In our model, technological returns are stochastic in nature and the adoptees are Bayesian learners. We solve for a stationary equilibrium for the mass of novel-technology adoptees and identify two effects that govern our results: (i) strategic substitutability effect and (ii) crowding out effect. Our results suggest that promotional measures to expedite the mass adoption of the novel technology need to be carefully implemented as they can have unforeseen inter-generational impacts arising from the interaction of the two effects. Our findings are especially relevant in the ongoing fight against climate change, particularly given the inter-generational nature of the costs and consequences involved in this fight to preserve the future of our planet.

On Bayesian integration in sensorimotor learning: Another look at Kording and Wolpert (2004)

Kording and Wolpert (2004), hereafter referred to as KW, describe an experiment where subjects engaged in a repeated task entailing movements of their finger. Subjects strove for accuracy in the stochastic environment and, on some trials, received mid-trial and post-trial feedback. KW claims that subjects learned the underlying stochastic distribution from the post-trial feedback of previous trials. KW also claims that subjects regarded mid-trial feedback that had a smaller visual size as more precise and they were therefore more sensitive to such mid-trial feedback. KW concludes that the observations are consistent with optimal Bayesian learning. Indeed, under mild assumptions, it is well-known that Bayesian learners will have posterior beliefs that converge to the true distribution. We note that the KW analysis is based on data that had been averaged across important trial-specific details and averaged across trials. Averaging data disregards possibly valuable information and its dangers have been known for some time. Notably, the KW analysis does not exclude non-Bayesian explanations. When we analyze the trial-level KW data, we find that subjects were less--not more--sensitive to mid-trial feedback when it had a smaller visual size. Our trial-level analysis also suggests a recency bias, rather than evidence that the subjects learned the stochastic distribution. In other words, we do not find that the observations are consistent with optimal Bayesian learning. In the KW dataset, it seems that evidence for optimal Bayesian learning is a statistical artifact of analyzing averaged data.

A real-time crash prediction fusion framework: An imbalance-aware strategy for collision avoidance systems

Real-time traffic crash prediction has been a major concern in the development of Collision Avoidance Systems (CASs) along with other intelligent and resilient transportation technologies. There has been a pronounced progress in the use of machine learning models for crash events assessment by the transportation safety research community in recent years. However, little attention has been paid so far to evaluating real-time crash occurrences within information fusion systems. The main aim of this paper is to design and validate an ensemble fusion framework founded on the use of various base classifiers that operate on fused features and a Meta classifier that learns from base classifiers’ results to acquire more performant crash predictions. A data-driven approach was adopted to investigate the potential of fusing four real-time and continuous categories of features namely physiological signals, driver maneuvering inputs, vehicle kinematics and weather covariates in order to systematically identify the crash strongest precursors through feature selection techniques. Moreover, a resampling-based scheme, including Bagging and Boosting, is conducted to generate diversity in learner combinations comprising Bayesian Learners (BL), k-Nearest Neighbors (kNN), Support Vector Machine (SVM) and Multilayer Perceptron (MLP). To ensure that the proposed framework provide powerful and stable decisions, an imbalance-learning strategy was adopted using the Synthetic Minority Oversampling TEchnique (SMOTE) to address the class imbalance problem as crash events usually occur in rare instances. The findings show that Boosting depicted the highest performance within the fusion scheme and can accomplish a maximum of 93.66% F1 score and 94.81% G-mean with Naïve Bayes, Bayesian Networks, k-NN and SVM with MLP as the Meta-classifier. To the best of our knowledge, this work presents the first attempt at establishing a fusing framework on the basis of data from the four aforementioned categories and fusion models while accounting for class imbalance. Overall, the method and findings provide new insights into crash prediction and can be harnessed as a promising tool to improve intervention efforts related to traffic intelligent transportation systems.

Design of Platform Reputation Systems: Optimal Information Disclosure

Reputation systems play a central role in a variety of marketplaces to eliminate information asymmetry between sellers and buyers. Despite their crucial role, the design of reputation systems remains a complicated issue. Some platforms try to disclose as much product information as possible through their reputation systems, by encouraging consumers to leave reviews or ratings. In contrast, some platforms disclose only partial product information to the public. Platforms, as the designers of such reputation systems, are thus an additional player added to conventional seller-buyer games. This paper studies the optimal information disclosure in a reputation system from the platform's profit standpoint. In a three-player game, sellers with different base quality decide investment in quality, the platform decides the amount of information about the product quality (i.e., ratings) to disclose through its reputation system, and the future consumer as the receiver makes the purchase decision after observing the information about the product quality. By modeling consumers as Bayesian learners, we specify conditions under which withholding some private information of the sellers can serve the platform's goal of maximizing profits by incentivizing seller investment in quality. We find that, although fully disclosing information can eliminate information asymmetry, it may hinder the sellers' incentive to invest in quality, which hurts the platform's profits. Two main effects are in favor of withholding private information: the quality improving effect, which makes sellers more willing to invest in quality, and the sales increasing effect, which leads to more transactions on the platform.

Incumbent Tenure Crowds Out Economic Voting

AbstractDoes the importance of the economy change during a government's time in office? Governments arguably become more responsible for current economic conditions as their tenure progresses. This might lead voters to hold experienced governments more accountable for economic conditions. However, voters also accumulate information about governments' competence over time. If voters are Bayesian learners, then this growing stock of information should crowd out the importance of current economic conditions. This article explores these divergent predictions about the relationship between tenure and the economic vote using three datasets. First, using country-level data from a diverse set of elections, the study finds that support for more experienced governments is less dependent on economic growth. Secondly, using individual-level data from sixty election surveys covering ten countries, the article shows that voters' perceptions of the economy have a greater impact on government support when the government is inexperienced. Finally, the article examines a municipal reform in Denmark that assigned some voters to new local incumbents and finds that these voters responded more strongly to the local economy. In conclusion, all three studies point in the same direction: economic voting decreases with time in office.

Text analytics based severity prediction of software bugs for apache projects

Severity i.e impact, extent and effect on software is a decisive attribute which decides how instantly the bug should be fixed. Predicting the severity of software bugs is important to improve the bug triaging and resolution process. To reduce the effort and time required in manual assessment of severity of newly reported bugs, many techniques and methods are used in past researches. To help software developers to utilize their resources efficiently, this study evaluates a number of machine learning techniques for predicting the severity of software bugs at system and component level. The techniques are evaluated on thirteen apache projects automatically extracted using the Bug Report Collection System tool. Severity is predicted based on the most frequent terms extracted from the summary of bugs using text mining. Performance metrics such as precision, recall and accuracy are used to interpret the results obtained from various techniques. The result of the study advocates that Boosting (an ensemble learner) technique outperforms other machine learning techniques such as Bayesian learners, decision tree, support vector machine applied in previous researches.

Orb-web spiders as Bayesian learners.

Orb-web spiders typically construct their webs with a vertical asymmetry: the hub, or meeting point of the radial threads, is often above the geometric center of the web. Previous explanations for this asymmetry involve differences in up/down running speed and mass, but fail to account adequately for ontogenetic changes in vertical asymmetry. The current article argues that the hub location is determined so as to maximize the expected number of prey and is updated, partially, in response to predation experience. A Bayesian model of spider learning from predation experience is presented and shown to be alone a better fit than spider mass to an existing empirical dataset. Combining this Bayesian model with the extant results on spider mass and differential running speeds ought to provide more thorough explanations for observed web asymmetry. The results of this theory-driven work positions orb-web spiders as a potentially ideal study family for animal Bayesian learning: predation experience is manifest in the spider's orb-web geometry, which is updated frequently, and is readily quantifiable. Spider orb webs ought to facilitate further theoretical and empirical work in animal cognition and learning.