Two other algorithms require the knowledge Markov Decision Processes (MDPs) offer a general framework of the optimal policy and its expected reward. We show to describe probabilistic planning problems of varying that the expected reward of the optimal policy is a lower complexity. The development of algorithms that act successfully bound for the expected performance of both strategies. in MDPs is important to many AI applications. Our final algorithm switches between the application of Since it is often impossible or intractable to evaluate MDP the optimal policy and the policy with the highest possible algorithms based on a theoretical analysis alone, the International outcome, which can be computed without notable overhead Probabilistic Planning Competition (IPPC) was introduced in the Trial-based Heuristic Tree Search (THTS) framework to allow a comparison based on experimental evaluation. (Keller and Helmert 2013). We show theoretically and empirically The idea is to approximate the quality of an MDP that all algorithms outperform the naïve base approach solver by performing a sequence of runs on a problem instance, that ignores the potential of optimizing evaluation and by using the average of the obtained results as runs in hindsight, and that it pays off to take suboptimal base an approximation of the expected reward.

Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the probability of given queries being true provided a set of mutually independent random variables, a model (a logic program) and some evidence. The core of solving this inference task involves translating the logic program to a propositional theory and using a model counter. In this paper, we show that for some problems that involve inductive definitions like reachability in a graph, the translation of logic programs to SAT can be expensive for the purpose of solving inference tasks. For such problems, direct implementation of stable model semantics allows for more efficient solving. We present two implementation techniques, based on unfounded set detection, that extend a propositional model counter to a stable model counter. Our experiments show that for particular problems, our approach can outperform a state-of-the-art probabilistic logic programming solver by several orders of magnitude in terms of running time and space requirements, and can solve instances of significantly larger sizes on which the current solver runs out of time or memory.

Many real-world Bayesian inference problems such as preference learning or trader valuation modeling in financial markets naturally use piecewise likelihoods. Unfortunately, exact closed-form inference in the underlying Bayesian graphical models is intractable in the general case and existing approximation techniques provide few guarantees on both approximation quality and efficiency. While (Markov Chain) Monte Carlo methods provide an attractive asymptotically unbiased approximation approach, rejection sampling and Metropolis-Hastings both prove inefficient in practice, and analytical derivation of Gibbs samplers require exponential space and time in the amount of data. In this work, we show how to transform problematic piecewise likelihoods into equivalent mixture models and then provide a blocked Gibbs sampling approach for this transformed model that achieves an exponential-to-linear reduction in space and time compared to a conventional Gibbs sampler. This enables fast, asymptotically unbiased Bayesian inference in a new expressive class of piecewise graphical models and empirically requires orders of magnitude less time than rejection, Metropolis-Hastings, and conventional Gibbs sampling methods to achieve the same level of accuracy.

Recent advances in Symbolic Dynamic Programming (SDP) combined withthe extended algebraic decision diagram (XADD) have provided exactsolutions for expressive subclasses of finite-horizon Hybrid MarkovDecision Processes (HMDPs) with mixed continuous and discrete stateand action parameters. Unfortunately, SDP suffers from two majordrawbacks: (1) it solves for all states and can be intractable formany problems that inherently have large optimal XADD value functionrepresentations; and (2) it cannot maintain compact (pruned) XADDrepresentations for domains with nonlinear dynamics and reward due tothe need for nonlinear constraint checking. In this work, wesimultaneously address both of these problems by introducing real-timeSDP (RTSDP). RTSDP addresses (1) by focusing the solution and valuerepresentation only on regions reachable from a set of initial statesand RTSDP addresses (2) by using visited states as witnesses ofreachable regions to assist in pruning irrelevant or unreachable(nonlinear) regions of the value function. To this end, RTSDP enjoysprovable convergence over the set of initial states and substantialspace and time savings over SDP as we demonstrate in a variety of hybrid domains ranging from inventory to reservoir to traffic control.

We present a planner named Transition Constraints for Parallel Planning (TCPP). TCPP constructs a new constraint model from domain transition graphs (DTG) of a given planning problem. TCPP encodes the constraint model by using table constraints that allow don't cares or wild cards as cell values. TCPP uses Minion the constraint solver to solve the constraint model and returns the parallel plan. Empirical results exhibit the efficiency of our planning system over state-of-the-art constraint-based planners.

Symmetric Positive Definite (SPD) matrices in the form of region covariances are considered rich descriptors for images and videos. Recent studies suggest that exploiting the Riemannian geometry of the SPD manifolds could lead to improved performances for vision applications. For tasks involving processing large-scale and dynamic data in computer vision, the underlying model is required to progressively and efficiently adapt itself to the new and unseen observations. Motivated by these requirements, this paper studies the problem of online dictionary learning on the SPD manifolds. We make use of the Stein divergence to recast the problem of online dictionary learning on the manifolds to a problem in Reproducing Kernel Hilbert Spaces, for which, we develop efficient algorithms by taking into account the geometric structure of the SPD manifolds. To our best knowledge, our work is the first study that provides a solution for online dictionary learning on the SPD manifolds. Empirical results on both large-scale image classification task and dynamic video processing tasks validate the superior performance of our approach as compared to several state-of-the-art algorithms.

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-order interaction structures. This paper introduces Tensor-variate Restricted Boltzmann Machines (TvRBMs) which generalize RBMs to capture the multiplicative interaction between data modes and the latent variables. TvRBMs are highly compact in that the number of free parameters grows only linear with the number of modes. We demonstrate the capacity of TvRBMs on three real-world applications: handwritten digit classification, face recognition and EEG-based alcoholic diagnosis. The learnt features of the model are more discriminative than the rivals, resulting in better classification performance.

Multi-label image classification is of significant interest due to its major role in real-world web image analysis applications such as large-scale image retrieval and browsing. Recently, matrix completion (MC) has been developed to deal with multi-label classification tasks. MC has distinct advantages, such as robustness to missing entries in the feature and label spaces and a natural ability to handle multi-label problems. However, current MC-based multi-label image classification methods only consider data represented by a single-view feature, therefore, do not precisely characterize images that contain several semantic concepts. An intuitive way to utilize multiple features taken from different views is to concatenate the different features into a long vector; however, this concatenation is prone to over-fitting and leads to high time complexity in MC-based image classification. Therefore, we present a novel multi-view learning model for MC-based image classification, called low-rank multi-view matrix completion (lrMMC), which first seeks a low-dimensional common representation of all views by utilizing the proposed low-rank multi-view learning (lrMVL) algorithm. In lrMVL, the common subspace is constrained to be low rank so that it is suitable for MC. In addition, combination weights are learned to explore complementarity between different views. An efficient solver based on fixed-point continuation (FPC) is developed for optimization, and the learned low-rank representation is then incorporated into MC-based image classification. Extensive experimentation on the challenging PASCAL VOC' 07 dataset demonstrates the superiority of lrMMC compared to other multi-label image classification approaches.

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance.

While the Web of data is attracting increasing interest and rapidly growing in size, the major support of information on the surface Web are still multimedia documents. Semantic annotation of texts is one of the main processes that are intended to facilitate meaning-based information exchange between computational agents. However, such annotation faces several challenges such as the heterogeneity of natural language expressions, the heterogeneity of documents structure and context dependencies. While a broad range of annotation approaches rely mainly or partly on the target textual context to disambiguate the extracted entities, in this paper we present an approach that relies mainly on formalized-knowledge expressed in RDF datasets to categorize and disambiguate noun phrases. In the proposed method, we represent the reference knowledge bases as co-occurrence matrices and the disambiguation problem as a 0-1 Integer Linear Programming (ILP) problem. The proposed approach is unsupervised and can be ported to any RDF knowledge base. The system implementing this approach, called KODA, shows very promising results w.r.t. state-of-the-art annotation tools in cross-domain experimentations.