In this paper, we address the problem of merging multiple imprecise probabilistic beliefs represented as Probabilistic Logic Programs (PLPs) obtained from multiple sources. Beliefs in each PLP are modeled as conditional events attached with probability bounds. The major task of syntax-based merging is to obtain the most rational probability bound for each conditional event from the original PLPs to form a new PLP. We require the minimal change principle to be followed so that each source gives up its beliefs as little as possible. Some instantiated merging operators are derived from our merging framework. Furthermore, we propose a set of postulates for merging PLPs, some of which extend the postulates for merging classical knowledge bases, whilst others are specific to the merging of probabilistic beliefs.

Linear causal models known as structural equation models (SEMs) are widely used for data analysis in the social sciences, economics, and artificial intelligence, in which random variables are assumed to be continuous and normally distributed. This paper deals with one fundamental problem in the applications of SEMs -- parameter identification. The paper uses the graphical models approach and provides a procedure for solving the identification problem in a special class of SEMs.

We consider the problem of testing whether two variables should be adjacent (either due to a direct effect between them, or due to a hidden common cause) given an observational distribution, and a set of causal assumptions encoded as a causal diagram. In other words, given a set of edges in the diagram known to be true, we are interested in testing whether another edge ought to be in the diagram. In fully observable faithful models this problem can be easily solved with conditional independence tests. Latent variables make the problem significantly harder since they can imply certain non-adjacent variable pairs, namely those connected by so called inducing paths, are not independent conditioned on any set of variables. We characterizewhich variable pairs can be determined to be non-adjacent by a class of constraints due to dormant independence, that is conditional independence in identifiable interventional distributions. Furthermore, we show that particular operations on joint distributions, which we call truncations are sufficient for exhibiting these non-adjacencies.This suggests a causal discovery procedure taking advantage of these constraints in the latent variable case can restrict itself to truncations.

Despite the success of Gaussian processes (GPs) in modelling spatial stochastic processes, dealing with large datasets is still challenging. The problem arises by the need to invert a potentially large covariance matrix during inference. In this paper we address the complexity problem by constructing a new stationary covariance function (Mercer kernel) that naturally provides a sparse covariance matrix. The sparseness of the matrix is defined by hyper-parameters optimised during learning. The new covariance function enables exact GP inference and performs comparatively to the squared-exponential one, at a lower computational cost. This allows the application of GPs to large-scale problems such as ore grade prediction in mining or 3D surface modelling. Experiments show that using the proposed covariance function, very sparse covariance matrices are normally obtained which can be effectively used for faster inference and less memory usage.

We investigate the problem of eliciting CP-nets in the well-known model of exact learning with equivalence and membership queries. The goal is to identify a preference ordering with a binary-valued CP-net by guiding the user through a sequence of queries. Each example is a dominance test on some pair of outcomes. In this setting, we show that acyclic CP-nets are not learnable with equivalence queries alone, while they are learnable with the help of membership queries if the supplied examples are restricted to swaps. A similar property holds for tree CP-nets with arbitrary examples. In fact, membership queries allow us to provide attribute-efficient algorithms for which the query complexity is only logarithmic in the number of attributes. Such results highlight the utility of this model for eliciting CP-nets in large multi-attribute domains.

As exact inference for first-order probabilistic graphical models at the propositional level can be formidably expensive, there is an ongoing effort to design efficient lifted inference algorithms for such models. This paper discusses directed first-order models that require an aggregation operator when a parent random variable is parameterized by logical variables that are not present in a child random variable. We introduce a new data structure, aggregation parfactors, to describe aggregation in directed first-order models. We show how to extend Milch et al.'s C-FOVE algorithm to perform lifted inference in the presence of aggregation parfactors. We also show that there are cases where the polynomial time complexity (in domain size of logical variables) of the C-FOVE algorithm can be reduced to logarithmic time complexity using aggregation parfactors.

First order decision diagrams (FODD) were recently introduced as a compact knowledge representation expressing functions over relational structures. FODDs represent numerical functions that, when constrained to the Boolean range, use only existential quantification. Previous work developed a set of operations over FODDs, showed how they can be used to solve relational Markov decision processes (RMDP) using dynamic programming algorithms, and demonstrated their success in solving stochastic planning problems from the International Planning Competition in the system FODD-Planner. A crucial ingredient of this scheme is a set of operations to remove redundancy in decision diagrams, thus keeping them compact. This paper makes three contributions. First, we introduce Generalized FODDs (GFODD) and combination algorithms for them, generalizing FODDs to arbitrary quantification. Second, we show how GFODDs can be used in principle to solve RMDPs with arbitrary quantification, and develop a particularly promising case where an arbitrary number of existential quantifiers is followed by an arbitrary number of universal quantifiers. Third, we develop a new approach to reduce FODDs and GFODDs using model checking. This yields a reduction that is complete for FODDs and provides a sound reduction procedure for GFODDs.

This paper deals with Decision-Making in the context of multiattribute utility theory and, more precisely, with the problem of efficiently determining the best alternative w.r.t. an agent's preferences (choice problem). We assume that alternatives are elements of a product set of attributes and that the agent's preferences are represented by a generalized additive decomposable (GAI) utility on this set. Such a function allows an efficient representation of interactions between attributes while preserving some decomposability of the model. GAI utilities can be compiled into graphical structures called GAI networks that can be exploited to solve choice problems using collect/distribute schemes essentially similar to those used in Bayesian networks. In this paper, rather than directly using this scheme on the GAI network for determining the most preferred alternative, we propose to work with another GAI function, acting as an upper-bound on utility values and enhancing the model's decomposability. This method still provides the exact optimal solution but speeds up significantly the search. It proves to be particularly useful when dealing with choice and ranking under constraints and within collective Decision-Making, where GAI nets tend to have a large size. We present an efficient algorithm for determining this new GAI function and provide experimental results highlighting the practical efficiency of our procedure.

CP-networks have been proposed as a simple and intuitive graphical tool for representing conditional ceteris paribus preference statements over the values of a set of variables. While the problem of reasoning with CP-networks has been receiving some attention, there are very few works that address the problem of learning CP-networks. In this work we investigate the task of learning CP-networks, given access to a set of pairwise comparisons. We first prove that the learning problem is intractable, even under several simplifying assumptions. We then present an algorithm that, under certain assumptions about the observed pairwise comparisons, identifies a CP-network that entails these comparisons. We finally show that the proposed algorithm is a PAC-learner, and, thus, that the CP-networks it induces accurately predict the user's preferences on previously unseen situations.

Automatic recognition of human activities is among the key capabilities of many intelligent systems with vision/perception. Most existing approaches to this problem require sophisticated feature extraction before classification can be performed. This paper presents a novel approach for human action recognition using only simple low-level visual features: motion captured from direct frame differencing. A codebook of key poses is first created from the training data through unsupervised clustering. Videos of actions are then coded as sequences of super-frames, defined as the key poses augmented with discriminative attributes. A weighted-sequence distance is proposed for comparing two super-frame sequences, which is further wrapped as a kernel embedded in a SVM classifier for the final classification. Compared with conventional methods, our approach provides a flexible non-parametric sequential structure with a corresponding distance measure for human action representation and classification without requiring complex feature extraction. The effectiveness of our approach is demonstrated with the widely-used KTH human activity dataset, for which the proposed method outperforms the existing state-of-the-art.