Multi-source multi-modal markers for Bayesian Networks: Application to the extremely preterm born brain

The preterm phenotype results from the interplay of multiple disorders affecting the brain and cognitive outcomes. Accurately characterising these interactions can reveal prematurity markers. Bayesian Networks (BNs) are powerful tools to disentangle these relationships, as they inherently measure associations between variables while mitigating confounding factors. We present Modified PC-HC (MPC-HC), a Bayesian Network (BN) structural learning algorithm. MPC-HC employs statistical testing and search-and-score techniques to explore equivalent classes. We employ MPC-HC to estimate BNs for extremely preterm (EP) young adults and full-term controls. Using MRI measurements and cognitive performance markers, we investigate predictive relationships and mutual influences through predictions and sensitivity analysis. We assess the confidence in the estimated BN structures using bootstrapping. Furthermore, MPC-HC's validation involves assessing its ability to recover benchmark BN structures. MPC-HC achieves an average prediction accuracy of 72.5% compared to 62.5% of PC, 64.5% of MMHC, and 71.5% of HC, while it outperforms PC, MMHC, and HC algorithms in reconstructing the true structure of benchmark BNs. The sensitivity analysis shows that MRI measurements mainly affect EP cognitive scores. Our work has two key contributions: first, the introduction and validation of a new BN structure learning method. Second, demonstrating the potential of BNs in modelling variable relationships, predicting variables of interest, modelling uncertainty, and evaluating how variables impact each other. Finally, we demonstrate this by characterising complex phenotypes, such as preterm birth, and discovering results consistent with literature findings.

Federated inference and belief sharing

This paper concerns the distributed intelligence or federated inference that emerges under belief-sharing among agents who share a common world-and world model. Imagine, for example, several animals keeping a lookout for predators. Their collective surveillance rests upon being able to communicate their beliefs-about what they see-among themselves. But, how is this possible? Here, we show how all the necessary components arise from minimising free energy. We use numerical studies to simulate the generation, acquisition and emergence of language in synthetic agents. Specifically, we consider inference, learning and selection as minimising the variational free energy of posterior (i.e., Bayesian) beliefs about the states, parameters and structure of generative models, respectively. The common theme-that attends these optimisation processes-is the selection of actions that minimise expected free energy, leading to active inference, learning and model selection (a.k.a., structure learning). We first illustrate the role of communication in resolving uncertainty about the latent states of a partially observed world, on which agents have complementary perspectives. We then consider the acquisition of the requisite language-entailed by a likelihood mapping from an agent's beliefs to their overt expression (e.g., speech)-showing that language can be transmitted across generations by active learning. Finally, we show that language is an emergent property of free energy minimisation, when agents operate within the same econiche. We conclude with a discussion of various perspectives on these phenomena; ranging from cultural niche construction, through federated learning, to the emergence of complexity in ensembles of self-organising systems.

The scaling of mental computation in a sorting task

Many cognitive models provide valuable insights into human behavior. Yet the algorithmic complexity of candidate models can fail to capture how human reaction times scale with increasing input complexity. In the current work, we investigate the algorithms underlying human cognitive processes. Computer science characterizes algorithms by their time and space complexity scaling with problem size. We propose to use participants' reaction times to study how human computations scale with increasing input complexity. We tested this approach in a task where participants had to sort sequences of rectangles by their size. Our results showed that reaction times scaled close to linearly with sequence length and that participants learned and actively used latent structure whenever it was provided. This behavior was in line with a computational model that used the observed sequences to form hypotheses about the latent structures, searching through candidate hypotheses in a directed fashion. These results enrich our understanding of plausible cognitive models for efficient mental sorting and pave the way for future studies using reaction times to investigate the scaling of mental computations across psychological domains.

Potential cognitive and neural benefits of a computerised cognitive training programme based on Structure Learning in healthy adults: study protocol for a randomised controlled trial

BACKGROUND

Cognitive flexibility refers to the capacity to shift between conceptual representations particularly in response to changes in instruction and feedback. It enables individuals to swiftly adapt to changes in their environment and has significant implications for learning. The present study focuses on investigating changes in cognitive flexibility following an intervention programme-Structure Learning training.

METHODS

Participants are pseudo-randomised to either the Training or Control group, while matched on age, sex, intelligence and cognitive flexibility performance. In the Training group, participants undergo around 2 weeks of training (at least 13 sessions) on Structure Learning. In the Control group, participants do not have to undergo any training and are never exposed to the Structure Learning task. The effects of Structure Learning training are investigated at both the behavioural and neural level. We measured covariates that can influence an individual's training performance before the training phase and outcome measures that can potentially show training benefits after the training phase. At the behavioural level, we investigated outcomes in both cognitive and social aspects with a primary focus on executive functions. At the neural level, we employed a multimodality approach and investigated potential changes to functional connectivity patterns, neurometabolite concentration in the frontal brain regions, and brain microstructure and myelination.

DISCUSSION

We reported the development of a novel training programme based on Structure Learning that aims to hone a general learning ability to potentially achieve extensive transfer benefits across various cognitive constructs. Potential transfer benefits can be exhibited through better performance in outcome measures between Training and Control participants, and positive associations between training performance and outcomes after the training in Training participants. Moreover, we attempt to substantiate behavioural findings with evidence of neural changes across different imaging modalities by the Structure Learning training.

TRIAL REGISTRATION

National Institutes of Health U.S. National Library of Medicine ClinicalTrials.gov NCT05611788. Registered on 7 November 2022.

PROTOCOL VERSION

11 May 2023.

Bayesian Coherence Analysis for Microcircuit Structure Learning

Functional microcircuits model the coordinated activity of neurons and play an important role in physiological computation and behaviors. Most existing methods to learn microcircuit structures are correlation-based and often generate dense microcircuits that cannot distinguish between direct and indirect association. We treat microcircuit structure learning as a Markov blanket discovery problem and propose Bayesian Coherence Analysis (BCA) which utilizes a Bayesian network architecture called Bayesian network with inverse-tree structure to efficiently and effectively detect Markov blankets for high-dimensional neural activity data. BCA achieved balanced sensitivity and specificity on simulated data. For the real-world anterior lateral motor cortex study, BCA identified microcircuit subtypes that predicted trial types with an accuracy of 0.92. BCA is a powerful method for microcircuit structure learning.

Adaptive learning is structure learning in time

People use information flexibly. They often combine multiple sources of relevant information over time in order to inform decisions with little or no interference from intervening irrelevant sources. They adjust the degree to which they use new information over time rationally in accordance with environmental statistics and their own uncertainty. They can even use information gained in one situation to solve a problem in a very different one. Learning flexibly rests on the ability to infer the context at a given time, and therefore knowing which pieces of information to combine and which to separate. We review the psychological and neural mechanisms behind adaptive learning and structure learning to outline how people pool together relevant information, demarcate contexts, prevent interference between information collected in different contexts, and transfer information from one context to another. By examining all of these processes through the lens of optimal inference we bridge concepts from multiple fields to provide a unified multi-system view of how the brain exploits structure in time to optimize learning.

Learning Bayesian networks from demographic and health survey data

Child mortality from preventable diseases such as pneumonia and diarrhoea in low and middle-income countries remains a serious global challenge. We combine knowledge with available Demographic and Health Survey (DHS) data from India, to construct Causal Bayesian Networks (CBNs) and investigate the factors associated with childhood diarrhoea. We make use of freeware tools to learn the graphical structure of the DHS data with score-based, constraint-based, and hybrid structure learning algorithms. We investigate the effect of missing values, sample size, and knowledge-based constraints on each of the structure learning algorithms and assess their accuracy with multiple scoring functions. Weaknesses in the survey methodology and data available, as well as the variability in the CBNs generated by the different algorithms, mean that it is not possible to learn a definitive CBN from data. However, knowledge-based constraints are found to be useful in reducing the variation in the graphs produced by the different algorithms, and produce graphs which are more reflective of the likely influential relationships in the data. Furthermore, valuable insights are gained into the performance and characteristics of the structure learning algorithms. Two score-based algorithms in particular, TABU and FGES, demonstrate many desirable qualities; (a) with sufficient data, they produce a graph which is similar to the reference graph, (b) they are relatively insensitive to missing values, and (c) behave well with knowledge-based constraints. The results provide a basis for further investigation of the DHS data and for a deeper understanding of the behaviour of the structure learning algorithms when applied to real-world settings.

Incidental binding between predictive relations

Knowledge of predictive relations is a core aspect of learning. Beyond individual relations, we also represent intuitive theories of the world, which include interrelated sets of relations. We asked whether individual predictive relations learned incidentally in the same context become associatively bound and whether they spontaneously influence later learning. Participants performed a cover task while watching three sequences of events. Each sequence contained the same set of events, but differed in how the events related to each other. The first two sequences each had two strong predictive relations (R1 & R2, and R3 & R4). The third contained either a consistent pairing of relations (R1 & R2) or an inconsistent pairing (R1 & R3). We found that participants' learning of the individual relations in the third sequence was affected by pairing consistency, suggesting the mind associates relations to each other as part of the intrinsic way it learns about the world. This was despite participants' minimal ability to verbally describe most of the relations they had learned. Thus, participants spontaneously developed the expectation that pairs of relations should cohere, and this affected their ability to learn new evidence. Such associative binding of relational information may help us build intuitive theories.

Finding structure in multi-armed bandits

How do humans search for rewards? This question is commonly studied using multi-armed bandit tasks, which require participants to trade off exploration and exploitation. Standard multi-armed bandits assume that each option has an independent reward distribution. However, learning about options independently is unrealistic, since in the real world options often share an underlying structure. We study a class of structured bandit tasks, which we use to probe how generalization guides exploration. In a structured multi-armed bandit, options have a correlation structure dictated by a latent function. We focus on bandits in which rewards are linear functions of an option's spatial position. Across 5 experiments, we find evidence that participants utilize functional structure to guide their exploration, and also exhibit a learning-to-learn effect across rounds, becoming progressively faster at identifying the latent function. Our experiments rule out several heuristic explanations and show that the same findings obtain with non-linear functions. Comparing several models of learning and decision making, we find that the best model of human behavior in our tasks combines three computational mechanisms: (1) function learning, (2) clustering of reward distributions across rounds, and (3) uncertainty-guided exploration. Our results suggest that human reinforcement learning can utilize latent structure in sophisticated ways to improve efficiency.

Structure learning and the posterior parietal cortex

We propose a theory of structure learning in the primate brain. We argue that the parietal cortex is critical for learning about relations among the objects and categories that populate a visual scene. We suggest that current deep learning models exhibit poor global scene understanding because they fail to perform the relational inferences that occur in the primate dorsal stream. We review studies of neural coding in primate posterior parietal cortex (PPC), drawing the conclusion that neurons in this brain area represent potentially high-dimensional inputs on a low-dimensional manifold that encodes the relative position of objects or features in physical space, and relations among entities in abstract conceptual space. We argue that this low-dimensional code supports generalisation of relational information, even in nonspatial domains. Finally, we propose that structure learning is grounded in the actions that primates take when they reach for objects or fixate them with their eyes. We sketch a model of how this might occur in neural circuits.

GatewayNet: a form of sequential rule mining

Background

The gateway hypothesis (and particularly the prediction of developmental stages in drug abuse) has been a subject of protracted debate since the 1970s. Extensive research has gone into this subject, but has yielded contradictory findings. We propose an algorithm for detecting both association and causation relationships given a discrete sequence of events, which we believe will be useful in addressing the validity of the gateway hypothesis.

To assess the gateway hypothesis, we developed the GatewayNet algorithm, a refinement of sequential rule mining called initiation rule mining. After a brief mathematical definition, we describe how to perform initiation rule mining and how to infer causal relationships from its rules (“gateway rules”).

We tested GatewayNet against data for which relationships were known. After constructing a transaction database using a first-order Markov chain, we mined it to produce a gateway network. We then discuss various incarnations of the gateway network.

We then evaluated the performance of GatewayNet on urine drug screening data collected from the emergency department at LSU Health Sciences Center in Shreveport. A de-identified database of urine drug screenings ordered by the department between August 1998 and June 2011 was collected and then restricted to patients having at least one screening succeeding their first positive drug screening result.

Results

In the synthetic data, a chain of gateway rules was found in the network which demonstrated causation. We did not find any evidence of gateway rules in the empirical data, but we were able to isolate two documented transitions into benzodiazepine use.

Conclusions

We conclude that GatewayNet may show promise not only for substance use data, but other data involving sequences of events. We also express future goals for GatewayNet, including optimizing it for speed.

Electronic supplementary material

The online version of this article (10.1186/s12911-019-0810-3) contains supplementary material, which is available to authorized users.

How the inference of hierarchical rules unfolds over time

Inductive reasoning, which entails reaching conclusions that are based on but go beyond available evidence, has long been of interest in cognitive science. Nevertheless, knowledge is still lacking as to the specific cognitive processes that underlie inductive reasoning. Here, we shed light on these processes in two ways. First, we characterized the timecourse of inductive reasoning in a rule induction task, using pupil dilation as a moment-by-moment measure of cognitive load. Participants' patterns of behavior and pupillary responses indicated that they engaged in rule inference on-line, and were surprised when additional evidence violated their inferred rules. Second, we sought to gain insight into how participants represented rules on this task - specifically, whether they would structure the rules hierarchically when possible. We predicted the cognitive load imposed by hierarchical representations, as well as by non-hierarchical, flat ones. We used task-evoked pupil dilation as a metric of cognitive load to infer, based on these predictions, which participants represented rules with flat or hierarchical structures. Participants categorized as representing the rules hierarchically or flat differed in task performance and self-reports of strategy. Hierarchical rule representation was associated with more efficient performance and more pronounced pupillary responses to rule violations on trials that afford a higher-order regularity, but with less efficient performance on trials that do not. Thus, differences in rule representation can be inferred from a physiological measure of cognitive load, and are associated with differences in performance. These results illustrate how pupillometry can provide a window into reasoning as it unfolds over time.

Structure Learning Under Missing Data

Causal discovery is the problem of learning the structure of a graphical causal model that approximates the true generating process that gave rise to observed data. In practical problems, including in causal discovery problems, missing data is a very common issue. In such cases, learning the true causal graph entails estimating the full data distribution, samples from which are not directly available. Attempting to instead apply existing structure learning algorithms to samples drawn from the observed data distribution, containing systematically missing entries, may well result in incorrect inferences due to selection bias. In this paper we discuss adjustments that must be made to existing structure learning algorithms to properly account for missing data. We first give an algorithm for the simpler setting where the underlying graph is unknown, but the missing data model is known. We then discuss approaches to the much more difficult case where only the observed data is given with no other additional information on the missingness model known. We validate our approach by simulations, showing that it outperforms standard structure learning algorithms in all of these settings.

The dynamic programming high-order Dynamic Bayesian Networks learning for identifying effective connectivity in human brain from fMRI

BACKGROUND

Determination of effective connectivity (EC) among brain regions using fMRI is helpful in understanding the underlying neural mechanisms. Dynamic Bayesian Networks (DBNs) are an appropriate class of probabilistic graphical temporal-models that have been used in past to model EC from fMRI, specifically order-one.

NEW-METHOD

High-order DBNs (HO-DBNs) have still not been explored for fMRI data. A fundamental problem faced in the structure-learning of HO-DBN is high computational-burden and low accuracy by the existing heuristic search techniques used for EC detection from fMRI. In this paper, we propose using dynamic programming (DP) principle along with integration of properties of scoring-function in a way to reduce search space for structure-learning of HO-DBNs and finally, for identifying EC from fMRI which has not been done yet to the best of our knowledge. The proposed exact search-&-score learning approach HO-DBN-DP is an extension of the technique which was originally devised for learning a BN's structure from static data (Singh and Moore, 2005).

RESULTS

The effectiveness in structure-learning is shown on synthetic fMRI dataset. The algorithm reaches globally-optimal solution in appreciably reduced time-complexity than the static counterpart due to integration of properties. The proof of optimality is provided.

COMPARISON

The results demonstrate that HO-DBN-DP is comparably more accurate and faster than currently used structure-learning algorithms used for identifying EC from fMRI. The real data EC from HO-DBN-DP shows consistency with previous literature than the classical Granger Causality method.

CONCLUSION

Hence, the DP algorithm can be employed for reliable EC estimates from experimental fMRI data.

Learning the Structure of Social Influence

We routinely observe others' choices and use them to guide our own. Whose choices influence us more, and why? Prior work has focused on the effect of perceived similarity between two individuals (self and others), such as the degree of overlap in past choices or explicitly recognizable group affiliations. In the real world, however, any dyadic relationship is part of a more complex social structure involving multiple social groups that are not directly observable. Here we suggest that human learners go beyond dyadic similarities in choice behaviors or explicit group memberships; they infer the structure of social influence by grouping individuals (including themselves) based on choices, and they use these groups to decide whose choices to follow. We propose a computational model that formalizes this idea, and we test the model predictions in a series of behavioral experiments. In Experiment 1, we reproduce a well-established finding that people's choices are more likely to be influenced by someone whose past choices are more similar to their own past choices, as predicted by our model as well as dyadic similarity models. In Experiments 2-5, we test a set of unique predictions of our model by looking at cases where the degree of choice overlap between individuals is equated, but their choices indicate a latent group structure. We then apply our model to prior empirical results on infants' understanding of others' preferences, presenting an alternative account of developmental changes. Finally, we discuss how our model relates to classical findings in the social influence literature and the theoretical implications of our model. Taken together, our findings demonstrate that structure learning is a powerful framework for explaining the influence of social information on decision making in a variety of contexts.

Automatic anatomical labeling of arteries and veins using conditional random fields

PURPOSE

For safe and reliable laparoscopic surgery, it is important to determine individual differences of blood vessels such as the position, shape, and branching structures. Consequently, a computer-assisted laparoscopy that displays blood vessel structures with anatomical labels would be extremely beneficial. This paper details an automated anatomical labeling method for abdominal arteries and veins extracted from 3D CT volumes.

METHODS

The proposed method represents a blood vessel tree as a probabilistic graphical model by conditional random fields (CRFs). An adaptive gradient algorithm is adopted for structure learning. The anatomical labeling of blood vessel branches is performed by maximum a posteriori estimation.

RESULTS

We applied the proposed method to 50 cases of arterial and portal phase abdominal X-ray CT volumes. The experimental results showed that the F-measure of the proposed method for abdominal arteries and veins was 94.4 and 86.9%, respectively.

CONCLUSION

We developed an automated anatomical labeling method to annotate each blood vessel branches of abdominal arteries and veins using CRF. The proposed method outperformed a state-of-the-art method.

On the inconsistency of ℓ 1-penalised sparse precision matrix estimation

Background

Various ℓ₁-penalised estimation methods such as graphical lasso and CLIME are widely used for sparse precision matrix estimation and learning of undirected network structure from data. Many of these methods have been shown to be consistent under various quantitative assumptions about the underlying true covariance matrix. Intuitively, these conditions are related to situations where the penalty term will dominate the optimisation.

Results

We explore the consistency of ℓ₁-based methods for a class of bipartite graphs motivated by the structure of models commonly used for gene regulatory networks. We show that all ℓ₁-based methods fail dramatically for models with nearly linear dependencies between the variables. We also study the consistency on models derived from real gene expression data and note that the assumptions needed for consistency never hold even for modest sized gene networks and ℓ₁-based methods also become unreliable in practice for larger networks.

Conclusions

Our results demonstrate that ℓ₁-penalised undirected network structure learning methods are unable to reliably learn many sparse bipartite graph structures, which arise often in gene expression data. Users of such methods should be aware of the consistency criteria of the methods and check if they are likely to be met in their application of interest.

Prediction of lung cancer incidence on the low-dose computed tomography arm of the National Lung Screening Trial: A dynamic Bayesian network

INTRODUCTION

Identifying high-risk lung cancer individuals at an early disease stage is the most effective way of improving survival. The landmark National Lung Screening Trial (NLST) demonstrated the utility of low-dose computed tomography (LDCT) imaging to reduce mortality (relative to X-ray screening). As a result of the NLST and other studies, imaging-based lung cancer screening programs are now being implemented. However, LDCT interpretation results in a high number of false positives. A set of dynamic Bayesian networks (DBN) were designed and evaluated to provide insight into how longitudinal data can be used to help inform lung cancer screening decisions.

METHODS

The LDCT arm of the NLST dataset was used to build and explore five DBNs for high-risk individuals. Three of these DBNs were built using a backward construction process, and two using structure learning methods. All models employ demographics, smoking status, cancer history, family lung cancer history, exposure risk factors, comorbidities related to lung cancer, and LDCT screening outcome information. Given the uncertainty arising from lung cancer screening, a cancer state-space model based on lung cancer staging was utilized to characterize the cancer status of an individual over time. The models were evaluated on balanced training and test sets of cancer and non-cancer cases to deal with data imbalance and overfitting.

RESULTS

Results were comparable to expert decisions. The average area under the curve (AUC) of the receiver operating characteristic (ROC) for the three intervention points of the NLST trial was higher than 0.75 for all models. Evaluation of the models on the complete LDCT arm of the NLST dataset (N=25,486) demonstrated satisfactory generalization. Consensus of predictions over similar cases is reported in concordance statistics between the models' and the physicians' predictions. The models' predictive ability with respect to missing data was also evaluated with the sample of cases that missed the second screening exam of the trial (N=417). The DBNs outperformed comparison models such as logistic regression and naïve Bayes.

CONCLUSION

The lung cancer screening DBNs demonstrated high discrimination and predictive power with the majority of cancer and non-cancer cases.

The intentional stance as structure learning: a computational perspective on mindreading

Recent theories of mindreading explain the recognition of action, intention, and belief of other agents in terms of generative architectures that model the causal relations between observables (e.g., observed movements) and their hidden causes (e.g., action goals and beliefs). Two kinds of probabilistic generative schemes have been proposed in cognitive science and robotics that link to a "theory theory" and "simulation theory" of mindreading, respectively. The former compares perceived actions to optimal plans derived from rationality principles and conceptual theories of others' minds. The latter reuses one's own internal (inverse and forward) models for action execution to perform a look-ahead mental simulation of perceived actions. Both theories, however, leave one question unanswered: how are the generative models - including task structure and parameters - learned in the first place? We start from Dennett's "intentional stance" proposal and characterize it within generative theories of action and intention recognition. We propose that humans use an intentional stance as a learning bias that sidesteps the (hard) structure learning problem and bootstraps the acquisition of generative models for others' actions. The intentional stance corresponds to a candidate structure in the generative scheme, which encodes a simplified belief-desire folk psychology and a hierarchical intention-to-action organization of behavior. This simple structure can be used as a proxy for the "true" generative structure of others' actions and intentions and is continuously grown and refined - via state and parameter learning - during interactions. In turn - as our computational simulations show - this can help solve mindreading problems and bootstrap the acquisition of useful causal models of both one's own and others' goal-directed actions.

Using multi-step proposal distribution for improved MCMC convergence in Bayesian network structure learning

Bayesian networks have become popular for modeling probabilistic relationships between entities. As their structure can also be given a causal interpretation about the studied system, they can be used to learn, for example, regulatory relationships of genes or proteins in biological networks and pathways. Inference of the Bayesian network structure is complicated by the size of the model structure space, necessitating the use of optimization methods or sampling techniques, such Markov Chain Monte Carlo (MCMC) methods. However, convergence of MCMC chains is in many cases slow and can become even a harder issue as the dataset size grows. We show here how to improve convergence in the Bayesian network structure space by using an adjustable proposal distribution with the possibility to propose a wide range of steps in the structure space, and demonstrate improved network structure inference by analyzing phosphoprotein data from the human primary T cell signaling network.

Stochastic margin-based structure learning of Bayesian network classifiers

The margin criterion for parameter learning in graphical models gained significant impact over the last years. We use the maximum margin score for discriminatively optimizing the structure of Bayesian network classifiers. Furthermore, greedy hill-climbing and simulated annealing search heuristics are applied to determine the classifier structures. In the experiments, we demonstrate the advantages of maximum margin optimized Bayesian network structures in terms of classification performance compared to traditionally used discriminative structure learning methods. Stochastic simulated annealing requires less score evaluations than greedy heuristics. Additionally, we compare generative and discriminative parameter learning on both generatively and discriminatively structured Bayesian network classifiers. Margin-optimized Bayesian network classifiers achieve similar classification performance as support vector machines. Moreover, missing feature values during classification can be handled by discriminatively optimized Bayesian network classifiers, a case where purely discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.