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Register a new userThe Complexity of Learning Acyclic Conditional Preference Networks
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Eisa Alanazi
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Learning of user preferences, as represented by, for example, Conditional Preference Networks (CP-nets), has become a core issue in AI research. Recent studies investigate learning of CP-nets from randomly chosen examples or from membership and equivalence queries. To assess the optimality of learning algorithms as well as to better understand the combinatorial structure of classes of CP-nets, it is helpful to calculate certain learning-theoretic information complexity parameters. This article focuses on the frequently studied case of learning from so-called swap examples, which express preferences among objects that differ in only one attribute. It presents bounds on or exact values of some well-studied information complexity parameters, namely the VC dimension, the teaching dimension, and the recursive teaching dimension, for classes of acyclic CP-nets. We further provide algorithms that learn tree-structured and general acyclic CP-nets from membership queries. Using our results on complexity parameters, we assess the optimality of our algorithms as well as that of another query learning algorithm for acyclic CP-nets presented in the literature. Our algorithms are near-optimal, and can, under certain assumptions, be adapted to the case when the membership oracle is faulty.
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Learning-based methods are increasingly popular for search algorithms in single-criterion optimization problems. In contrast, for multiple-criteria optimization there are significantly fewer approaches despite the existence of numerous applications. Constrained path-planning for Autonomous Ground Vehicles (AGV) is one such application, where an AGV is typically deployed in disaster relief or search and rescue applications in off-road environments. The agent can be faced with the following dilemma : optimize a source-destination path according to a known criterion and an uncertain criterion under operational constraints. The known criterion is associated to the cost of the path, representing the distance. The uncertain criterion represents the feasibility of driving through the path without requiring human intervention. It depends on various external parameters such as the physics of the vehicle, the state of the explored terrains or weather conditions. In this work, we leverage knowledge acquired through offline simulations by training a neural network model to predict the uncertain criterion. We integrate this model inside a path-planner which can solve problems online. Finally, we conduct experiments on realistic AGV scenarios which illustrate that the proposed framework requires human intervention less frequently, trading for a limited increase in the path distance.
Combinatorial preference aggregation has many applications in AI. Given the exponential nature of these preferences, compact representations are needed and ($m$)CP-nets are among the most studied ones. Sequential and global voting are two ways to aggregate preferences over CP-nets. In the former, preferences are aggregated feature-by-feature. Hence, when preferences have specific feature dependencies, sequential voting may exhibit voting paradoxes, i.e., it might select sub-optimal outcomes. To avoid paradoxes in sequential voting, one has often assumed the $mathcal{O}$-legality restriction, which imposes a shared topological order among all the CP-nets. On the contrary, in global voting, CP-nets are considered as a whole during preference aggregation. For this reason, global voting is immune from paradoxes, and there is no need to impose restrictions over the CP-nets topological structure. Sequential voting over $mathcal{O}$-legal CP-nets has extensively been investigated. On the other hand, global voting over non-$mathcal{O}$-legal CP-nets has not carefully been analyzed, despite it was stated in the literature that a theoretical comparison between global and sequential voting was promising and a precise complexity analysis for global voting has been asked for multiple times. In quite few works, very partial results on the complexity of global voting over CP-nets have been given. We start to fill this gap by carrying out a thorough complexity analysis of Pareto and majority global voting over not necessarily $mathcal{O}$-legal acyclic binary polynomially connected (m)CP-nets. We settle these problems in the polynomial hierarchy, and some of them in PTIME or LOGSPACE, whereas EXPTIME was the previously known upper bound for most of them. We show various tight lower bounds and matching upper bounds for problems that up to date did not have any explicit non-obvious lower bound.
It is an enduring question how to combine revealed preference (RP) and stated preference (SP) data to analyze travel behavior. This study presents a framework of multitask learning deep neural networks (MTLDNNs) for this question, and demonstrates that MTLDNNs are more generic than the traditional nested logit (NL) method, due to its capacity of automatic feature learning and soft constraints. About 1,500 MTLDNN models are designed and applied to the survey data that was collected in Singapore and focused on the RP of four current travel modes and the SP with autonomous vehicles (AV) as the one new travel mode in addition to those in RP. We found that MTLDNNs consistently outperform six benchmark models and particularly the classical NL models by about 5% prediction accuracy in both RP and SP datasets. This performance improvement can be mainly attributed to the soft constraints specific to MTLDNNs, including its innovative architectural design and regularization methods, but not much to the generic capacity of automatic feature learning endowed by a standard feedforward DNN architecture. Besides prediction, MTLDNNs are also interpretable. The empirical results show that AV is mainly the substitute of driving and AV alternative-specific variables are more important than the socio-economic variables in determining AV adoption. Overall, this study introduces a new MTLDNN framework to combine RP and SP, and demonstrates its theoretical flexibility and empirical power for prediction and interpretation. Future studies can design new MTLDNN architectures to reflect the speciality of RP and SP and extend this work to other behavioral analysis.
A matching is a set of edges in a graph with no common endpoint. A matching $M$ is called acyclic if the induced subgraph on the endpoints of the edges in $M$ is acyclic. Given a graph $G$ and an integer $k$, Acyclic Matching Problem seeks for an acyclic matching of size $k$ in $G$. The problem is known to be NP-complete. In this paper, we investigate the complexity of the problem in different aspects. First, we prove that the problem remains NP-complete for the class of planar bipartite graphs with maximum degree three and girth of arbitrary large. Also, the problem remains NP-complete for the class of planar line graphs with maximum degree four. Moreover, we study the parameterized complexity of the problem. In particular, we prove that the problem is W[1]-hard on bipartite graphs with respect to the parameter $k$. On the other hand, the problem is fixed parameter tractable with respect to $k$, for line graphs, $C_4$-free graphs and every proper minor-closed class of graphs (including bounded tree-width and planar graphs).
There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used to guide rewriting processes after learning from algebraic reasoning examples produced by humans. To enable the neural network to recognise patterns of algebraic expressions with non-deterministic sizes, reduced partial trees are used to represent the expressions. Also, to represent both top-down and bottom-up information of the expressions, a centralisation technique is used to improve the reduced partial trees. Besides, symbolic association vectors and rule application records are used to improve the rewriting processes. Experimental results reveal that the algebraic reasoning examples can be accurately learnt only if the feedforward neural network has enough hidden layers. Also, the centralisation technique, the symbolic association vectors and the rule application records can reduce error rates of reasoning. In particular, the above approaches have led to 4.6% error rate of reasoning on a dataset of linear equations, differentials and integrals.
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