Tanya Braun

Lifted Junction Tree Algorithm

We look at probabilistic first-order formalisms where the domain objects are known. In these formalisms, the standard approach for inference is lifted variable elimination. To benefit from the advantages of the junction tree algorithm for inference in the first-order setting, we transfer the idea of lifting to the junction tree algorithm. Our lifted junction tree algorithm aims at reducing computations by introducing first-order junction trees that compactly represent symmetries. First experiments show that we speed up the computation time compared to the propositional version. When querying for multiple marginals, the lifted junction tree algorithm performs better than using lifted VE to infer each marginal individually.

Counting and Conjunctive Queries in the Lifted Junction Tree Algorithm

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a knowledge base and LVE in its computations. We extend LJT with a full formal specification of its algorithm steps incorporating (i) the lifting tool of counting and (ii) answering of conjunctive queries. Given multiple queries, e.g., in machine learning applications, our approach enables us to compute answers faster than the current LJT and existing approaches tailored for single queries.

Preventing Groundings and Handling Evidence in the Lifted Junction Tree Algorithm

For inference in probabilistic formalisms with first-order constructs, lifted variable elimination (LVE) is one of the standard approaches for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a specific representation of a first-order knowledge base and LVE in its computations. Unfortunately, LJT induces unnecessary groundings in cases where the standard LVE algorithm, GC-FOVE, has a fully lifted run. Additionally, LJT does not handle evidence explicitly. We extend LJT (i) to identify and prevent unnecessary groundings and (ii) to effectively handle evidence in a lifted manner. Given multiple queries, e.g., in machine learning applications, our extension computes answers faster than LJT and GC-FOVE.

Lifted Most Probable Explanation

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries, boiling down to computing marginal distributions. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a knowledge base and LVE in its computations. Another type of query asks for a most probable explanation (MPE) for given events. The purpose of this paper is twofold: (i) We formalise how to compute an MPE in a lifted way with LVE and LJT. (ii) We present a case study in the area of IT security for risk analysis. A lifted computation of MPEs exploits symmetries, while providing a correct and exact result equivalent to one computed on ground level.

Lifted Dynamic Junction Tree Algorithm

Probabilistic models involving relational and temporal aspects need exact and efficient inference algorithms. Existing approaches are approximative, include unnecessary grounding, or do not consider the relational and temporal aspects of the models. One approach for efficient reasoning on relational static models given multiple queries is the lifted junction tree algorithm. In addition, for propositional temporal models, the interface algorithm allows for efficient reasoning. To leverage the advantages of the two algorithms for relational temporal models, we present the lifted dynamic junction tree algorithm, an exact algorithm to answer multiple queries efficiently for probabilistic relational temporal models with known domains by reusing computations for multiple queries and multiple time steps. First experiments show computational savings while appropriately accounting for relational and temporal aspects of models.

Parameterised Queries and Lifted Query Answering

A standard approach for inference in probabilistic formalisms with first-order constructs is lifted variable elimination (LVE) for single queries. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) employs a first-order cluster representation of a model and LVE as a subroutine. Both algorithms answer conjunctive queries of propositional random variables, shattering the model on the query, which causes unnecessary groundings for conjunctive queries of interchangeable variables. This paper presents parameterised queries as a means to avoid groundings, applying the lifting idea to queries. Parameterised queries enable LVE and LJT to compute answers faster, while compactly representing queries and answers.

Towards Preventing Unnecessary Groundings in the Lifted Dynamic Junction Tree Algorithm

The lifted dynamic junction tree algorithm (LDJT) answers filtering and prediction queries efficiently for probabilistic relational temporal models by building and then reusing a first-order cluster representation of a knowledge base for multiple queries and time steps. Unfortunately, a non-ideal elimination order can lead to unnecessary groundings.

Fusing First-Order Knowledge Compilation and the Lifted Junction Tree Algorithm

Standard approaches for inference in probabilistic formalisms with first-order constructs include lifted variable elimination (LVE) for single queries as well as first-order knowledge compilation (FOKC) based on weighted model counting. To handle multiple queries efficiently, the lifted junction tree algorithm (LJT) uses a first-order cluster representation of a model and LVE as a subroutine in its computations. For certain inputs, the implementation of LVE and, as a result, LJT ground parts of a model where FOKC runs without groundings. The purpose of this paper is to prepare LJT as a backbone for lifted query answering and to use any exact inference algorithm as subroutine. Fusing LJT and FOKC, by setting FOKC as a subroutine, allows us to compute answers faster than FOKC alone and LJT with LVE for certain inputs.