# Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting

@inproceedings{Gribkoff2014UnderstandingTC, title={Understanding the Complexity of Lifted Inference and Asymmetric Weighted Model Counting}, author={Eric Gribkoff and Guy Van den Broeck and Dan Suciu}, booktitle={AAAI Workshop: Statistical Relational Artificial Intelligence}, year={2014} }

We highlight our work on lifted inference for the asymmetric Weighted First-Order Model Counting problem (WFOMC), which counts the assignments that satisfy a given sentence in first-order logic. [... ] Key Method First, we discuss how adding negation can lower the query complexity, and describe the essential element (resolution) necessary to extend a previous algorithm for positive queries to handle queries with negation. Second, we describe our novel dichotomy result for a non-trivial fragment of first-order… Expand

## 23 Citations

Lifted Inference with Tree Axioms

- Computer Science, MathematicsKR
- 2021

Any two-variable sentence ϕ with the addition of a tree axiom is extended, stating that some distinguished binary relation in ϕ forms a tree in the graph-theoretic sense.

Symmetric Weighted First-Order Model Counting

- Computer Science, MathematicsPODS
- 2015

This paper proves that all γ-acyclic queries have polynomial time data complexity, and proves that, for every fragment FOk, k ≥ 2, the combined complexity of FOMC (or WFOMC) is #P-complete.

The Complexity of Bayesian Networks Specified by Propositional and Relational Languages

- Computer ScienceArtif. Intell.
- 2018

Open-World Probabilistic Databases: An Abridged Report

- Computer ScienceIJCAI
- 2017

This paper lifts the existing data complexity dichotomy of probabilistic databases, and proposes an efficient evaluation algorithm for unions of conjunctive queries, which shows that query evaluation can become harder for non-monotone queries.

Dichotomies for Queries with Negation in Probabilistic Databases

- Computer ScienceTODS
- 2016

The tractability frontier of two classes of relational algebra queries in tuple-independent probabilistic databases is charted, which consists of queries with join, projection, selection, and negation but without repeating relation symbols and union.

A Tutorial on Query Answering and Reasoning over Probabilistic Knowledge Bases

- Computer ScienceReasoning Web
- 2018

This tutorial is dedicated to give an understanding of various query answering and reasoning tasks that can be used to exploit the full potential of probabilistic knowledge bases.

On Constrained Open-World Probabilistic Databases

- Computer ScienceIJCAI
- 2019

This work provides an algorithm for one class of queries, and establishes a basic hardness result for another, and proposes an efficient and tight approximation for a largeclass of queries.

A Query Engine for Probabilistic Preferences

- Computer ScienceSIGMOD Conference
- 2018

An implementation of a query engine that supports querying probabilistic preferences alongside relational data and a novel inference algorithm for conjunctive queries over RIM, which significantly outperforms the state of the art in terms of both asymptotic and empirical execution cost.

Lifted Probabilistic Inference for Asymmetric Graphical Models

- Computer ScienceAAAI
- 2015

This work presents a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain, which leads to improved probability estimates while remaining unbiased.

SlimShot: In-Database Probabilistic Inference for Knowledge Bases

- Computer ScienceProc. VLDB Endow.
- 2016

SlimShot is described, a probabilistic inference engine for knowledge bases that uses a simple Monte Carlo-based inference, with three key enhancements: it combines sampling with safe query evaluation, and it estimates a conditional probability by jointly computing the numerator and denominator.

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