12 research outputs found
Improving package recommendations through query relaxation
Recommendation systems aim to identify items that are likely to be of
interest to users. In many cases, users are interested in package
recommendations as collections of items. For example, a dietitian may wish to
derive a dietary plan as a collection of recipes that is nutritionally
balanced, and a travel agent may want to produce a vacation package as a
coordinated collection of travel and hotel reservations. Recent work has
explored extending recommendation systems to support packages of items. These
systems need to solve complex combinatorial problems, enforcing various
properties and constraints defined on sets of items. Introducing constraints on
packages makes recommendation queries harder to evaluate, but also harder to
express: Queries that are under-specified produce too many answers, whereas
queries that are over-specified frequently miss interesting solutions.
In this paper, we study query relaxation techniques that target package
recommendation systems. Our work offers three key insights: First, even when
the original query result is not empty, relaxing constraints can produce
preferable solutions. Second, a solution due to relaxation can only be
preferred if it improves some property specified by the query. Third,
relaxation should not treat all constraints as equals: some constraints are
more important to the users than others. Our contributions are threefold: (a)
we define the problem of deriving package recommendations through query
relaxation, (b) we design and experimentally evaluate heuristics that relax
query constraints to derive interesting packages, and (c) we present a crowd
study that evaluates the sensitivity of real users to different kinds of
constraints and demonstrates that query relaxation is a powerful tool in
diversifying package recommendations
Scaling Package Queries to a Billion Tuples via Hierarchical Partitioning and Customized Optimization
A package query returns a package -- a multiset of tuples -- that maximizes
or minimizes a linear objective function subject to linear constraints, thereby
enabling in-database decision support. Prior work has established the
equivalence of package queries to Integer Linear Programs (ILPs) and developed
the SketchRefine algorithm for package query processing. While this algorithm
was an important first step toward supporting prescriptive analytics scalably
inside a relational database, it struggles when the data size grows beyond a
few hundred million tuples or when the constraints become very tight. In this
paper, we present Progressive Shading, a novel algorithm for processing package
queries that can scale efficiently to billions of tuples and gracefully handle
tight constraints. Progressive Shading solves a sequence of optimization
problems over a hierarchy of relations, each resulting from an ever-finer
partitioning of the original tuples into homogeneous groups until the original
relation is obtained. This strategy avoids the premature discarding of
high-quality tuples that can occur with SketchRefine. Our novel partitioning
scheme, Dynamic Low Variance, can handle very large relations with multiple
attributes and can dynamically adapt to both concentrated and spread-out sets
of attribute values, provably outperforming traditional partitioning schemes
such as KD-Tree. We further optimize our system by replacing our off-the-shelf
optimization software with customized ILP and LP solvers, called Dual Reducer
and Parallel Dual Simplex respectively, that are highly accurate and orders of
magnitude faster
Learning and Verifying Quantified Boolean Queries by Example
To help a user specify and verify quantified queries — a class of database queries known to be very challenging for all but the most expert users — one can question the user on whether certain data objects are answers or non-answers to her intended query. In this paper, we analyze the number of questions needed to learn or verify qhorn queries, a special class of Boolean quantified queries whose underlying form is conjunctions of quantified Horn expressions. We provide optimal polynomial-question and polynomial-time learning and verification algorithms for two subclasses of the class qhorn with upper constant limits on a query’s causal density