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Identifying latent structure in large data matrices is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes that are locally co-regulated by shared biological mechanisms. To do this, we develop a Bayesian statistical model for biclustering to infer subsets of co-regulated genes whose covariation may be observed in only a subset of the samples. Our biclustering method, BicMix, has desirable properties, including allowing overcomplete representations of the data, computational tractability, and jointly modeling unknown confounders and biological signals. Compared with related biclustering methods, BicMix recovers latent structure with higher precision across diverse simulation scenarios. Further, we develop a method to recover gene co-expression networks from the estimated sparse biclustering matrices. We apply BicMix to breast cancer gene expression data and recover a gene co-expression network that is differential across ER+ and ER- samples.

Since the use of information and communication technologies has now become indispensable for the development of human activity, governments have assumed the responsibility of ensuring access to them, as is the case in Mexico, generating a series of public policies aimed at that end. However, these politics have not generated the expected results since there are yet large differences to internet connectivity. This research presents an analysis of the availability and use of information and communication technologies. Diverse studies indicate that there is a verifiable inequality in terms of access to technologies, this difference is remarkable between municipalities and between regions. The analysis has allowed to know the main activities that the population makes through the ICT with the objective of determining the actions in matters of digital policies that must be considered by the local government. From the analysis performed it can be concluded that the majority of the population that Internet accesses does it through a desktop, laptop computer or a mobile phone. The most actions performed by the population through the internet are actions of entertainment and downloading software, as well as the search for general information, but participating in government affairs is not a priority issue. The population interested in public affairs is the one with the highest educational level, then that the institution requires the development of mechanisms to strengthen citizen participation in the taking of public affairs. It is also required to increase the communications infrastructure then that a greater percentage of the population can access the Internet. The programs on the use of technologies that must be developed by the government must be adapted. The study shows that the completion of procedures is not a priority issue, then that the implementation of electronic services may not have much impact on the Entity. It is necessary at first then to promote the development of the population's capacities to use of communication technologies. As a result, in this moment not have conditions to guarantee the success of an e-government policy such as the implementation of electronic payments and the use of mobile applications. It is necessary to overcome connectivity deficiencies and develop digital literacy actions to ensure the productive use of technologies. Elia Martínez | Guillermo De la Torre-Gea"Analysis of the ICT user Profile for e-goverment through Bayesian Networks" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd2407.pdf Article URL: http://www.ijtsrd.com/other-scientific-research-area/other/2407/analysis-of-the-ict-user-profile-for-e-goverment--through-bayesian-networks/elia-martínez

Structure learning of Bayesian networks is an important problem that arises in numerous machine learning applications. In this work, we present a novel approach for learning the structure of Bayesian networks using the solution of an appropriately constructed traveling salesman problem. In our approach, one computes an optimal ordering (partially ordered set) of random variables using methods for the traveling salesman problem. This ordering significantly reduces the search space for the subsequent greedy optimization that computes the final structure of the Bayesian network. We demonstrate our approach of learning Bayesian networks on real world census and weather datasets. In both cases, we demonstrate that the approach very accurately captures dependencies between random variables. We check the accuracy of the predictions based on independent studies in both application domains.

We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of idealizations are being made which can be relaxed by an appeal to Bayesian Networks.

One of the problems often encountered in vibration analysis is unbalanced or imbalanced, namely the occurrence of a shift in the center of mass from the center of rotation to cause high vibrations. Unbalance itself is divided into two, namely static and dynamic unbalance. Identification of the right type of unbalance must be done because each type of unbalance requires different handling. Therefore, this study aims to design a system to identify the type of unbalance based on the required parameters. The system design determines the input and then builds an algorithm by combining vibration analysis methods and Bayesian networks (BN). Systems and applications are built using MATLAB. After the application is finished, testing is carried out using vibration measurement data obtained from a demo machine that has previously been conditioned for damage. The BN method has been successfully applied to the unbalance diagnosis system. When there is evidence of large amplitude in 1X the frequency spectrum and the value of the static phase range, the percentage of static unbalance from 26.8% increases to 75%. The system can predict all testing data quickly and precisely for the six experiments.

We propose a Multi-Layer Network based on the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional lattice. The Latent Variable Model (LVM) is the basic building block of a quadtree hierarchy built on top of a bottom layer of random variables that represent pixels of an image, a feature map, or more generally a collection of spatially distributed discrete variables. The multi-layer architecture implements a hierarchical data representation that, via belief propagation, can be used for learning and inference. Typical uses are pattern completion, correction and classification. The FGrn paradigm provides great flexibility and modularity and appears as a promising candidate for building deep networks: the system can be easily extended by introducing new and different (in cardinality and in type) variables. Prior knowledge, or supervised information, can be introduced at different scales. The FGrn paradigm provides a handy way for building all kinds of architectures by interconnecting only three types of units: Single Input Single Output (SISO) blocks, Sources and Replicators. The network is designed like a circuit diagram and the belief messages flow bidirectionally in the whole system. The learning algorithms operate only locally within each block. The framework is demonstrated in this paper in a three-layer structure applied to images extracted from a standard data set.

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time- evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically-generated data, data from an analog electronic circuit, and cardio-respiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on dynamical Bayesian inference that facilitates the simultaneous detection of time-varying synchronization, directionality of influence, and coupling functions. It can distinguish unsynchronized dynamics from noise-induced phase slips. The method is based on phase dynamics, with Bayesian inference of the time- evolving parameters being achieved by shaping the prior densities to incorporate knowledge of previous samples. We now present the method in detail using numerically-generated data, data from an analog electronic circuit, and cardio-respiratory data. We also generalize the method to encompass networks of interacting oscillators and thus demonstrate its applicability to small-scale networks.

Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are included in such a model, then the set of possible marginal distributions over the remaining (observed) variables is generally complex, and not represented by any DAG. Larger classes of mixed graphical models, which use multiple edge types, have been introduced to overcome this; however, these classes do not represent all the models which can arise as margins of DAGs. In this paper we show that this is because ordinary mixed graphs are fundamentally insufficiently rich to capture the variety of marginal models. We introduce a new class of hyper-graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represented by at least one mDAG, and provide graphical results towards characterizing when two such marginal models are the same. Finally we show that mDAGs correctly capture the marginal structure of causally-interpreted DAGs under interventions on the observed variables.

This thesis investigates the stability of the random multiaccess protocols, slotted Carrier Sense Multiple Access (CSMA) and slotted CSMA/ collision Detection(CD), utilizing one power level and two power levels to create beneficial power capture effect. Use of more than two equally spaced power levels provides no significant improvement in the throughout achievable when realistic capture thresholds are considered. The investigation centers on a technique known as pseudo-Bayesian stability. Another task of this thesis is to stabilize multi-channel slotted CSMA and slotted CSMA/CD with pseudo-Bayesian technique. The multichannel slotted CSMA and slotted CSMA/CD show a large improvement in throughput over a traditional single channel with a combined bit rate.

Meteorological remote sensing efforts have advanced operational decision making and scientific research over the last half-century by providing high-quality global observations of the land, atmosphere, and ocean. The continued development of convolutional neural networks (CNNs) and Bayesian neural networks shows potential for allowing some of these datasets to be synthetically produced where they cannot be directly observed. In this thesis, global precipitation measurement mission (GPM) data is used to train a rain-type classification Bayesian CNN (BCNN) using passive microwave data. Additionally, regression CNNs and BCNNs are trained to predict precipitation using GOES-16 multispectral infrared data over a tropical maritime region. The rain-type classification BCNN shows a 17% improvement in accuracy over existing literature, and the regression models demonstrate a proof of concept in using GPM radar data and geostationary radiances to train skillful CNNs and BCNNs to predict radar reflectivity and rain rate. The experiments demonstrate both the promise of using these data sources to train accurate models and the possible advantages of using BCNNs to quantify and better understand prediction uncertainty for these applications.

The application of Bayesian Neural Networks(BNN) to discriminate neutrino events from backgrounds in reactor neutrino experiments has been described in Ref.\cite{key-1}. In the paper, BNN are also used to identify neutrino events in reactor neutrino experiments, but the numbers of photoelectrons received by PMTs are used as inputs to BNN in the paper, not the reconstructed energy and position of events. The samples of neutrino events and three major backgrounds from the Monte-Carlo simulation of a toy detector are generated in the signal region. Compared to the BNN method in Ref.\cite{key-1}, more $^{8}$He/$^{9}$Li background and uncorrelated background in the signal region can be rejected by the BNN method in the paper, but more fast neutron background events in the signal region are unidentified using the BNN method in the paper. The uncorrelated background to signal ratio and the $^{8}$He/$^{9}$Li background to signal ratio are significantly improved using the BNN method in the paper in comparison with the BNN method in Ref.\cite{key-1}. But the fast neutron background to signal ratio in the signal region is a bit larger than the one in Ref.\cite{key-1}.

To obtain uncertainty estimates with real-world Bayesian deep learning models, practical inference approximations are needed. Dropout variational inference (VI) for example has been used for machine vision and medical applications, but VI can severely underestimates model uncertainty. Alpha-divergences are alternative divergences to VI's KL objective, which are able to avoid VI's uncertainty underestimation. But these are hard to use in practice: existing techniques can only use Gaussian approximating distributions, and require existing models to be changed radically, thus are of limited use for practitioners. We propose a re-parametrisation of the alpha-divergence objectives, deriving a simple inference technique which, together with dropout, can be easily implemented with existing models by simply changing the loss of the model. We demonstrate improved uncertainty estimates and accuracy compared to VI in dropout networks. We study our model's epistemic uncertainty far away from the data using adversarial images, showing that these can be distinguished from non-adversarial images by examining our model's uncertainty.

Learning graphical models from data is an important problem with wide applications, ranging from genomics to the social sciences. Nowadays datasets typically have upwards of thousands---sometimes tens or hundreds of thousands---of variables and far fewer samples. To meet this challenge, we develop a new R package called sparsebn for learning the structure of large, sparse graphical models with a focus on Bayesian networks. While there are many existing packages for this task within the R ecosystem, this package focuses on the unique setting of learning large networks from high-dimensional data, possibly with interventions. As such, the methods provided place a premium on scalability and consistency in a high-dimensional setting. Furthermore, in the presence of interventions, the methods implemented here achieve the goal of learning a causal network from data. The sparsebn package is open-source and available on CRAN.

Learning graphical models from data is an important problem with wide applications, ranging from genomics to the social sciences. Nowadays datasets typically have upwards of thousands---sometimes tens or hundreds of thousands---of variables and far fewer samples. To meet this challenge, we develop a new R package called sparsebn for learning the structure of large, sparse graphical models with a focus on Bayesian networks. While there are many existing packages for this task within the R ecosystem, this package focuses on the unique setting of learning large networks from high-dimensional data, possibly with interventions. As such, the methods provided place a premium on scalability and consistency in a high-dimensional setting. Furthermore, in the presence of interventions, the methods implemented here achieve the goal of learning a causal network from data. The sparsebn package is open-source and available on CRAN.

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing of group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging a mixture of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel insights on the relationships between human brain networks and creativity.

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or high creative reasoning group. It is of paramount importance to develop statistical methods for testing of global and local changes in the structural interconnections among brain regions across groups. We develop a general Bayesian procedure for inference and testing of group differences in the network structure, which relies on a nonparametric representation for the conditional probability mass function associated with a network-valued random variable. By leveraging a mixture of low-rank factorizations, we allow simple global and local hypothesis testing adjusting for multiplicity. An efficient Gibbs sampler is defined for posterior computation. We provide theoretical results on the flexibility of the model and assess testing performance in simulations. The approach is applied to provide novel insights on the relationships between human brain networks and creativity.

Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior (Heckerman et al., 1995). Its favourable theoretical properties descend from assuming a uniform prior both on the space of the network structures and on the space of the parameters of the network. In this paper, we revisit the limitations of these assumptions; and we introduce an alternative set of assumptions and the resulting score: the Bayesian Dirichlet sparse (BDs) empirical Bayes marginal likelihood with a marginal uniform (MU) graph prior. We evaluate its performance in an extensive simulation study, showing that MU+BDs is more accurate than U+BDeu both in learning the structure of the network and in predicting new observations, while not being computationally more complex to estimate.

Estimation of origin-destination (OD) demand plays a key role in successful transportation studies. In this paper, we consider the estimation of time-varying day-to-day OD flows given data on traffic volumes in a transportation network for a sequence of days. We propose a dynamic linear model (DLM) in order to represent the stochastic evolution of OD flows over time. DLM's are Bayesian state-space models which can capture non-stationarity. We take into account the hierarchical relationships between the distribution of OD flows among routes and the assignment of traffic volumes on links. Route choice probabilities are obtained through a utility model based on past route costs. We propose a Markov chain Monte Carlo algorithm, which integrates Gibbs sampling and a forward filtering backward sampling technique, in order to approximate the joint posterior distribution of mean OD flows and parameters of the route choice model. Our approach can be applied to congested networks and in the case when data are available on only a subset of links. We illustrate the application of our approach through simulated experiments on a test network from the literature.

This article is from BMC Systems Biology , volume 8 . Abstract Background: Genome-wide time-series data provide a rich set of information for discovering gene regulatory relationships. As genome-wide data for mammalian systems are being generated, it is critical to develop network inference methods that can handle tens of thousands of genes efficiently, provide a systematic framework for the integration of multiple data sources, and yield robust, accurate and compact gene-to-gene relationships. Results: We developed and applied ScanBMA, a Bayesian inference method that incorporates external information to improve the accuracy of the inferred network. In particular, we developed a new strategy to efficiently search the model space, applied data transformations to reduce the effect of spurious relationships, and adopted the g-prior to guide the search for candidate regulators. Our method is highly computationally efficient, thus addressing the scalability issue with network inference. The method is implemented as the ScanBMA function in the networkBMA Bioconductor software package. Conclusions: We compared ScanBMA to other popular methods using time series yeast data as well as time-series simulated data from the DREAM competition. We found that ScanBMA produced more compact networks with a greater proportion of true positives than the competing methods. Specifically, ScanBMA generally produced more favorable areas under the Receiver-Operating Characteristic and Precision-Recall curves than other regression-based methods and mutual-information based methods. In addition, ScanBMA is competitive with other network inference methods in terms of running time.

A current popular approach to representing time in Bayesian belief networks is through Dynamic Bayesian Networks (DBNs) (Dean & Kanazawa, 1989). DBNs connect sequences of entire Bayes networks, each representing a situation at a snapshot in time. The authors present an alternative method for incorporating time into Bayesian belief networks that utilizes abstractions of temporal representations. This method maintains the principled Bayesian approach to reasoning under uncertainty, providing explicit representation of sequence and potentially complex temporal relationships, while also decreasing overall network complexity compared to DBNs.

We present a novel approach to anomaly detection in Bayesian networks, enabling both the detection and explanation of anomalous cases in a dataset. By exploiting the structure of a Bayesian network, our algorithm is able to efficiently search for local maxima of data conflict between closely related variables. Benchmark tests using data simulated from complex Bayesian networks show that our approach provides a significant improvement over techniques that search for anomalies using the entire network, rather than its subsets. We conclude with demonstrations of the unique explanatory power of our approach in determining the observation(s) responsible for an anomaly.

A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining algebraic conditional plausibility measures. It is shown that algebraic conditional plausibility measures can be represented using Bayesian networks.

Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed "quantum". However, the term "quantum" should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modeling situation, say forecasting the weather or the stock market--it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.

Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we will show is equivalent to standard textbook quantum mechanics. Therefore, this extension will be termed "quantum". However, the term "quantum" should not be taken to imply this extension is necessarily only of utility in situations traditionally thought of as in the domain of quantum mechanics. In principle, it may be employed in any modeling situation, say forecasting the weather or the stock market--it is up to experiment to determine if this extension is useful in practice. Even restricting to the domain of quantum mechanics, with this new formulation the advantages of Bayesian networks can be maintained for models incorporating quantum and mixed classical-quantum behavior. The use of these will be illustrated by various basic examples. Parrondo's paradox refers to the situation where two, multi-round games with a fixed winning criteria, both with probability greater than one-half for one player to win, are combined. Using a possibly biased coin to determine the rule to employ for each round, paradoxically, the previously losing player now wins the combined game with probability greater than one-half. Using the extended Bayesian networks, we will formulate and analyze classical observed, classical hidden, and quantum versions of a game that displays this paradox, finding bounds for the discrepancy from naive expectations for the occurrence of the paradox. A quantum paradox inspired by Parrondo's paradox will also be analyzed. We will prove a bound for the discrepancy from naive expectations for this paradox as well. Games involving quantum walks that achieve this bound will be presented.

Explains how Bayesian networks can tackle the limitations of pure data-driven statistical machine learning methods when applied to observational data. This is the lecture I was due to present at the NHS Health and Care Analytics Conference, 5 July 2023. For the back story on this see: https://wherearethenumbers.substack.com/p/an-update-on-my-nhs-conference-cancellation

Maternal mortality has shown a considerable decrease in countries where the rate of development is higher. This is not the case for Mexico where a large number of annual maternal deaths are still perceived, which turns out to be a public health problem in which the World Health Organization (WHO) considers indigenous populations with a higher rate of maternal deaths, as is the case in the state of Oaxaca. The aim of this paper is to carry out an analysis of maternal deaths during the period 2014-2016 in the municipalities of this state in order to identify the main causes that cause it, factors that intervene in it and municipalities with the highest rate of this problem. The analysis has revealed that the National Institute of Social Security (IMSS) is the site where the highest number of deaths occurred, as well as identifying the main causes that lead to maternal mortality, determining that it is not enough to have Public and Private Health institutions, but they must have a better care system and equipment for care, without leaving aside the cultural aspect of the inhabitants of the municipalities of the state of Oaxaca. Araceli Pinacho-Ríos | Guillermo De la Torre-Gea"Analysis of Maternal Deaths in Oaxaca through Bayesian Networks" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: http://www.ijtsrd.com/papers/ijtsrd10758.pdf  http://www.ijtsrd.com/computer-science/data-miining/10758/analysis-of-maternal-deaths-in-oaxaca-through-bayesian-networks/araceli-pinacho-ríos

We present a new implementation of quantum computation that treats quantum computers as a special type of Bayesian Network called a QuDot Net. QuDot Nets allow for the efficient representation of some qubit systems. Single qubit quantum gates can be implemented as edge transformations on QuDot Nets. The X, H, R(k), M and SWAP gates are discussed in detail and results show linear scaling as the number of qubits are increased. We show that measurement and semi-quantum control gates can be efficiently implemented using QuDot Nets and present results from a QuDot Net implementation of the terminal Quantum Fourier Transform. We show how QuDot Nets can implement coherent control gates using multi-digraphs by labelling parallel edges. Lastly, we discuss implications to quantum foundations if a classical implementation of quantum computation is realized.

Rigorous Bayesian Computational Sensor Networks are developed to quantify uncertainty in (1) model-based state estimates incorporating sensor data, (2) model parameters, (3) sensor node model parameter values (e.g., location, noise), and (4) input sources (e.g., cracks holes). These decentralized methods have low computational complexity and perform Bayesian estimation in general distributed measurement systems (i.e., sensor networks). A model of the dynamic behavior and distribution of the underlying physical phenomenon is used to obtain a continuous form from the discrete time and space samples provided by a sensor network. This approach was applied to the aircraft structural health monitoring problem. Structural health monitoring (SHM) deals with evaluating structures for changes in their characteristics, predicting useful lifetime without maintenance, and recommending maintenance strategies to increase lifetime and reduce downtime. Current aircraft construction often involves fiber-reinforced laminated composite materials which offer certain advantages, but can suffer internal damage with little external evidence. We developed specific Bayesian computational models of SHM transducers (e.g., ultrasound) acting in both undamaged and damages materials.

Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous spaces. In particular. mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore 1999). In this paper, we propose a kind of Bayesian network in which low-dimensional mixtures of Gaussians over different subsets of the domain's variables are combined into a coherent joint probability model over the entire domain. The network is also capable of modelling complex dependencies between discrete variables and continuous variables without requiring discretization of the continuous variables. We present efficient heuristic algorithms for automatically learning these networks from data and perform comparative experiments illustrating how well these networks model real scientific data and synthetic data. We also briefly discuss some possible improvements to the networks. as well as their possible application to anomaly detection, classification probabilistic inference, and compression.

The performed project focused on a new paradigm of planning systems that are based on a combination of Bayesian networks and structural equation models. We focused on theoretical issues that surround combining the two in a practical planning system, developing the foundations for, and building a prototype of such system. The approach and the system built allow for efficient, yet normatively correct, treatment of various types of information, uncertainty, and utility. It is especially powerful in complex situations where the available information is heterogeneous and consists of a mixture of deterministic and uncertain relationships among discrete and continuous variables. Our main contributions are: (1) two state of the art stochastic sampling algorithm for approximate inference in graphical models, both (2) analysis of problems related to combining probabilistic information, (3) an module for interactive construction of causal graphical models and search for opportunities, (4) algorithm for learning graphical models from small data sets, and (5) a prototype of the system, used by over 5,000 people world-wide.

The performed project focused on a new paradigm of planning systems that are based on a combination of Bayesian networks and structural equation models. We focused on theoretical issues that surround combining the two in a practical planning system, developing the foundations for, and building a prototype of such system. The approach and the system built allow for efficient, yet normatively correct, treatment of various types of information, uncertainty, and utility. It is especially powerful in complex situations where the available information is heterogeneous and consists of a mixture of deterministic and uncertain relationships among discrete and continuous variables. Our main contributions are: (1) two state of the art stochastic sampling algorithm for approximate inference in graphical models, both (2) analysis of problems related to combining probabilistic information, (3) an module for interactive construction of causal graphical models and search for opportunities, (4) algorithm for learning graphical models from small data sets, and (5) a prototype of the system, used by over 5,000 people world-wide.

This paper is intended to be a pedagogical introduction to quantum Bayesian networks (QB nets), as I personally use them to represent mixed states (i.e., density matrices, and open quantum systems). A special effort is made to make contact with notions used in textbooks on quantum Shannon Information Theory (quantum SIT), such as the one by Mark Wilde (arXiv:1106.1445)

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures. Our framework of `generalised Bayesian networks' replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, Popescu-Rohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$-separation theorem to our setting. Secondly, we find that the theory-independent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and general-probabilistic correlations.

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures. Our framework of `generalised Bayesian networks' replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, Popescu-Rohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$-separation theorem to our setting. Secondly, we find that the theory-independent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and general-probabilistic correlations.

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures. Our framework of `generalised Bayesian networks' replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, Popescu-Rohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$-separation theorem to our setting. Secondly, we find that the theory-independent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and general-probabilistic correlations.

Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities. Inspired by this connection, we generalise the formalism of classical Bayesian networks in order to investigate non-classical correlations in arbitrary causal structures. Our framework of `generalised Bayesian networks' replaces latent variables with the resources of any generalised probabilistic theory, most importantly quantum theory, but also, for example, Popescu-Rohrlich boxes. We obtain three main sets of results. Firstly, we prove that all of the observable conditional independences required by the classical theory also hold in our generalisation; to obtain this, we extend the classical $d$-separation theorem to our setting. Secondly, we find that the theory-independent constraints on probabilities can go beyond these conditional independences. For example we find that no probabilistic theory predicts perfect correlation between three parties using only bipartite common causes. Finally, we begin a classification of those causal structures, such as the Bell scenario, that may yield a separation between classical, quantum and general-probabilistic correlations.

In this paper, we present a Case Based Reasoning (CBR) system for the retrieval of medical cases made up of a series of images with semantic information (such as the patient age, sex and medical history).

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. We propose a novel algorithm for this task, able to scale to large domains and large treewidths. Our novel approach consistently outperforms the state of the art on data sets with up to ten thousand variables.

We evaluate the uncertainty quality in neural networks using anomaly detection. We extract uncertainty measures (e.g. entropy) from the predictions of candidate models, use those measures as features for an anomaly detector, and gauge how well the detector differentiates known from unknown classes. We assign higher uncertainty quality to candidate models that lead to better detectors. We also propose a novel method for sampling a variational approximation of a Bayesian neural network, called One-Sample Bayesian Approximation (OSBA). We experiment on two datasets, MNIST and CIFAR10. We compare the following candidate neural network models: Maximum Likelihood, Bayesian Dropout, OSBA, and --- for MNIST --- the standard variational approximation. We show that Bayesian Dropout and OSBA provide better uncertainty information than Maximum Likelihood, and are essentially equivalent to the standard variational approximation, but much faster.

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Unsupervised estimation of latent variable models is a fundamental problem central to numerous applications of machine learning and statistics. This work presents a principled approach for estimating broad classes of such models, including probabilistic topic models and latent linear Bayesian networks, using only second-order observed moments. The sufficient conditions for identifiability of these models are primarily based on weak expansion constraints on the topic-word matrix, for topic models, and on the directed acyclic graph, for Bayesian networks. Because no assumptions are made on the distribution among the latent variables, the approach can handle arbitrary correlations among the topics or latent factors. In addition, a tractable learning method via $\ell_1$ optimization is proposed and studied in numerical experiments.

We analyse a quantum-like Bayesian Network that puts together cause/effect relationships and semantic similarities between events. These semantic similarities constitute acausal connections according to the Synchronicity principle and provide new relationships to quantum like probabilistic graphical models. As a consequence, beliefs (or any other event) can be represented in vector spaces, in which quantum parameters are determined by the similarities that these vectors share between them. Events attached by a semantic meaning do not need to have an explanation in terms of cause and effect.

Our research question was whether we could develop a feasible technique, using Bayesian networks, to diagnose gaps in student knowledge. Thirty-four college-age participants completed tasks designed to measure conceptual knowledge, procedural knowledge, and problem-solving skills related to circuit analysis. A Bayesian network was used to model the knowledge dependencies among the circuit analysis concepts. Preliminary results suggested that the Bayesian network was generally working as intended. When high- and low-performing groups were formed on the basis of posterior probabilities, significant group differences were found favoring the high-performing group with respect to circuit definitions and circuit analysis problems, for both actual and self-assessments, and higher major GPA. The Bayesian network was able to predict participants' performance on a problem-solving item on average 75% of the time. The findings of this study are promising for our long-term goal of developing scalable and feasible online automated reasoning techniques to diagnose student knowledge gaps. (Contains 12 tables and 2 figures.) [Appended are: (1) Node-Voltage Analysis Problem-Solving Procedure (Kaiser, 2003); and (2) Bayesian Network.]

Migration has long been a topic of interest in Georgia, given its small economy, population, and unique history and culture. The main objective of this study is to examine the factors affecting emigration and immigration in Georgia and identify the dependencies among various macroeconomic variables, such as international remittances, trade, foreign direct investment (FDI), inflation, real interest rates, and employment. Using data spanning from 2002 to 2023, the study applies a machine learning technique, specifically Bayesian Networks, to analyze these relationships. The findings are discussed, and conclusions are drawn, along with recommendations for both the government and researchers for further exploration. To our knowledge, this is the first study to apply the Bayesian Network algorithm to investigate these dynamics in Georgia, filling an important research gap. The results indicate that both immigration and emigration are affected by remittances paid, with emigration also being dependent on employment. It was found that remittances received and exports are directly influenced by remittances paid, while imports are affected by both exports and employment. Additionally, remittances received are directly dependent on imports, and the real interest rate is influenced by both imports and inflation (CPI). FDI is shown to be dependent on inflation, imports, and remittances received. Furthermore, both emigration and immigration are dependent on exports, imports, and remittances received, with immigration also exhibiting a dependency on FDI.

Enhancing Reliability in Photonuclear Cross-Section Fitting with Bayesian Neural Networks 作者： Qian-KunSun 1,2 YueZhang 3 Zi-RuiHao 3 Hong-WeiWang 1,2,3 Gong-TaoFan 1,2,3 Hang-HuaXu 3 Long-XiangLiu 3 ShengJin 1,2 Yu-XuanYang 1,4 Kai-JieChen 1,5 Zhen-WeiWang 1,2 作者单位： 1. Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China 2. University of Chinese Academy of Sciences, Beijing 100049, China 3. Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China 4. School of Physics and Microelectronics, Zhengzhou university, Zhengzhou 450001, China 5. School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China 通讯作者： Qian-KunSun Email:[email protected] YueZhang Email:[email protected] Hong-WeiWang Email:[email protected] 提交时间： 2024-11-19 12:05:40 摘要: This study investigates photonuclear reaction $(\gamma,n)$ cross-sections using Bayesian neural network (BNN) analysis. After determining the optimal network architecture, which features two hidden layers, each with 50 hidden nodes, training was conducted for 30,000 iterations to ensure comprehensive data capture. By analyzing the distribution of absolute errors positively correlated with the cross-section for the isotope $^{159}$Tb, as well as the relative errors unrelated to the cross-section, we confirmed that the network effectively captured the data features without overfitting. Comparison with the TENDL-2021 Database demonstrated the BNN’s reliability in fitting photonuclear cross-sections with lower average errors. The predictions for nuclei with single and double giant dipole resonance peak cross-sections, the accurate determination of the photoneutron reaction threshold in the low-energy region, and the precise description of trends in the high-energy cross-sections further demonstrate the network’s generalization ability on the validation set. This can be attributed to the consistency of the training data. By using consistent training sets from different laboratories, Bayesian neural networks can predict nearby unknown cross-sections based on existing laboratory data, thereby estimating the potential differences between other laboratories’ existing data and their own measurement results. Experimental measurements of photonuclear reactions on the newly constructed SLEGS beamline will contribute to clarifying the differences in cross-sections within the existing data. Photoneutron reaction Bayesian neural network Machine learning Gamma source SLEGS 来自： 孙乾坤 分类： 物理学 >> 核物理学 说明： 已被Nuclear Science and Techniques期刊接收 投稿状态： 已被期刊接收 引用： ChinaXiv:202411.00202 (或此版本 ChinaXiv:202411.00202V1 ) DOI:10.12074/202411.00202 CSTR:32003.36.ChinaXiv.202411.00202 科创链TXID： 197016ef-a392-4705-b927-8824ed0ffe4c 推荐引用方式： Qian-KunSun,YueZhang,Zi-RuiHao,Hong-WeiWang,Gong-TaoFan,Hang-HuaXu,Long-XiangLiu,ShengJin,Yu-XuanYang,Kai-JieChen,Zhen-WeiWang.Enhancing Reliability in Photonuclear Cross-Section Fitting with Bayesian Neural Networks.中国科学院科技论文预发布平台.[DOI:10.12074/202411.00202] 版本历史 [V1] 2024-11-19 12:05:40 ChinaXiv:202411.00202V1 下载全文

Judea Pearl is a professor at UCLA and a winner of the Turing Award, that's generally recognized as the Nobel Prize of computing. He is one of the seminal figures in the field of artificial intelligence, computer science, and statistics. He has developed and championed probabilistic approaches to AI, including Bayesian Networks and profound ideas in causality in general. These ideas are important not just for AI, but to our understanding and practice of science. But in the field of AI, the idea of causality, cause and effect, to many, lies at the core of what is currently missing and

We present an algorithm for model-based reinforcement learning that combines Bayesian neural networks (BNNs) with random roll-outs and stochastic optimization for policy learning. The BNNs are trained by minimizing $\alpha$-divergences, allowing us to capture complicated statistical patterns in the transition dynamics, e.g. multi-modality and heteroskedasticity, which are usually missed by other common modeling approaches. We illustrate the performance of our method by solving a challenging benchmark where model-based approaches usually fail and by obtaining promising results in a real-world scenario for controlling a gas turbine.