Ph.D. Dissertation Proposal Probabilities and Sets in Preference Querying

User preferences in databases are attracting increasing interests with the boom of information systems and the trend of personalization. In the literature, there are two different framework on this topic, namely quantitative approaches and qualitative approaches. The former assumes the availability of a scoring function, while the latter does not. Instead, in qualitative approaches, preferences are expressed using preference formulas. We investigate three advanced topics on preferences stemming from those frameworks. First, we study top-k queries over uncertain data in the quantitative framework. We formulate three intuitive semantic properties for top-k queries in probabilistic databases, and propose Global-Topk query semantics which satisfies them to a great degree. We also design efficient dynamic programming algorithms for query evaluation. Second, we observe that so far all work on top-k queries in probabilistic database focus on ordinal scores, while there are applications where cardinal scores are more appropriate. This motivates our work on preference strength, where we consider the magnitude of score in addition to the order they establish over tuples. Finally, as a counterpart to the top-k query in the quantitative framework, we explore the set preference problem in the qualitative framework. Observing the fact that preferences can also be collective in this case, our goal is to tackle this second-order problem with first-order tools. We propose a logical framework for set preferences. Candidate sets are represented using profiles consisting of scalar features. This reduces set preferences to tuple preferences over set profiles. We also propose algorithms to compute the “best” sets. 1 Research Motivations 1.1 Top-k Queries over Uncertain Data Top-k queries, as one type of preference queries, have been extensively studied in multimedia databases [35], middleware systems [34], data cleaning [22], core technology in relational databases [26, 27] etc. In the top-k problem, each tuple is given a score, and users are interested in k tuples with the highest scores. One the other hand, the study of incompleteness and uncertainty in databases has long been an interest of the database community [28, 10, 23, 1, 20, 41, 33]. Recently, this interest has been rekindled by an increasing demand for managing rich data, often incomplete and uncertain, emerging from scientific data management, sensor data management, data cleaning, information extraction etc. We study here the top-k problem in probabilistic databases. As a motivating example, let us consider the following graduate admission example. Example 1 A graduate admission committee need to select two winners of a fellowship. They narrow the candidates down to the following short list: Name Overall Score Aidan 0.65 Bob 0.55 Chris 0.45 Prob. of Coming 0.3 0.9 0.4 where the overall score is the normalized score of each candidate based on their qualifications, and the probability of acceptance is derived from historical statistics on candidates with similar qualifications and background. The committee want to make offers to the best two candidates who will take the offer. This decision problem can be formulated as a top-k query over the above probabilistic relation, where k 2. In Example 1, each tuple is associated with an event, which is that the candidate will accept the offer. The probability of the event is shown next to each tuple. In this example, all the events of tuples are independent, and tuples are therefore said to be independent. Such a relation is said to be simple. 1.2 Preference Strength When investigating top-k queries over uncertain data, like other works in the literature, we make the assumption that score is ordinal. That is, given two tuples t1 and t2, we only use the information such as “the score of t1 is higher than that of t2”. In other words, only the order of tuples induced by the scores matters, the actually magnitude of the score of each tuple does not. However, this assumption might not hold in some cases. Example 2 Considering the following two simplified lotteries. In each lottery, the two outcomes are exclusive. By choosing one, we essentially pose a top-k query, where k 1. Let us assume that the score of each choice equals to the amount of Reward in each lottery. Under a top-k semantics using ordinal scores, if we choose o1 (resp. o2) in Lottery 1, then we will choose o1 (resp. o 1 2) in Lottery 2. Because only the order of scores matter in the semantics, not the actual magnitude. On the other hand, one might choose o1 in Lottery 1, and o2 in Lottery 2 in practice. A reasonable explanation for this behavior is that, when there is a “significantly better” choice, we might want to take more risk. In fact, this is exactly how lottery attracts the crowd. Lottery 1: Outcome Reward ($) o1 100 o2 5 Prob. 0.3 0.7 Lottery 2: Outcome Reward ($) o1 6 o2 5 Prob. 0.3 0.7 Example 2 illustrates an application where it is appropriate to consider cardinal scores. 1.3 Set Preferences The research on preferences[7, 30, 31, 11, 8] has almost exclusively focused on tuple preferences which express preference relationships between individual tuples in a relation. We observe that in decision making a user sometimes needs to make a group decision based not only on the individual object properties but also on the properties of the group as a whole.