Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConstrained Bayesian Networks: Theory, Optimization, and Applications
106
0
0.0
(
0
)
Added by
Michael Huth
Publication date
2017
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data for the learning of causal network structure or probability values at nodes are available. Constrained Bayesian Networks generalize a Bayesian Network such that probabilities can be symbolic, arithmetic expressions and where the meaning of the network is constrained by finitely many formulas from the theory of the reals. A formal semantics for constrained Bayesian Networks over first-order logic of the reals is given, which enables non-linear and non-convex optimisation algorithms that rely on decision procedures for this logic, and supports the composition of several constrained Bayesian Networks. A non-trivial case study in arms control, where few or no data are available to assess the effectiveness of an arms inspection process, evaluates our approach. An open-access prototype implementation of these foundations and their algorithms uses the SMT solver Z3 as decision procedure, leverages an open-source package for Bayesian inference to symbolic computation, and is evaluated experimentally.
rate research
Read More
Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be in regions of the input space. Output-Constrained BNNs (OC-BNN) represent an interpretable approach of enforcing a range of constraints, fully consistent with the Bayesian framework and amenable to black-box inference. We demonstrate how OC-BNNs improve model robustness and prevent the prediction of infeasible outputs in two real-world applications of healthcare and robotics.
Semantic Web is actually an extension of the current one in that it represents information more meaningfully for humans and computers alike. It enables the description of contents and services in machine-readable form, and enables annotating, discovering, publishing, advertising and composing services to be automated. It was developed based on Ontology, which is considered as the backbone of the Semantic Web. In other words, the current Web is transformed from being machine-readable to machine-understandable. In fact, Ontology is a key technique with which to annotate semantics and provide a common, comprehensible foundation for resources on the Semantic Web. Moreover, Ontology can provide a common vocabulary, a grammar for publishing data, and can supply a semantic description of data which can be used to preserve the Ontologies and keep them ready for inference. This paper provides basic concepts of web services and the Semantic Web, defines the structure and the main applications of ontology, and provides many relevant terms are explained in order to provide a basic understanding of ontologies.
This paper deals with the following problem: modify a Bayesian network to satisfy a given set of probability constraints by only change its conditional probability tables, and the probability distribution of the resulting network should be as close as possible to that of the original network. We propose to solve this problem by extending IPFP (iterative proportional fitting procedure) to probability distributions represented by Bayesian networks. The resulting algorithm E-IPFP is further developed to D-IPFP, which reduces the computational cost by decomposing a global EIPFP into a set of smaller local E-IPFP problems. Limited analysis is provided, including the convergence proofs of the two algorithms. Computer experiments were conducted to validate the algorithms. The results are consistent with the theoretical analysis.
The content ranking problem in a social news website, is typically a function that maximizes a scalar metric of interest like dwell-time. However, like in most real-world applications we are interested in more than one metric---for instance simultaneously maximizing click-through rate, monetization metrics, dwell-time---and also satisfy the traffic requirements promised to different publishers. All this needs to be done on online data and under the settings where the objective function and the constraints can dynamically change; this could happen if for instance new publishers are added, some contracts are adjusted, or if some contracts are over. In this paper, we formulate this problem as a constrained, dynamic, multi-objective optimization problem. We propose a novel framework that extends a successful genetic optimization algorithm, NSGA-II, to solve this online, data-driven problem. We design the modules of NSGA-II to suit our problem. We evaluate optimization performance using Hypervolume and introduce a confidence interval metric for assessing the practicality of a solution. We demonstrate the application of this framework on a real-world Article Ranking problem. We observe that we make considerable improvements in both time and performance over a brute-force baseline technique that is currently in production.
We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we use the Hamiltonian Monte Carlo method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fideilty data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
