Tractability in probabilistic databases

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Generalized Lineage-Aware Temporal Windows: Supporting Outer and Anti Joins in Temporal-Probabilistic Databases

The result of a temporal-probabilistic (TP) join with negation includes, at each time point, the probability with which a tuple of a positive relation ${\bf p}$ matches none of the tuples in a negative relation ${\bf n}$, for a given join condition $\theta$. TP outer and anti joins thus resemble the characteristics of relational outer and anti joins also in the case when there exist time points at which input tuples from ${\bf p}$ have non-zero probabilities to be $true$ and input tuples from ${\bf n}$ have non-zero probabilities to be $false$, respectively. For the computation of TP joins with negation, we introduce generalized lineage-aware temporal windows, a mechanism that binds an output interval to the lineages of all the matching valid tuples of each input relation. We group the windows of two TP relations into three disjoint sets based on the way attributes, lineage expressions and intervals are produced. We compute all windows in an incremental manner, and we show that pipelined computations allow for the direct integration of our approach into PostgreSQL. We thereby alleviate the prevalent redundancies in the interval computations of existing approaches, which is proven by an extensive experimental evaluation with real-world datasets

10 Years of Probabilistic Querying – What Next?

Over the past decade, the two research areas of probabilistic databases and probabilistic programming have intensively studied the problem of making structured probabilistic inference scalable, but — so far — both areas developed almost independently of one another. While probabilistic databases have focused on describing tractable query classes based on the structure of query plans and data lineage, probabilistic programming has contributed sophisticated inference techniques based on knowledge compilation and lifted (first-order) inference. Both fields have developed their own variants of — both exact and approximate — top-k algorithms for query evaluation, and both investigate query optimization techniques known from SQL, Datalog, and Prolog, which all calls for a more intensive study of the commonalities and integration of the two fields. Moreover, we believe that natural-language processing and information extraction will remain a driving factor and in fact a longstanding challenge for developing expressive representation models which can be combined with structured probabilistic inference — also for the next decades to come

A dichotomy for non-repeating queries with negation in probabilistic databases

This paper shows that any non-repeating conjunctive rela-tional query with negation has either polynomial time or #P-hard data complexity on tuple-independent probabilis-tic databases. This result extends a dichotomy by Dalvi and Suciu for non-repeating conjunctive queries to queries with negation. The tractable queries with negation are precisely the hierarchical ones and can be recognised efficiently. 1

Faster Query Answering in Probabilistic Databases using Read-Once Functions

A boolean expression is in read-once form if each of its variables appears exactly once. When the variables denote independent events in a probability space, the probability of the event denoted by the whole expression in read-once form can be computed in polynomial time (whereas the general problem for arbitrary expressions is #P-complete). Known approaches to checking read-once property seem to require putting these expressions in disjunctive normal form. In this paper, we tell a better story for a large subclass of boolean event expressions: those that are generated by conjunctive queries without self-joins and on tuple-independent probabilistic databases. We first show that given a tuple-independent representation and the provenance graph of an SPJ query plan without self-joins, we can, without using the DNF of a result event expression, efficiently compute its co-occurrence graph. From this, the read-once form can already, if it exists, be computed efficiently using existing techniques. Our second and key contribution is a complete, efficient, and simple to implement algorithm for computing the read-once forms (whenever they exist) directly, using a new concept, that of co-table graph, which can be significantly smaller than the co-occurrence graph.Comment: Accepted in ICDT 201

Factorised Representations of Query Results

Query tractability has been traditionally defined as a function of input database and query sizes, or of both input and output sizes, where the query result is represented as a bag of tuples. In this report, we introduce a framework that allows to investigate tractability beyond this setting. The key insight is that, although the cardinality of a query result can be exponential, its structure can be very regular and thus factorisable into a nested representation whose size is only polynomial in the size of both the input database and query. For a given query result, there may be several equivalent representations, and we quantify the regularity of the result by its readability, which is the minimum over all its representations of the maximum number of occurrences of any tuple in that representation. We give a characterisation of select-project-join queries based on the bounds on readability of their results for any input database. We complement it with an algorithm that can find asymptotically optimal upper bounds and corresponding factorised representations.Comment: 44 pages, 13 figure

Oblivious Bounds on the Probability of Boolean Functions

This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an exact characterization of optimal oblivious bounds, i.e. when the new probabilities are chosen independent of the probabilities of all other variables. Our motivation comes from the weighted model counting problem (or, equivalently, the problem of computing the probability of a Boolean function), which is #P-hard in general. By performing several dissociations, one can transform a Boolean formula whose probability is difficult to compute, into one whose probability is easy to compute, and which is guaranteed to provide an upper or lower bound on the probability of the original formula by choosing appropriate probabilities for the dissociated variables. Our new bounds shed light on the connection between previous relaxation-based and model-based approximations and unify them as concrete choices in a larger design space. We also show how our theory allows a standard relational database management system (DBMS) to both upper and lower bound hard probabilistic queries in guaranteed polynomial time.Comment: 34 pages, 14 figures, supersedes: http://arxiv.org/abs/1105.281