Evidence reasoning for event inference in smart transport video surveillance

In this paper we present a new event recognition framework, based on the Dempster-Shafer theory of evidence, which combines the evidence from multiple atomic events detected by low-level computer vision analytics. The proposed framework employs evidential network modelling of composite events. This approach can effectively handle the uncertainty of the detected events, whilst inferring high-level events that have semantic meaning with high degrees of belief. Our scheme has been comprehensively evaluated against various scenarios that simulate passenger behaviour on public transport platforms such as buses and trains. The average accuracy rate of our method is 81% in comparison to 76% by a standard rule-based method.

Global Sensitivity Analysis for MAP Inference in Graphical Models

We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

IDS: A Divide-and-Conquer Algorithm for Inference in Polytree-Shaped Credal Networks

A credal network is a graph-theoretic model that represents imprecision in joint probability distributions. An inference in a credal net aims at computing an interval for the probability of an event of interest. Algorithms for inference in credal networks can be divided into exact and approximate. The selection of an algorithm is based on a trade off that ponders how much time someone wants to spend in a particular calculation against the quality of the computed values. This paper presents an algorithm, called IDS, that combines exact and approximate methods for computing inferences in polytree-shaped credal networks. The algorithm provides an approach to trade time and precision when making inferences in credal nets

Generalized loopy 2U: A new algorithm for approximate inference in credal networks

Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.

Generalized Loopy 2U: A New Algorithm for Approximate Inference in Credal Networks

Credal nets generalize Bayesian nets by relaxing the requirement of precision of probabilities. Credal nets are considerably more expressive than Bayesian nets, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal nets. The algorithm is based on an important representation result we prove for general credal nets: that any credal net can be equivalently reformulated as a credal net with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal net is updated by L2U, a loopy approximate algorithm for binary credal nets. Thus, we generalize L2U to non-binary credal nets, obtaining an accurate and scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences is evaluated by empirical tests.

Inference with multinomial data: why to weaken the prior strength

This paper considers inference from multinomial data and addresses the problem of choosing the strength of the Dirichlet prior under a mean-squared error criterion. We compare the Maxi-mum Likelihood Estimator (MLE) and the most commonly used Bayesian estimators obtained by assuming a prior Dirichlet distribution with non-informative prior parameters, that is, the parameters of the Dirichlet are equal and altogether sum up to the so called strength of the prior. Under this criterion, MLE becomes more preferable than the Bayesian estimators at the increase of the number of categories k of the multinomial, because non-informative Bayesian estimators induce a region where they are dominant that quickly shrinks with the increase of k. This can be avoided if the strength of the prior is not kept constant but decreased with the number of categories. We argue that the strength should decrease at least k times faster than usual estimators do.

Inference in Credal Networks Through Integer Programming

A credal network associates a directed acyclic graph with a collection of sets of probability measures; it offers a compact representation for sets of multivariate distributions. In this paper we present a new algorithm for inference in credal networks based on an integer programming reformulation. We are concerned with computation of lower/upper probabilities for a variable in a given credal network. Experiments reported in this paper indicate that this new algorithm has better performance than existing ones for some important classes of networks.

Anytime Marginal MAP Inference

This paper presents a new anytime algorithm for the marginal MAP problem in graphical models of bounded treewidth. We show asymptotic convergence and theoretical error bounds for any fixed step. Experiments show that it compares well to a state-of-the-art systematic search algorithm.

Inference in credal networks using multilinear programming

A credal network is a graphical tool for representation and manipulation of uncertainty, where probability values may be imprecise or indeterminate. A credal network associates a directed acyclic graph with a collection of sets of probability measures; in this context, inference is the computation of tight lower and upper bounds for conditional probabilities. In this paper we present new algorithms for inference in credal networks based on multilinear programming techniques. Experiments indicate that these new algorithms have better performance than existing ones, in the sense that they can produce more accurate results in larger networks.

A survey of location inference techniques on Twitter

The increasing popularity of the social networking service, Twitter, has made it more involved in day-to-day communications, strengthening social relationships and information dissemination. Conversations on Twitter are now being explored as indicators within early warning systems to alert of imminent natural disasters such earthquakes and aid prompt emergency responses to crime. Producers are privileged to have limitless access to market perception from consumer comments on social media and microblogs. Targeted advertising can be made more effective based on user profile information such as demography, interests and location. While these applications have proven beneficial, the ability to effectively infer the location of Twitter users has even more immense value. However, accurately identifying where a message originated from or author’s location remains a challenge thus essentially driving research in that regard. In this paper, we survey a range of techniques applied to infer the location of Twitter users from inception to state-of-the-art. We find significant improvements over time in the granularity levels and better accuracy with results driven by refinements to algorithms and inclusion of more spatial features.

Evidential event inference in transport video surveillance

This paper presents a new framework for multi-subject event inference in surveillance video, where measurements produced by low-level vision analytics usually are noisy, incomplete or incorrect. Our goal is to infer the composite events undertaken by each subject from noise observations. To achieve this, we consider the temporal characteristics of event relations and propose a method to correctly associate the detected events with individual subjects. The Dempster–Shafer (DS) theory of belief functions is used to infer events of interest from the results of our vision analytics and to measure conflicts occurring during the event association. Our system is evaluated against a number of videos that present passenger behaviours on a public transport platform namely buses at different levels of complexity. The experimental results demonstrate that by reasoning with spatio-temporal correlations, the proposed method achieves a satisfying performance when associating atomic events and recognising composite events involving multiple subjects in dynamic environments.

The Complexity of MAP Inference in Bayesian Networks Specified Through Logical Languages

We study the computational complexity of finding maximum a posteriori configurations in Bayesian networks whose probabilities are specified by logical formulas. This approach leads to a fine grained study in which local information such as context-sensitive independence and determinism can be considered. It also allows us to characterize more precisely the jump from tractability to NP-hardness and beyond, and to consider the complexity introduced by evidence alone.

Inference in Polytrees with Sets of Probabilities

Inferences in directed acyclic graphs associated with probability intervals and sets of probabilities are NP-hard, even for polytrees. We propose: 1) an improvement on Tessem’s A/R algorithm for inferences on polytrees associated with probability intervals; 2) a new algorithm for approximate inferences based on local search; 3) branch-and-bound algorithms that combine the previous techniques. The first two algorithms produce complementary approximate solutions, while branch-and-bound procedures can generate either exact or approximate solutions. We report improvements on existing techniques for inference with probability sets and intervals, in some cases reducing computational effort by several orders of magnitude.