Dependability modeling and evaluation is aimed at investigating that a system performs its function correctly in time. A usual way to achieve a high reliability, is to design redundant systems that contain several replicas of the same subsystem or component. State space methods for dependability analysis may suffer of the state space explosion problem in such a kind of situation. Combinatorial models, on the other hand, require the simplified assumption of statistical independence; however, in case of redundant systems, this does not guarantee a reduced number of modeled elements. In order to provide a more compact system representation, parametric system modeling has been investigated in the literature, in such a way that a set of replicas of a given subsystem is parameterized so that only one representative instance is explicitly included. While modeling aspects can be suitably addressed by these approaches, analytical tools working on parametric characterizations are often more difficult to be defined and the standard approach is to 'unfold' the parametric model, in order to exploit standard analysis algorithms working at the unfolded 'ground' level. Moreover, parameterized combinatorial methods still require the statistical independence assumption. In the present paper we consider the formalism of Parametric Fault Tree (PFT) and we show how it can be related to Probabilistic Horn Abduction (PHA). Since PHA is a framework where both modeling and analysis can be performed in a restricted first-order language, we aim at showing that converting a PFT into a PHA knowledge base will allow an approach to dependability analysis directly exploiting parametric representation. We will show that classical qualitative and quantitative dependability measures can be characterized within PHA. Furthermore, additional modeling aspects (such as noisy gates and local dependencies) as well as additional reliability measures (such as posterior probability analysis) can be naturally addressed by this conversion. A simple example of a multi-processor system with several replicated units is used to illustrate the approach.

Nonmonotonic influences have associated an ambiguous sign. These ambiguous signs typically give rise to uninformative results upon inference. We argue that a nonmonotonic influence can be associated with a more informative sign that indicates its effect in the current state of the network. To capture this effect, we introduce the concept of situational sign. Furthermore, if the network converts to a state in which all variables that provoke the nonmonotonicity have been observed, a nonmonotonic influence reduces to a monotonic one. We study the persistence and propagation of situational signs upon inference and give a method for establishing the sign of a reduced influence.

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying truth-degrees. Working within a very general framework for fuzzy logic which is able to capture a variety of types of inference under uncertainty, such as truth-functional fuzzy logics and certain types of probabilistic inference, we show how the idea of rational change from 'crisp' base revision, as embodied by the idea of partial meet revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy revision and illustrate how the operation works in several important special instances of the framework.

The motivation for this paper is to apply Bayesian structure learning using Model Averaging in large-scale networks. Currently, Bayesian model averaging algorithm is applicable to networks with only tens of variables, restrained by its super-exponential complexity. We present a novel framework, called LSBN(Large-Scale Bayesian Network), making it possible to handle networks with infinite size by following the principle of divide-and-conquer. The method of LSBN comprises three steps. In general, LSBN first performs the partition by using a second-order partition strategy, which achieves more robust results. LSBN conducts sampling and structure learning within each overlapping community after the community is isolated from other variables by Markov Blanket. Finally LSBN employs an efficient algorithm, to merge structures of overlapping communities into a whole. In comparison with other four state-of-art large-scale network structure learning algorithms such as ARACNE, PC, Greedy Search and MMHC, LSBN shows comparable results in five common benchmark datasets, evaluated by precision, recall and f-score. What's more, LSBN makes it possible to learn large-scale Bayesian structure by Model Averaging which used to be intractable. In summary, LSBN provides an scalable and parallel framework for the reconstruction of network structures. Besides, the complete information of overlapping communities serves as the byproduct, which could be used to mine meaningful clusters in biological networks, such as protein-protein-interaction network or gene regulatory network, as well as in social network.

Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficient relational variational inference algorithm that factors largescale probability models into simpler variational models, composed of mixtures of iid (Bernoulli) random variables. The algorithm takes probability relational models of largescale hybrid systems and converts them to a close-to-optimal variational models. Then, it efficiently calculates marginal probabilities on the variational models by using a latent (or lifted) variable elimination or a lifted stochastic sampling. This inference is unique because it maintains the relational structure upon individual observations and during inference steps.

Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning.

Understanding the adaptation process of plants to drought stress is essential in improving management practices, breeding strategies as well as engineering viable crops for a sustainable agriculture in the coming decades. Hyper-spectral imaging provides a particularly promising approach to gain such understanding since it allows to discover non-destructively spectral characteristics of plants governed primarily by scattering and absorption characteristics of the leaf internal structure and biochemical constituents. Several drought stress indices have been derived using hyper-spectral imaging. However, they are typically based on few hyper-spectral images only, rely on interpretations of experts, and consider few wavelengths only. In this study, we present the first data-driven approach to discovering spectral drought stress indices, treating it as an unsupervised labeling problem at massive scale. To make use of short range dependencies of spectral wavelengths, we develop an online variational Bayes algorithm for latent Dirichlet allocation with convolved Dirichlet regularizer. This approach scales to massive datasets and, hence, provides a more objective complement to plant physiological practices. The spectral topics found conform to plant physiological knowledge and can be computed in a fraction of the time compared to existing LDA approaches.

EDML is a recently proposed algorithm for learning MAP parameters in Bayesian networks. In this paper, we present a number of new advances and insights on the EDML algorithm. First, we provide the multivalued extension of EDML, originally proposed for Bayesian networks over binary variables. Next, we identify a simplified characterization of EDML that further implies a simple fixed-point algorithm for the convex optimization problem that underlies it. This characterization further reveals a connection between EDML and EM: a fixed point of EDML is a fixed point of EM, and vice versa. We thus identify also a new characterization of EM fixed points, but in the semantics of EDML. Finally, we propose a hybrid EDML/EM algorithm that takes advantage of the improved empirical convergence behavior of EDML, while maintaining the monotonic improvement property of EM.

Active Learning (AL) is increasingly important in a broad range of applications. Two main AL principles to obtain accurate classification with few labeled data are refinement of the current decision boundary and exploration of poorly sampled regions. In this paper we derive a novel AL scheme that balances these two principles in a natural way. In contrast to many AL strategies, which are based on an estimated class conditional probability ^p(y|x), a key component of our approach is to view this quantity as a random variable, hence explicitly considering the uncertainty in its estimated value. Our main contribution is a novel mathematical framework for uncertainty-based AL, and a corresponding AL scheme, where the uncertainty in ^p(y|x) is modeled by a second-order distribution. On the practical side, we show how to approximate such second-order distributions for kernel density classification. Finally, we find that over a large number of UCI, USPS and Caltech4 datasets, our AL scheme achieves significantly better learning curves than popular AL methods such as uncertainty sampling and error reduction sampling, when all use the same kernel density classifier.

Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in social sciences and marketing, "analytical ability" in educational testing, or "inflation" in economics). This leads to the development of measurement instruments to record noisy indirect evidence for such unobserved variables such as surveys, tests and price indexes. In such problems, there are postulated latent variables and a given measurement model. At the same time, other unantecipated latent variables can add further unmeasured confounding to the observed variables. The problem is how to deal with unantecipated latents variables. In this paper, we provide a method loosely inspired by canonical correlation that makes use of background information concerning the "known" latent variables. Given a partially specified structure, it provides a structure learning approach to detect "unknown unknowns," the confounding effect of potentially infinitely many other latent variables. This is done without explicitly modeling such extra latent factors. Because of the special structure of the problem, we are able to exploit a new variation of composite likelihood fitting to efficiently learn this structure. Validation is provided with experiments in synthetic data and the analysis of a large survey done with a sample of over 100,000 staff members of the National Health Service of the United Kingdom.