Search-Based Exact Lifted Inference

2021 ◽  
Keyword(s):  
Lifted Inference

scholarly journals Lower complexity bounds for lifted inference

2014 ◽  
Vol 15 (2) ◽  
pp. 246-263 ◽  
Author(s):  
MANFRED JAEGER
Keyword(s):  
Knowledge Bases ◽  
Modeling Languages ◽  
Complexity Bounds ◽  
Lifted Inference ◽  
Probabilistic Relational Models ◽  
Lower Complexity ◽  
Logical Modeling ◽  
Inference Techniques ◽  
And Function ◽  
Lower Complexity Bounds

AbstractOne of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation language, rather than on the level of ground, propositional instances of the model. Numerous approaches for such “lifted inference” techniques have been proposed. While it has been demonstrated that these techniques will lead to significantly more efficient inference on some specific models, there are only very recent and still quite restricted results that show the feasibility of lifted inference on certain syntactically defined classes of models. Lower complexity bounds that imply some limitations for the feasibility of lifted inference on more expressive model classes were established earlier in Jaeger (2000; Jaeger, M. 2000. On the complexity of inference about probabilistic relational models. Artificial Intelligence 117, 297–308). However, it is not immediate that these results also apply to the type of modeling languages that currently receive the most attention, i.e., weighted, quantifier-free formulas. In this paper we extend these earlier results, and show that under the assumption that NETIME≠ETIME, there is no polynomial lifted inference algorithm for knowledge bases of weighted, quantifier-, and function-free formulas. Further strengthening earlier results, this is also shown to hold for approximate inference and for knowledge bases not containing the equality predicate.

scholarly journals Software Product Line Analysis Using Variability-aware Datalog

2021 ◽  
Author(s):  
Ramy Shahin ◽  
Murad Akhundov ◽  
marsha chechik
Keyword(s):  
Research Problem ◽  
Product Line ◽  
Product Lines ◽  
C Language ◽  
Lifted Inference ◽  
Software Analysis ◽  
Software Product ◽  
Database Size ◽  
Fundamental Research ◽  
Line Engineering

Applying program analyses to Software Product Lines (SPLs) has been a fundamental research problem at the intersection<br>of Product Line Engineering and software analysis. Different attempts have been made to "lift" particular product-level analyses to run on the entire product line. In this paper, we tackle the class of Datalog-based analyses (e.g., pointer and taint analyses), study the theoretical aspects of lifting Datalog inference, and implement a lifted inference algorithm inside the Souffl  Datalog engine. We evaluate our implementation on a set of Java and C-language benchmark product lines. We show significant savings in processing time and fact database size (billions of times faster on one of the benchmarks) compared to brute-force analysis of each product individually.

scholarly journals Software Product Line Analysis Using Variability-aware Datalog

2021 ◽  
Author(s):  
Ramy Shahin ◽  
Murad Akhundov ◽  
marsha chechik
Keyword(s):  
Research Problem ◽  
Product Line ◽  
Product Lines ◽  
C Language ◽  
Lifted Inference ◽  
Software Analysis ◽  
Software Product ◽  
Database Size ◽  
Fundamental Research ◽  
Line Engineering

Applying program analyses to Software Product Lines (SPLs) has been a fundamental research problem at the intersection<br>of Product Line Engineering and software analysis. Different attempts have been made to "lift" particular product-level analyses to run on the entire product line. In this paper, we tackle the class of Datalog-based analyses (e.g., pointer and taint analyses), study the theoretical aspects of lifting Datalog inference, and implement a lifted inference algorithm inside the Souffl  Datalog engine. We evaluate our implementation on a set of Java and C-language benchmark product lines. We show significant savings in processing time and fact database size (billions of times faster on one of the benchmarks) compared to brute-force analysis of each product individually.

scholarly journals Efficient Inference for Untied MLNs

2017 ◽  
Author(s):  
Somdeb Sarkhel ◽  
Deepak Venugopal ◽  
Nicholas Ruozzi ◽  
Vibhav Gogate
Keyword(s):  
Graphical Models ◽  
Scaling Up ◽  
Partition Functions ◽  
Markov Logic ◽  
Practical Applications ◽  
Lifted Inference ◽  
Hard Time ◽  
Inference Algorithms ◽  
Order Of Magnitude ◽  
Symmetric Approximation

We address the problem of scaling up local-search or sampling-based inference in Markov logic networks (MLNs) that have large shared sub-structures but no (or few) tied weights. Such untied MLNs are ubiquitous in practical applications. However, they have very few symmetries, and as a result lifted inference algorithms--the dominant approach for scaling up inference--perform poorly on them. The key idea in our approach is to reduce the hard, time-consuming sub-task in sampling algorithms, computing the sum of weights of features that satisfy a full assignment, to the problem of computing a set of partition functions of graphical models, each defined over the logical variables in a first-order formula. The importance of this reduction is that when the treewidth of all the graphical models is small, it yields an order of magnitude speedup. When the treewidth is large, we propose an over-symmetric approximation and experimentally demonstrate that it is both fast and accurate.

Lifted Inference with Tree Axioms

2021 ◽  
Author(s):  
Timothy van Bremen ◽  
Ondřej Kuželka
Keyword(s):  
Binary Relation ◽  
Domain Size ◽  
Weighted Sum ◽  
Order Model ◽  
Lifted Inference ◽  
Past Work ◽  
First Order ◽  
Graph Theoretic ◽  
Model Counting ◽  
The Given

We consider the problem of weighted first-order model counting (WFOMC): given a first-order sentence ϕ and domain size n ∈ ℕ, determine the weighted sum of models of ϕ over the domain {1, ..., n}. Past work has shown that any sentence using at most two logical variables admits an algorithm for WFOMC that runs in time polynomial in the given domain size (Van den Broeck 2011; Van den Broeck, Meert, and Darwiche 2014). In this paper, we extend this result to any two-variable sentence ϕ with the addition of a tree axiom, stating that some distinguished binary relation in ϕ forms a tree in the graph-theoretic sense.

scholarly journals Lifted Variable Elimination for Probabilistic Logic Programming

2014 ◽  
Vol 14 (4-5) ◽  
pp. 681-695 ◽  
Author(s):  
ELENA BELLODI ◽  
EVELINA LAMMA ◽  
FABRIZIO RIGUZZI ◽  
VITOR SANTOS COSTA ◽  
RICCARDO ZESE
Keyword(s):  
Logic Programming ◽  
Random Variables ◽  
Probabilistic Logic ◽  
Probabilistic Logic Programming ◽  
Lifted Inference ◽  
Logical Frameworks ◽  
Variable Elimination ◽  
Causal Independence ◽  
Order Variable ◽  
Distribution Semantics

AbstractLifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances. Even if various authors have underlined its importance for probabilistic logic programming (PLP), lifted inference has been applied up to now only to relational languages outside of logic programming. In this paper we adapt Generalized Counting First Order Variable Elimination (GC-FOVE) to the problem of computing the probability of queries to probabilistic logic programs under the distribution semantics. In particular, we extend the Prolog Factor Language (PFL) to include two new types of factors that are needed for representing ProbLog programs. These factors take into account the existing causal independence relationships among random variables and are managed by the extension to variable elimination proposed by Zhang and Poole for dealing with convergent variables and heterogeneous factors. Two new operators are added to GC-FOVE for treating heterogeneous factors. The resulting algorithm, called LP2for Lifted Probabilistic Logic Programming, has been implemented by modifying the PFL implementation of GC-FOVE and tested on three benchmarks for lifted inference. A comparison with PITA and ProbLog2 shows the potential of the approach.

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