Database query optimisation based on measures of regret

The query optimiser in a database management system (DBMS) is responsible for �nding a good order in which to execute the operators in a given query. However, in practice the query optimiser does not usually guarantee to �nd the best plan. This is often due to the non-availability of precise statistical data or inaccurate assumptions made by the optimiser. In this thesis we propose a robust approach to logical query optimisation that takes into account the unreliability in database statistics during the optimisation process. In particular, we study the ordering problem for selection operators and for join operators, where selectivities are modelled as intervals rather than exact values. As a measure of optimality, we use a concept from decision theory called minmax regret optimisation (MRO). When using interval selectivities, the decision problem for selection operator ordering turns out to be NP-hard. After investigating properties of the problem and identifying special cases which can be solved in polynomial time, we develop a novel heuristic for solving the general selection ordering problem in polynomial time. Experimental evaluation of the heuristic using synthetic data, the Star Schema Benchmark and real-world data sets shows that it outperforms other heuristics (which take an optimistic, pessimistic or midpoint approach) and also produces plans whose regret is on average very close to optimal. The general join ordering problem is known to be NP-hard, even for exact selectivities. So, for interval selectivities, we restrict our investigation to sets of join operators which form a chain and to plans that correspond to left-deep join trees. We investigate properties of the problem and use these, along with ideas from the selection ordering heuristic and other algorithms in the literature, to develop a polynomial-time heuristic tailored for the join ordering problem. Experimental evaluation of the heuristic shows that, once again, it performs better than the optimistic, pessimistic and midpoint heuristics. In addition, the results show that the heuristic produces plans whose regret is on average even closer to the optimal than for selection ordering

Database query optimisation based on measures of regret

The query optimiser in a database management system (DBMS) is responsible for �nding a good order in which to execute the operators in a given query. However, in practice the query optimiser does not usually guarantee to �nd the best plan. This is often due to the non-availability of precise statistical data or inaccurate assumptions made by the optimiser. In this thesis we propose a robust approach to logical query optimisation that takes into account the unreliability in database statistics during the optimisation process. In particular, we study the ordering problem for selection operators and for join operators, where selectivities are modelled as intervals rather than exact values. As a measure of optimality, we use a concept from decision theory called minmax regret optimisation (MRO). When using interval selectivities, the decision problem for selection operator ordering turns out to be NP-hard. After investigating properties of the problem and identifying special cases which can be solved in polynomial time, we develop a novel heuristic for solving the general selection ordering problem in polynomial time. Experimental evaluation of the heuristic using synthetic data, the Star Schema Benchmark and real-world data sets shows that it outperforms other heuristics (which take an optimistic, pessimistic or midpoint approach) and also produces plans whose regret is on average very close to optimal. The general join ordering problem is known to be NP-hard, even for exact selectivities. So, for interval selectivities, we restrict our investigation to sets of join operators which form a chain and to plans that correspond to left-deep join trees. We investigate properties of the problem and use these, along with ideas from the selection ordering heuristic and other algorithms in the literature, to develop a polynomial-time heuristic tailored for the join ordering problem. Experimental evaluation of the heuristic shows that, once again, it performs better than the optimistic, pessimistic and midpoint heuristics. In addition, the results show that the heuristic produces plans whose regret is on average even closer to the optimal than for selection ordering

Ordering selection operators under partial ignorance

Optimising queries in real-world situations under imperfect conditions is still a problem that has not been fully solved. We consider finding the optimal order in which to execute a given set of selection operators under partial ignorance of their selectivities. The selectivities are modelled as intervals rather than exact values and we apply a concept from decision theory, the minimisation of the maximum regret, as a measure of optimality. The associated decision problem turns out to be NP-hard, which renders a brute-force approach to solving it impractical. Nevertheless, by investigating properties of the problem and identifying special cases which can be solved in polynomial time, we gain insight that we use to develop a novel heuristic for solving the general problem. We also evaluate minmax regret query optimisation experimentally, showing that it outperforms a currently employed strategy of optimisers that uses mean values for uncertain parameters

Differential Privacy, Property Testing, and Perturbations

Controlling the dissemination of information about ourselves has become a minefield in the modern age. We release data about ourselves every day and don’t always fully understand what information is contained in this data. It is often the case that the combination of seemingly innocuous pieces of data can be combined to reveal more sensitive information about ourselves than we intended. Differential privacy has developed as a technique to prevent this type of privacy leakage. It borrows ideas from information theory to inject enough uncertainty into the data so that sensitive information is provably absent from the privatised data. Current research in differential privacy walks the fine line between removing sensitive information while allowing non-sensitive information to be released. At its heart, this thesis is about the study of information. Many of the results can be formulated as asking a subset of the questions: does the data you have contain enough information to learn what you would like to learn? and how can I affect the data to ensure you can’t discern sensitive information? We will often approach the former question from both directions: information theoretic lower bounds on recovery and algorithmic upper bounds. We begin with an information theoretic lower bound for graphon estimation. This explores the fundamental limits of how much information about the underlying population is contained in a finite sample of data. We then move on to exploring the connection between information theoretic results and privacy in the context of linear inverse problems. We find that there is a discrepancy between how the inverse problems community and the privacy community view good recovery of information. Next, we explore black-box testing for privacy. We argue that the amount of information required to verify the privacy guarantee of an algorithm, without access to the internals of the algorithm, is lower bounded by the amount of information required to break the privacy guarantee. Finally, we explore a setting where imposing privacy is a help rather than a hindrance: online linear optimisation. We argue that private algorithms have the right kind of stability guarantee to ensure low regret for online linear optimisation.PHDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143940/1/amcm_1.pd

Ranking algorithms for implicit feedback

This report presents novel algorithms to use eye movements as an implicit relevance feedback in order to improve the performance of the searches. The algorithms are evaluated on "Transport Rank Five" Dataset which were previously collected in Task 8.3. We demonstrated that simple linear combination or tensor product of eye movement and image features can improve the retrieval accuracy

Addressing practical challenges of Bayesian optimisation

This thesis focuses on addressing several challenges in applying Bayesian optimisation in real world problems. The contributions of this thesis are new Bayesian optimisation algorithms for three practical problems: finding stable solutions, optimising cascaded processes and privacy-aware optimisation