The Sentential Decision Diagram (SDD) is a recently proposed representation of Boolean functions, containing Ordered Binary Decision Diagrams (OBDDs) as a distinguished subclass. While OBDDs are characterized by total variable orders, SDDs are characterized by dissections of variable orders, known as vtrees. Despite this generality, SDDs retain a number of properties, such as canonicity and a polytime apply operator, that have been critical to the practical success of OBDDs. Moreover, upper bounds on the size of SDDs were also given, which are tighter than comparable upper bounds on the size of OBDDs. In this paper, we analyze more closely some of the theoretical properties of SDDs and their size. In particular, we consider the impact of basing decisions on sentences (using dissections as in SDDs), in comparison to basing decisions on variables (using total variable orders as in OBDDs). Here, we identify a class of Boolean functions where basing decisions on sentences using dissections of a variable order can lead to exponentially more compact SDDs, compared to OBDDs based on the same variable order. Moreover, we identify a fundamental property of the decompositions that underlie SDDs and use it to show how certain changes to a vtree can also lead to exponential differences in the size of an SDD.

In this paper we introduce the notion of mapping-based knowledge base (MKB) to formalize the situation where both the extensional and the intensional level of the ontology are determined by suitable mappings to a set of (relational) data sources. This allows for making the intensional level of the ontology as dynamic as traditionally the extensional level is. To do so, we resort to the meta-modeling capabilities of higher-order Description Logics, which allow us to see concepts and roles as individuals, and vice versa. The challenge in this setting is to design tractable query answering algorithms. Besides the definition of MKBs, our main result is that answering instance queries posed to MKBs expressed in Hi(DL-LiteR) can be done efficiently. In particular, we define a query rewriting technique that produces first-order (SQL) queries to be posed to the data sources.

The existing classification-based policy iteration (CBPI) algorithms can be divided into two categories: direct policy iteration (DPI) methods that directly assign the output of the classifier (the approximate greedy policy w.r.t.~the current policy) to the next policy, and conservative policy iteration (CPI) methods in which the new policy is a mixture distribution of the current policy and the output of the classifier. The conservative policy update gives CPI a desirable feature, namely the guarantee that the policies generated by this algorithm improve at each iteration. We provide a detailed algorithmic and theoretical comparison of these two classes of CBPI algorithms. Our results reveal that in order to achieve the same level of accuracy, CPI requires more iterations, and thus, more samples than the DPI algorithm. Furthermore, CPI may converge to suboptimal policies whose performance is not better than DPI's.

In recent times, crowdsourcing over social networks has emerged as an active tool for complex task execution. In this paper, we address the problem faced by a planner to incentivize agents in the network to execute a task and also help in recruiting other agents for this purpose. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We define a set of fairness properties that should be ideally satisfied by a crowdsourcing mechanism. We prove that no mechanism can satisfy all these properties simultaneously. We relax some of these properties and define their approximate counterparts. Under appropriate approximate fairness criteria, we obtain a non-trivial family of payment mechanisms. Moreover, we provide precise characterizations of cost critical and time critical mechanisms.

Key challenges to widespread deployment of mobile robots to interact with humans in real-world domains include the ability to: (a) robustly represent and revise domain knowledge; (b) autonomously adapt sensing and processing to the task at hand; and (c) learn from unreliable high-level human feedback. Partially observable Markov decision processes (POMDPs) have been used to plan sensing and navigation in different application domains. It is however a challenge to include common sense knowledge obtained from sensory or human inputs in POMDPs. In addition, information extracted from sensory and human inputs may have varying levels of relevance to current and future tasks. On the other hand, although a non-monotonic logic programming paradigm such as Answer Set Programming (ASP) is wellsuited for common sense reasoning, it is unable to model the uncertainty in real-world sensing and navigation (Gelfond 2008). This paper presents a hybrid framework that integrates ASP, hierarchical POMDPs (Zhang and Sridharan 2012) and psychophysics principles to address the challenges stated above. Experimental results in simulation and on mobile robots deployed in indoor domains show that the framework results in reliable and efficient operation.

The current state-of-the-art algorithm for optimal coalition structure generation is IDP-IP — an algorithm that combines IDP (a dynamic programming algorithm due to Rahwan and Jennings, AAAI'08) with IP (a tree-search algorithm due to Rahwan et al., JAIR'09). In this paper we analyse IDP-IP, highlight its limitations, and then develop a new approach for combining IDP with IP that overcomes these limitations.

Hashing, which tries to learn similarity-preserving binary codes for data representation, has been widely used for efficient nearest neighbor search in massive databases due to its fast query speed and low storage cost. Because it is NP hard to directly compute the best binary codes for a given data set, mainstream hashing methods typically adopt a two-stage strategy. In the first stage, several projected dimensions of real values are generated. Then in the second stage, the real values will be quantized into binary codes by thresholding. Currently, most existing methods use one single bit to quantize each projected dimension. One problem with this single-bit quantization (SBQ) is that the threshold typically lies in the region of the highest point density and consequently a lot of neighboring points close to the threshold will be hashed to totally different bits, which is unexpected according to the principle of hashing. In this paper, we propose a novel quantization strategy, called double-bit quantization (DBQ), to solve the problem of SBQ. The basic idea of DBQ is to quantize each projected dimension into double bits with adaptively learned thresholds. Extensive experiments on two real data sets show that our DBQ strategy can significantly outperform traditional SBQ strategy for hashing.

As an emerging machine learning and information retrieval technique, the matrix completion has been successfully applied to solve many scientific applications, such as collaborative prediction in information retrieval, video completion in computer vision, \emph{etc}. The matrix completion is to recover a low-rank matrix with a fraction of its entries arbitrarily corrupted. Instead of solving the popularly used trace norm or nuclear norm based objective, we directly minimize the original formulations of trace norm and rank norm. We propose a novel Schatten $p$-Norm optimization framework that unifies different norm formulations. An efficient algorithm is derived to solve the new objective and followed by the rigorous theoretical proof on the convergence. The previous main solution strategy for this problem requires computing singular value decompositions - a task that requires increasingly cost as matrix sizes and rank increase. Our algorithm has closed form solution in each iteration, hence it converges fast. As a consequence, our algorithm has the capacity of solving large-scale matrix completion problems. Empirical studies on the recommendation system data sets demonstrate the promising performance of our new optimization framework and efficient algorithm.

It has been shown recently that the complexity of belief tracking in deterministic conformant and contingent planning is exponential in a width parameter that is often bounded and small. In this work, we introduce a new width notion that applies to non-deterministic conformant and contingent problems as well. We also develop a belief tracking algorithm for non-deterministic problems that is exponential in the problem width, analyze the width of non-deterministic benchmarks, compare the new notion to the previous one over deterministic problems, and present experimental results.

A central component in many applications is the underlying data management layer. In Data-Web applications, the central component of this layer is the triple store. It is thus evident that finding the most adequate store for the application to develop is of crucial importance for individual projects as well as for data integration on the Data Web in general. In this paper, we propose a generic benchmark creation procedure for SPARQL, which we apply to the DBpedia knowledge base. In contrast to previous approaches, our benchmark is based on queries that were actually issued by humans and applications against existing RDF data not resembling a relational schema. In addition, our approach does not only take the query string but also the features of the queries into consideration during the benchmark generation process. Our generic procedure for benchmark creation is based on query-log mining, SPARQL feature analysis and clustering. After presenting the method underlying our benchmark generation algorithm, we use the generated benchmark to compare the popular triple store implementations Virtuoso, Sesame, Jena-TDB, and BigOWLIM.