Infinite Probabilistic Databases

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries

Spontaneous Analogy by Piggybacking on a Perceptual System

Most computational models of analogy assume they are given a delineated source domain and often a specified target domain. These systems do not address how analogs can be isolated from large domains and spontaneously retrieved from long-term memory, a process we call spontaneous analogy. We present a system that represents relational structures as feature bags. Using this representation, our system leverages perceptual algorithms to automatically create an ontology of relational structures and to efficiently retrieve analogs for new relational structures from long-term memory. We provide a demonstration of our approach that takes a set of unsegmented stories, constructs an ontology of analogical schemas (corresponding to plot devices), and uses this ontology to efficiently find analogs within new stories, yielding significant time-savings over linear analog retrieval at a small accuracy cost.Comment: Proceedings of the 35th Meeting of the Cognitive Science Society, 201

Scalable Querying of Nested Data

While large-scale distributed data processing platforms have become an attractive target for query processing, these systems are problematic for applications that deal with nested collections. Programmers are forced either to perform non-trivial translations of collection programs or to employ automated flattening procedures, both of which lead to performance problems. These challenges only worsen for nested collections with skewed cardinalities, where both handcrafted rewriting and automated flattening are unable to enforce load balancing across partitions. In this work, we propose a framework that translates a program manipulating nested collections into a set of semantically equivalent shredded queries that can be efficiently evaluated. The framework employs a combination of query compilation techniques, an efficient data representation for nested collections, and automated skew-handling. We provide an extensive experimental evaluation, demonstrating significant improvements provided by the framework in diverse scenarios for nested collection programs

The fermion bag approach to lattice field theories

We propose a new approach to the fermion sign problem in systems where there is a coupling $U$ such that when it is infinite the fermions are paired into bosons and there is no fermion permutation sign to worry about. We argue that as $U$ becomes finite fermions are liberated but are naturally confined to regions which we refer to as {\em fermion bags}. The fermion sign problem is then confined to these bags and may be solved using the determinantal trick. In the parameter regime where the fermion bags are small and their typical size does not grow with the system size, construction of Monte Carlo methods that are far more efficient than conventional algorithms should be possible. In the region where the fermion bags grow with system size, the fermion bag approach continues to provide an alternative approach to the problem but may lose its main advantage in terms of efficiency. The fermion bag approach also provides new insights and solutions to sign problems. A natural solution to the "silver blaze problem" also emerges. Using the three dimensional massless lattice Thirring model as an example we introduce the fermion bag approach and demonstrate some of these features. We compute the critical exponents at the quantum phase transition and find $\nu=0.87(2)$ and $\eta=0.62(2)$.Comment: 31 pages, 9 figures, 5 table

A Semantics-Based Approach to Design of Query Languages for Partial Information

Most of work on partial information in databases asks which operations of standard languages, like relational algebra, can still be performed correctly in the presence of nulls. In this paper a different point of view is advocated. We believe that the semantics of partiality must be clearly understood and it should give us new design principles for languages for databases with partial information. There are different sources of partial information, such as missing information and conflicts that occur when different databases are merged. In this paper, we develop a common semantic framework for them which can be applied in a context more general than the flat relational model. This ordered semantics, which is based on ideas used in the semantics of programming languages, cleanly intergrates all kinds of partial information and serves as a tool to establish connections between them. Analyzing properties of semantic domains of types suitable for representing partial information, we come up with operations that are naturally associated with those types, and we organize programming syntax around these operations. We show how the languages that we obtain can be used to ask typical queries about incomplete information in relational databases, and how they can express some previously proposed languages. Finally, we discuss a few related topics such as mixing traditional constraints with partial information and extending semantics and languages to accommodate bags and recursive types