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Semantics of negative sequential patterns

arXiv.org Artificial Intelligence

In the field of pattern mining, a negative sequential pattern is specified by means of a sequence consisting of events to occur and of other events, called negative events, to be absent. For instance, containment of the pattern $\langle a\ \neg b\ c\rangle$ arises with an occurrence of a and a subsequent occurrence of c but no occurrence of b in between. This article is to shed light on the ambiguity of such a seemingly intuitive notation and we identify eight possible semantics for the containment relation between a pattern and a sequence. These semantics are illustrated and formally studied, in particular we propose dominance and equivalence relations between them. Also we prove that support is anti-monotonic for some of these semantics. Some of the results are discussed with the aim of developing algorithms to extract efficiently frequent negative patterns.


Preference Orders on Families of Sets - When Can Impossibility Results Be Avoided?

Journal of Artificial Intelligence Research

Lifting a preference order on elements of some universe to a preference order on subsets of this universe is often guided by postulated properties the lifted order should have. Well-known impossibility results pose severe limits on when such liftings exist if all non-empty subsets of the universe are to be ordered. The extent to which these negative results carry over to other families of sets is not known. In this paper, we consider families of sets that induce connected subgraphs in graphs. For such families, common in applications, we study whether lifted orders satisfying the well-studied axioms of dominance and (strict) independence exist for every or, in another setting, for some underlying order on elements (strong and weak orderability). We characterize families that are strongly and weakly orderable under dominance and strict independence, and obtain a tight bound on the class of families that are strongly orderable under dominance and independence.


A Bayesian Choice Model for Eliminating Feedback Loops

arXiv.org Machine Learning

Self-reinforcing feedback loops in personalization systems are typically caused by users choosing from a limited set of alternatives presented systematically based on previous choices. We propose a Bayesian choice model built on Luce axioms that explicitly accounts for users' limited exposure to alternatives. Our model is fair---it does not impose negative bias towards unpresented alternatives, and practical---preference estimates are accurately inferred upon observing a small number of interactions. It also allows efficient sampling, leading to a straightforward online presentation mechanism based on Thompson sampling. Our approach achieves low regret in learning to present upon exploration of only a small fraction of possible presentations. The proposed structure can be reused as a building block in interactive systems, e.g., recommender systems, free of feedback loops.


Differentiating Concepts and Instances for Knowledge Graph Embedding

arXiv.org Artificial Intelligence

Concepts, which represent a group of different instances sharing common properties, are essential information in knowledge representation. Most conventional knowledge embedding methods encode both entities (concepts and instances) and relations as vectors in a low dimensional semantic space equally, ignoring the difference between concepts and instances. In this paper, we propose a novel knowledge graph embedding model named TransC by differentiating concepts and instances. Specifically, TransC encodes each concept in knowledge graph as a sphere and each instance as a vector in the same semantic space. We use the relative positions to model the relations between concepts and instances (i.e., instanceOf), and the relations between concepts and sub-concepts (i.e., subClassOf). We evaluate our model on both link prediction and triple classification tasks on the dataset based on YAGO. Experimental results show that TransC outperforms state-of-the-art methods, and captures the semantic transitivity for instanceOf and subClassOf relation. Our codes and datasets can be obtained from https:// github.com/davidlvxin/TransC.


On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators

arXiv.org Artificial Intelligence

Darwiche and Pearl's seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most of the suggestions made have resulted in a form of `reductionism' that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka `Independence', characteristic of `admissible' revision operators, remain commendably more modest. In this paper, we supplement both the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states that are associated with a `proper ordinal interval' (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of a large number of AGM era postulates, including Superexpansion, that are not sound for admissible operators in general.


Cycles and Intractability in a Large Class of Aggregation Rules

Journal of Artificial Intelligence Research

We introduce the (j,k)-Kemeny rule -- a generalization of Kemeny's voting rule that aggregates j-chotomous weak orders into a k-chotomous weak order. Special cases of (j,k)-Kemeny include approval voting, the mean rule and Borda mean rule, as well as the Borda count and plurality voting. Why, then, is the winner problem computationally tractable for each of these other rules, but intractable for Kemeny? We show that intractability of winner determination for the (j,k)-Kemeny rule first appears at the j=3, k=3 level. The proof rests on a reduction of max cut to a related problem on weighted tournaments, and reveals that computational complexity arises from the cyclic part in the fundamental decomposition of a weighted tournament into cyclic and cocyclic components. Thus the existence of majority cycles -- the engine driving both Arrow's impossibility theorem and the Gibbard-Satterthwaite theorem -- also serves as a source of computational complexity in social choice.


COBRA: A Fast and Simple Method for Active Clustering with Pairwise Constraints

arXiv.org Machine Learning

Clustering is inherently ill-posed: there often exist multiple valid clusterings of a single dataset, and without any additional information a clustering system has no way of knowing which clustering it should produce. This motivates the use of constraints in clustering, as they allow users to communicate their interests to the clustering system. Active constraint-based clustering algorithms select the most useful constraints to query, aiming to produce a good clustering using as few constraints as possible. We propose COBRA, an active method that first over-clusters the data by running K-means with a $K$ that is intended to be too large, and subsequently merges the resulting small clusters into larger ones based on pairwise constraints. In its merging step, COBRA is able to keep the number of pairwise queries low by maximally exploiting constraint transitivity and entailment. We experimentally show that COBRA outperforms the state of the art in terms of clustering quality and runtime, without requiring the number of clusters in advance.


On the Transitivity of Hypernym-Hyponym Relations in Data-Driven Lexical Taxonomies

AAAI Conferences

Taxonomy is indispensable in understanding natural language. A variety of large scale, usage-based, data-driven lexical taxonomies have been constructed in recent years.Hypernym-hyponym relationship, which is considered as the backbone of lexical taxonomies can not only be used to categorize the data but also enables generalization. In particular, we focus on one of the most prominent properties of the hypernym-hyponym relationship, namely, transitivity, which has a significant implication for many applications. We show that, unlike human crafted ontologies and taxonomies, transitivity does not always hold in data-drivenlexical taxonomies. We introduce a supervised approach to detect whether transitivity holds for any given pair of hypernym-hyponym relationships. Besides solving the inferencing problem, we also use the transitivity to derive new hypernym-hyponym relationships for data-driven lexical taxonomies. We conduct extensive experiments to show the effectiveness of our approach.


Combining Existential Rules and Transitivity: Next Steps

arXiv.org Artificial Intelligence

We consider existential rules (aka Datalog+) as a formalism for specifying ontologies. In recent years, many classes of existential rules have been exhibited for which conjunctive query (CQ) entailment is decidable. However, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. In this paper, we address the issue of whether transitivity can be safely combined with decidable classes of existential rules. First, we prove that transitivity is incompatible with one of the simplest decidable classes, namely aGRD (acyclic graph of rule dependencies), which clarifies the landscape of `finite expansion sets' of rules. Second, we show that transitivity can be safely added to linear rules (a subclass of guarded rules, which generalizes the description logic DL-Lite-R) in the case of atomic CQs, and also for general CQs if we place a minor syntactic restriction on the rule set. This is shown by means of a novel query rewriting algorithm that is specially tailored to handle transitivity rules. Third, for the identified decidable cases, we pinpoint the combined and data complexities of query entailment.


Graph Aggregation

arXiv.org Artificial Intelligence

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference orders), when consolidating conflicting views regarding the relationships between arguments in a debate (graphs as abstract argumentation frameworks), or when computing a consensus between several alternative clusterings of a given dataset (graphs as equivalence relations). In this paper, we introduce a formal framework for graph aggregation grounded in social choice theory. Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule. We consider both common properties of graphs, such as transitivity and reflexivity, and arbitrary properties expressible in certain fragments of modal logic. Our results establish several connections between the types of properties preserved under aggregation and the choice-theoretic axioms satisfied by the rules used. The most important of these results is a powerful impossibility theorem that generalises Arrow's seminal result for the aggregation of preference orders to a large collection of different types of graphs.