Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods

It's very significant to correctly identify the hierarchical relation among attributes correctly when constructing a diagnosis test.As we know,there are various methods to identify the hierarchical relation among attributes in different cognitive diagnosis models(CDMs).Rule Space Model(RSM) is a kind of great influence CDM which was developed by Tatsuoka and her associates.In RSM,the task of attribute identification is performed after the test items have already been developed.And then an incidence Q matrix can be determined which reflects hierarchical relation.However,in Leighton,Gierl and Hunka's(2004) Attribute Hierarchy Method(AHM) the organization of attributes(attributes,number of attributes and attribute hierarchical relation) should be determined before developing the test items.In RSM and AHM the importance of correctly identifying the attributes and their hierarchical relation cannot be overstated,and the attributes and their hierarchical relations serve as the most important input variables to the models because they provide the basis for interpreting the results.The hierarchical relation among attributes describes the domain knowledge structures.Understanding the domain knowledge structures in highly specific detail provides a rational basis for proposing and evaluating potential improvements in the measurement of general proficiency.Otherwise,improvement remains largely a trial-and-error process.It has been proved that is not reliable to get the hierarchical relation by analyzing the test items,even the resulting hierarchical relations are not unique.Now,structure learning of Bayesian Networks would be introduced to study the hierarchical relation from the examinees' attribute mastery patterns.On the one hand,this paper conducted a simulation study in which Cui,Leighton and Zheng(2006)'s attribute hierarchical relation was employed,and the sample size of 5000 was used.In the simulated study,different sliping rates was considered for the purpose of testing the robustness of Bayesian structure learning.On the other hand,this paper conducted an empirical study to research the attributes which were commonly used in different numeration representation system converting,and the sample size was 189.Also the hierarchical relation generated by Bayesian structure learning and the hierarchical relation extracted by domain expert was compared.The result of simulation study and empirical study all showed the Bayesian Networks was a very useful tool in determining the hierarchical relation among attributes in the realm of education measurement and psychometrics.It is proved that the result for reference is valuable through structure learning of Bayesian Networks in simulated experiments and practical application.Meanwhile,the Bayesian Networks also can be used to test the hierarchical relation in RSM.

A classic approach for learning Bayesian networks from data is to identify a maximum a posteriori (MAP) network structure. In the case of discrete Bayesian networks, MAP networks are selected by maximising one of several possible Bayesian–Dirichlet (BD) scores; the most famous is the Bayesian–Dirichlet equivalent uniform (BDeu) score from Heckerman et al. (Mach Learn 20(3):197–243, 1995). The key properties of BDeu arise from its uniform prior over the parameters of each local distribution in the network, which makes structure learning computationally efficient; it does not require the elicitation of prior knowledge from experts; and it satisfies score equivalence. In this paper we will review the derivation and the properties of BD scores, and of BDeu in particular, and we will link them to the corresponding entropy estimates to study them from an information theoretic perspective. To this end, we will work in the context of the foundational work of Giffin and Caticha (Proceedings of the 27th international workshop on Bayesian inference and maximum entropy methods in science and engineering, pp 74–84, 2007), who showed that Bayesian inference can be framed as a particular case of the maximum relative entropy principle. We will use this connection to show that BDeu should not be used for structure learning from sparse data, since it violates the maximum relative entropy principle; and that it is also problematic from a more classic Bayesian model selection perspective, because it produces Bayes factors that are sensitive to the value of its only hyperparameter. Using a large simulation study, we found in our previous work [Scutari in J Mach Learn Res (Proc Track PGM 2016) 52:438–448, 2016] that the Bayesian–Dirichlet sparse (BDs) score seems to provide better accuracy in structure learning; in this paper we further show that BDs does not suffer from the issues above, and we recommend to use it for sparse data instead of BDeu. Finally, will show that these issues are in fact different aspects of the same problem and a consequence of the distributional assumptions of the prior.

We present a general framework for defining priors on model structure and sampling from the posterior using the Metropolis-Hastings algorithm. The key ideas are that structure priors are defined via a probability tree and that the proposal distribution for the Metropolis-Hastings algorithm is defined using the prior, thereby defining a cheaply computable acceptance probability. We have applied this approach to Bayesian net structure learning using a number of priors and proposal distributions. Our results show that these must be chosen appropriately for this approach to be successful.

The paper proposes a structural Bayesian network learning in a biological decision-theoretic intelligent agent model to solve a herding problem. The proposed structural learning methods show that an agent can update its world model by changing the structure of its Bayesian network with the data gathered by experience. The structural learning of the Bayesian network is accomplished by implementing a score based greedy search algorithm. The search algorithm is designed heuristically and exhaustively. A complexity analysis for the search algorithms is performed. Intelligent agent software, IntelliAgent, is written to simulate the herding problem with one sheep and one dog.

We propose a Gibbs sampler for structure learning in directed acyclic graph (DAG) models. The standard Markov chain Monte Carlo algorithms used for learning DAGs are random-walk Metropolis-Hastings samplers. These samplers are guaranteed to converge asymptotically but often mix slowly when exploring the large graph spaces that arise in structure learning. In each step, the sampler we propose draws entire sets of parents for multiple nodes from the appropriate conditional distribution. This provides an efficient way to make large moves in graph space, permitting faster mixing whilst retaining asymptotic guarantees of convergence. The conditional distribution is related to variable selection with candidate parents playing the role of covariates or inputs. We empirically examine the performance of the sampler using several simulated and real data examples. The proposed method gives robust results in diverse settings, outperforming several existing Bayesian and frequentist methods. In addition, our empirical results shed some light on the relative merits of Bayesian and constraint-based methods for structure learning.

This thesis concerns graphical models, mainly with discrete variables, a class of probabilistic models that can be understood pictorially using an interaction graph. Some classical graphical models includes the naive Bayes classifier and the Ising model, where the interaction graph of the former has directed edges, and the latter has undirected edges. At the core of graphical models is the concept of conditional independence; X is conditionally independent of Y given variable Z if by knowing Z, Y is irrelevant for X. Having access to such knowledge typically simplifies the model and hence the interaction graph. For classification problems, the structure of the interaction graph may be of lesser importance, whereas the structure may be essential in problems where the goal is the understand the underlying phenomenon. A large number of different graphical models exists with special structures of the interaction; graphs with both directed and undirected edges, both discrete and continuous variables etc. Common to all these is that the graphical structure must be learned either from data, also referred to as structure learning, or specified through expert knowledge. Given an interaction graph, calculating posterior probabilities, also known as inference, is essential in graphical models. Although both structure learning and inference are, in general, NP-complete problems there exist efficient heuristics for both, and even exact methods for inference. Most notably is the junction tree algorithm.

Bayesian econometric methods have enjoyed an increase in popularity in recent years. Econometricians, empirical economists, and policymakers are increasingly making use of Bayesian methods. The Oxford Handbook of Bayesian Econometrics is a single source about Bayesian methods in specialized fields. It contains articles by leading Bayesians on the latest developments in their specific fields of expertise. The volume provides broad coverage of the application of Bayesian econometrics in the major fields of economics and related disciplines, including macroeconomics, microeconomics, finance, and marketing. It reviews the state of the art in Bayesian econometric methodology, with articles on posterior simulation and Markov chain Monte Carlo methods, Bayesian nonparametric techniques, and the specialized tools used by Bayesian time series econometricians such as state space models and particle filtering. It also includes articles on Bayesian principles and methodology.

This paper describes the ESIDE-Depian intrusion detection and prevention system, which uses Bayesian structural and parametric learning and also evidence propagation and adaptation, in order to improve the accuracy and manageability of network intrusion detection systems (NIDS). Current NIDS do not consider the two main detection paradigms, i.e. misuse detection and anomaly detection, in an unified style, so the analysis is not inherently complete. Besides, historical data are not generally used, neither for analysis nor for sequential adaptation of the knowledge representation models used for detection; hence this wealthy information about the essence and the potential trends of the target system is not commonly considered. Thus, by the generalized use of Bayesian belief networks, ESIDE-Depian achieves the main goal of detecting and preventing both well-known and also zero-day attacks with excellent results, by means of unified real-time analysis of network traffic.

Radars have been an important tool for mankind since its inception. Several object tracking algorithms have been overlaid over the conventional radar to improve the accuracy of detection. Bayesian methods like Kalman and Particle filters is one such example, where the occurrence of the target at various positions is tracked probabilistically. The objective here is to devise an adaptive target tracking system using a combination of Kalman and particle filters, to improve the accuracy while optimizing the rate of convergence with respect to the basic Bayesian methods. It was observed that Kalman and Particle both have good accuracy of detection at lower accelerations with accuracy decreasing sharply at accelerations above 50 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This trends of decreasing accuracy at higher accelerations is mitigated with the proposed system where the accuracy reduces below 90% at accelerations above 100 m/s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> .

In road environment, road obstacle tracking is able to extract important information for driving safety. Indeed, kinematic characteristics estimation (relative position, relative speed, ...) provides a clearer road scene comprehension. This estimate is one of the important parameters of driver assistance systems. However, only one sensor generally does not allow to detect quickly (all the potentially dangerous obstacles) in all the directions, under all the atmospheric conditions. Moreover, the degree of obstacle recognition is different according to the sensor used. Multiplication of sensors makes it possible to face these various problems. Amalgamated information will represent entities in further details and with less uncertainty than with only one source. A system of higher level has been thus developed in order to have a robust management of all tracks and measurements coming from various sensors. This system, applied to radar and lidar measurements combination, gives important obstacles characteristics present in the front bumper of our experimental vehicle (VELAC: LASMEA's experimental vehicle for driving assistance). This state estimate is based on the use of various Bayesian methods (Extended Kalman Filter and Particle Filter). Here we will use the fusion of two-obstacle tracking delivered by two independent systems: track-to-track fusion. These two systems propose estimates characterizing obstacles positions and relative speeds. Fusion estimation is based on the use of extended Kalman filter (EKF) or particle filters. A comparison of these two methods is presented in this article.

This chapter deals with the problem of non-linear and non-Gaussian states and parameters estimation using Bayesian methods. The performances of various conventional and state-of-the-art state estimation techniques are compared when they are utilized to achieve this objective. These techniques include the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF). In the current work, the authors consider two systems (biological model and power system) to perform evaluation of estimation algorithms. The results of the comparative studies show that the UKF provides a higher accuracy than the EKF due to the limited ability of EKF to accurately estimate the mean and covariance matrix of the estimated states through lineralization of the nonlinear process model. The results also show that the PF provides a significant improvement over the UKF because, unlike UKF, PF is not restricted by linear-Gaussian assumptions which greatly extends the range of problems that can be tackled.

Event Abstract Back to Event Structure learning in human sequential decision-making Humans daily perform sequential decision-making under uncertainty to choose products, services, careers, and jobs. Studies of sequential decision-making in humans frequently find suboptimal performance relative to an ideal actor that knows the task that generates reward in the environment. This has led to conclusions about how we explore new courses of actions and exploit what we have learned. We argue, however, that humans have uncertainty about both the task and environmental structure, and that task and structure learning can potentially explain much better how people schedule actions, including behaviors previously deemed sub-optimal. We illustrate the task structure learning problem with an important special case that controls optimal exploration/exploitation. In particular, we formulate the structure learning problem using mixtures of two reward models'two-arm and one-arm bandit models'and solve the optimal action selection using Bayesian Reinforcement Learning. These two reward models represent extremes in both the exploration'exploitation tradeoff and computational difficulty'one model needs to balance exploration'exploitation and use long future horizons to compute actions, while the other needs no look-ahead and the action selection is greedy. In simulations, we show that optimal learning with uncertainty about the task structure can produce a range of qualitative behaviors deemed suboptimal in previous studies on sequential binary choice. In our experiments, each of 16 subjects (8 females) ran on 32 bandit tasks, a block of 16 in a two-arm bandits and a block of 16 one-arm bandits. Within blocks, the presentation order was randomized, and the order of the one-arm bandits was randomized across subjects. On average, each task required 48 choices. For two-arm bandits, the subjects made 1194 choices across the 16 tasks, and 925 for the one-arm bandits. Our results show that humans rapidly learn and exploit new reward structure'human behavior tracks the behavior of our structure learning model but is not explained by models that assume the task is known. Other kinds of reward structure learning may account for a broad variety of human decision-making performance. In particular, allowing dependence between the probability of reward at a site and previous actions can produce large changes in decision-making behavior. For instance, in a "foraging" model where reward is collected from a site and probabilistically replenished, optimal strategies will produce choice sequences that alternate between reward sites. Thus, uncertainty about the independence of reward on previous actions can produce a continuum of behavior, from maximization to probability matching. Instead of explaining behavior in terms of the idiosyncrasies of a learning rule, structure learning constitutes a fully rational response to uncertainty about the causal structure of rewards in the environment. Our hope is that, by expanding the range of normative hypotheses for human decision-making, we can begin to develop more principled accounts of human sequential decision-making behavior. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Structure learning in human sequential decision-making. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.238 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 03 Feb 2009; Published Online: 03 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Local search algorithm in ordering space is a good method which can effectively improve the efficiency of bayesian network structure learning. However, the existing algorithms usually have problems such as insufficient order optimization, low learning accuracy, and easy stop at a local optimal. In order to solve these problems, the local search algorithm in ordering space is studied, and a new method to improve the accuracy of bayesian network structure learning by optimizing order search operator is proposed. Combining the iterative local search algorithm with the window operator to search the neighborhood of a given order in the ordering space, the probability of the algorithm falling into the local optimal value is reduced, and the network structure with higher quality is obtained. Experimental results show that comparing with the bayesian network structure learning algorithm in network structure space, the learning efficiency of the present algorithm is improved by 54.12%. Comparing with the bayesian network structure learning algorithm in ordering space, the learning accuracy of the present algorithm is improved by 2.33%.

The key goals in learning Bayesian networks (BNs) from data are to identify significant statistical relationships between variables and to build a Directed Acyclic Graph (DAG) that represents these relationships through Joint Probability Distributions. Most research relies on score-based or conditional test methods for model selection. However, when using real-world data, it can be challenging to identify whether the learned DAG represents the underlying relations inherent in the limited datasets, particularly when evaluating data obtained from multiple independent sources. This study presents a methodology to assess the credible interval for both the existence and direction of each edge within Bayesian networks derived from data. Furthermore, it explores the fusion of models acquired from distinct and independent datasets. This approach enables the Bayesian learning of Bayesian Networks (BNs) from data by treating the uncertainty associated with the existence and orientation of each edge as a random variable. By evaluating the probability of the orientation of each edge, it is possible to suggest the existence of a potential latent variable within the dataset. If an edge exhibits equiprobable directions and is verified to exist, it becomes a plausible hypothesis for a latent variable. The Fast Causal Algorithm, originally introduced by [1], is the foundation of this approach. Finally, by employing a maximum a posteriori estimation, the most prominent edges and their respective orientations are identified and employed to create the leading DAG. We present our findings in simulated datasets with different length sizes. By comparing the structure of the learned DAGs with existing structures and evaluating the inference capabilities of the final BN, we establish that our approach achieves results comparable to the most recent studies in the field, while offering insights into the model’s reliability and improving the use of the data.

A Bayesian network (BN) is a probabilistic graphical model that can model complex and nonlinear relationships. Its structural learning from data is an NP-hard problem because of its search-space size. One method to perform structural learning is a search and score approach, which uses a search algorithm and structural score. A study comparing 15 algorithms showed that hill climbing (HC) and tabu search (TABU) performed the best overall on the tests. This work performs a deeper analysis of the application of the adaptive genetic algorithm with varying population size (AGAVaPS) on the BN structural learning problem, which a preliminary test showed that it had the potential to perform well on. AGAVaPS is a genetic algorithm that uses the concept of life, where each solution is in the population for a number of iterations. Each individual also has its own mutation rate, and there is a small probability of undergoing mutation twice. Parameter analysis of AGAVaPS in BN structural leaning was performed. Also, AGAVaPS was compared to HC and TABU for six literature datasets considering F1 score, structural Hamming distance (SHD), balanced scoring function (BSF), Bayesian information criterion (BIC), and execution time. HC and TABU performed basically the same for all the tests made. AGAVaPS performed better than the other algorithms for F1 score, SHD, and BIC, showing that it can perform well and is a good choice for BN structural learning.