Tag Archives: Bayesian Networks

Example of learning a Bayesian network using expert knowledge

H. Amirkhani, M. Rahmati, P. J. F. Lucas and A. Hommersom, Exploiting Experts’ Knowledge for Structure Learning of Bayesian Networks, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, no. 11, pp. 2154-2170, DOI: 10.1109/TPAMI.2016.2636828.

Learning Bayesian network structures from data is known to be hard, mainly because the number of candidate graphs is super-exponential in the number of variables. Furthermore, using observational data alone, the true causal graph is not discernible from other graphs that model the same set of conditional independencies. In this paper, it is investigated whether Bayesian network structure learning can be improved by exploiting the opinions of multiple domain experts regarding cause-effect relationships. In practice, experts have different individual probabilities of correctly labeling the inclusion or exclusion of edges in the structure. The accuracy of each expert is modeled by three parameters. Two new scoring functions are introduced that score each candidate graph based on the data and experts’ opinions, taking into account their accuracy parameters. In the first scoring function, the experts’ accuracies are estimated using an expectation-maximization-based algorithm and the estimated accuracies are explicitly used in the scoring process. The second function marginalizes out the accuracy parameters to obtain more robust scores when it is not possible to obtain a good estimate of experts’ accuracies. The experimental results on simulated and real world datasets show that exploiting experts’ knowledge can improve the structure learning if we take the experts’ accuracies into account.

Example of application of bayesian network learning and inference to robotics, and a brief but useful related work on learning by imitation

Dan Song; Ek, C.H.; Huebner, K.; Kragic, D., Task-Based Robot Grasp Planning Using Probabilistic Inference, Robotics, IEEE Transactions on , vol.31, no.3, pp.546,561, June 2015, DOI: 10.1109/TRO.2015.2409912.

Grasping and manipulating everyday objects in a goal-directed manner is an important ability of a service robot. The robot needs to reason about task requirements and ground these in the sensorimotor information. Grasping and interaction with objects are challenging in real-world scenarios, where sensorimotor uncertainty is prevalent. This paper presents a probabilistic framework for the representation and modeling of robot-grasping tasks. The framework consists of Gaussian mixture models for generic data discretization, and discrete Bayesian networks for encoding the probabilistic relations among various task-relevant variables, including object and action features as well as task constraints. We evaluate the framework using a grasp database generated in a simulated environment including a human and two robot hand models. The generative modeling approach allows the prediction of grasping tasks given uncertain sensory data, as well as object and grasp selection in a task-oriented manner. Furthermore, the graphical model framework provides insights into dependencies between variables and features relevant for object grasping.

Brief but nice related work about structured prediction (MRFs, CRFs, etc.)

Bratieres, S.; Quadrianto, N.; Ghahramani, Z., GPstruct: Bayesian Structured Prediction Using Gaussian Processes, Pattern Analysis and Machine Intelligence, IEEE Transactions on , vol.37, no.7, pp.1514,1520, July 1 2015, DOI: 10.1109/TPAMI.2014.2366151.

We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M ^3 N), and structured support vector machines (SVMstruct), which embody only a subset of its properties. We present an inference procedure based on Markov Chain Monte Carlo. The framework can be instantiated for a wide range of structured objects such as linear chains, trees, grids, and other general graphs. As a proof of concept, the model is benchmarked on several natural language processing tasks and a video gesture segmentation task involving a linear chain structure. We show prediction accuracies for GPstruct which are comparable to or exceeding those of CRFs and SVMstruct.

How to bypass the NP-hardness of estimating the best explanation of given data (instantiated as MAP, i.e., Maximum A Posteriori, not as maximum likelihood) in discrete Bayesian Networks, through distinction of relevant and irrelevant variables

Johan Kwisthout, Most frugal explanations in Bayesian networks, Artificial Intelligence, Volume 218, January 2015, Pages 56-73, ISSN 0004-3702, DOI: 10.1016/j.artint.2014.10.001

Inferring the most probable explanation to a set of variables, given a partial observation of the remaining variables, is one of the canonical computational problems in Bayesian networks, with widespread applications in AI and beyond. This problem, known as MAP, is computationally intractable (NP-hard) and remains so even when only an approximate solution is sought. We propose a heuristic formulation of the MAP problem, denoted as Inference to the Most Frugal Explanation (MFE), based on the observation that many intermediate variables (that are neither observed nor to be explained) are irrelevant with respect to the outcome of the explanatory process. An explanation based on few samples (often even a singleton sample) from these irrelevant variables is typically almost as good as an explanation based on (the computationally costly) marginalization over these variables. We show that while MFE is computationally intractable in general (as is MAP), it can be tractably approximated under plausible situational constraints, and its inferences are fairly robust with respect to which intermediate variables are considered to be relevant.