scholarly journals Lifted Variable Elimination: Decoupling the Operators from the Constraint Language

2013 ◽  
Vol 47 ◽  
pp. 393-439 ◽  
Author(s):  
N. Taghipour ◽  
D. Fierens ◽  
J. Davis ◽  
H. Blockeel
Keyword(s):  
Graphical Models ◽  
Probabilistic Inference ◽  
Relational Algebra ◽  
Exact Inference ◽  
Semantic Level ◽  
Lifted Inference ◽  
Variable Elimination ◽  
Constraint Language ◽  
Inference Algorithms ◽  
Powerful Constraint

Lifted probabilistic inference algorithms exploit regularities in the structure of graphical models to perform inference more efficiently. More specifically, they identify groups of interchangeable variables and perform inference once per group, as opposed to once per variable. The groups are defined by means of constraints, so the flexibility of the grouping is determined by the expressivity of the constraint language. Existing approaches for exact lifted inference use specific languages for (in)equality constraints, which often have limited expressivity. In this article, we decouple lifted inference from the constraint language. We define operators for lifted inference in terms of relational algebra operators, so that they operate on the semantic level (the constraints' extension) rather than on the syntactic level, making them language-independent. As a result, lifted inference can be performed using more powerful constraint languages, which provide more opportunities for lifting. We empirically demonstrate that this can improve inference efficiency by orders of magnitude, allowing exact inference where until now only approximate inference was feasible.

Leveraging Variable Elimination for Efficiently Reasoning about Qualitative Constraints

2018 ◽  
Vol 27 (04) ◽  
pp. 1860001 ◽  
Author(s):  
Michael Sioutis ◽  
Zhiguo Long ◽  
Sanjiang Li
Keyword(s):  
Graphical Models ◽  
State Of The Art ◽  
Exact Inference ◽  
Local Consistency ◽  
Constraint Networks ◽  
Constraint Network ◽  
Variable Elimination ◽  
Region Connection Calculus ◽  
Effective Manner ◽  
Novel Algorithm

We introduce, study, and evaluate a novel algorithm in the context of qualitative constraint-based spatial and temporal reasoning that is based on the idea of variable elimination, a simple and general exact inference approach in probabilistic graphical models. Given a qualitative constraint network [Formula: see text], our algorithm utilizes a particular directional local consistency, which we denote by [Formula: see text]-consistency, in order to efficiently decide the satisfiability of [Formula: see text]. Our discussion is restricted to distributive subclasses of relations, i.e., sets of relations closed under converse, intersection, and weak composition and for which weak composition distributes over non-empty intersections for all of their relations. We demonstrate that enforcing [Formula: see text]-consistency in a given qualitative constraint network defined over a distributive subclass of relations allows us to decide its satisfiability, and obtain similar useful results for the problems of minimal labelling and redundancy. Further, we present a generic method that allows extracting a scenario from a satisfiable network, i.e., an atomic satisfiable subnetwork of that network, in a very simple and effective manner. The experimentation that we have conducted with random and real-world qualitative constraint networks defined over a distributive subclass of relations of the Region Connection Calculus and the Interval Algebra, shows that our approach exhibits unparalleled performance against state-of-the-art approaches for checking the satisfiability of such constraint networks.

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.

scholarly journals PROBABILISTIC INFERENCE IN BAYESIAN INSURANCE NETWORK

2021 ◽  
Author(s):  
Ya. S. Bondarenko ◽  
D. O. Rachko ◽  
A. O. Rozlyvan
Keyword(s):  
Road Traffic Accident ◽  
Traffic Accident ◽  
Road Traffic ◽  
Probabilistic Inference ◽  
Conditional Probabilities ◽  
Prediction Problem ◽  
Exact Inference ◽  
Elimination Algorithm ◽  
Variable Elimination ◽  
Financial Losses

In this paper, the technique to solve the prediction problem of reparation of the financial losses caused by a road traffic accident is solved. Exact inference is represented using the Sum-Product Variable Elimination algorithm, Sum-Product Variable Elimination algorithm for computing conditional probabilities, Max-Product Variable Elimination algorithm for MAP, Max-Sum-Product Variable Elimination algorithm for marginal MAP. Reasoning patterns are presented graphically and descriptively.

scholarly journals Lifted Message Passing for Hybrid Probabilistic Inference

2019 ◽  
Author(s):  
Yuqiao Chen ◽  
Nicholas Ruozzi ◽  
Sriraam Natarajan
Keyword(s):  
Message Passing ◽  
Computational Cost ◽  
Markov Logic Networks ◽  
Markov Logic ◽  
Lifted Inference ◽  
Particle Sampling ◽  
Variable Elimination ◽  
Inference Algorithms ◽  
Arbitrary Potential ◽  
Inference Methods

Lifted inference algorithms for first-order logic models, e.g., Markov logic networks (MLNs), have been of significant interest in recent years.  Lifted inference methods exploit model symmetries in order to reduce the size of the model and, consequently, the computational cost of inference.  In this work, we consider the problem of lifted inference in MLNs with continuous or both discrete and continuous groundings. Existing work on lifting with continuous groundings has mostly been limited to special classes of models, e.g., Gaussian models, for which variable elimination or message-passing updates can be computed exactly.  Here, we develop approximate lifted inference schemes based on particle sampling.  We demonstrate empirically that our approximate lifting schemes perform comparably to existing state-of-the-art for models for Gaussian MLNs, while having the flexibility to be applied to models with arbitrary potential functions.

scholarly journals Efficient Symbolic Integration for Probabilistic Inference

2018 ◽  
Author(s):  
Samuel Kolb ◽  
Martin Mladenov ◽  
Scott Sanner ◽  
Vaishak Belle ◽  
Kristian Kersting
Keyword(s):  
Graphical Models ◽  
Probabilistic Inference ◽  
Computational Cost ◽  
Inference Problems ◽  
Inference Algorithms ◽  
Model Counting ◽  
Probability Spaces ◽  
Weighted Model ◽  
Computational Reduction ◽  
Parametrized Solutions

Weighted model integration (WMI) extends weighted model counting (WMC) to the integration of functions over mixed discrete-continuous probability spaces. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI are generally limited either by the range of amenable theories, or in terms of performance. To address both limitations, we propose the use of extended algebraic decision diagrams (XADDs) as a compilation language for WMI. Aside from tackling typical WMI problems, XADDs also enable partial WMI yielding parametrized solutions. To overcome the main roadblock of XADDs -- the computational cost of integration -- we formulate a novel and powerful exact symbolic dynamic programming (SDP) algorithm that seamlessly handles Boolean, integer-valued and real variables, and is able to effectively cache partial computations, unlike its predecessor. Our empirical results demonstrate that these contributions can lead to a significant computational reduction over existing probabilistic inference algorithms.

scholarly journals State-Space Abstractions for Probabilistic Inference: A Systematic Review

2018 ◽  
Vol 63 ◽  
pp. 789-848 ◽  
Author(s):  
Stefan Lüdtke ◽  
Max Schröder ◽  
Frank Krüger ◽  
Sebastian Bader ◽  
Thomas Kirste
Keyword(s):  
State Space ◽  
Probabilistic Inference ◽  
Future Research ◽  
Lifted Inference ◽  
Research Areas ◽  
Research Fields ◽  
Compact Representations ◽  
Inference Algorithms ◽  
Human Behavior Recognition ◽  
High Level

Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a propositional level, and thus cannot capture the symmetries and redundancies that are present in these tasks. Algorithms that exploit those symmetries have been devised in different research fields, for example by the lifted inference-, multiple object tracking-, and modeling and simulation-communities. The common idea, that we call state space abstraction, is to perform inference over compact representations of sets of symmetric states. Although they are concerned with a similar topic, the relationship between these approaches has not been investigated systematically. This survey provides the following contributions. We perform a systematic literature review to outline the state of the art in probabilistic inference methods exploiting symmetries. From an initial set of more than 4,000 papers, we identify 116 relevant papers. Furthermore, we provide new high-level categories that classify the approaches, based on common properties of the approaches. The research areas underlying each of the categories are introduced concisely. Researchers from different fields that are confronted with a state space explosion problem in a probabilistic system can use this classification to identify possible solutions. Finally, based on this conceptualization, we identify potentials for future research, as some relevant application domains are not addressed by current approaches.

scholarly journals Probabilistic Inference for Predicate Constraint Satisfaction

2020 ◽  
Vol 34 (02) ◽  
pp. 1644-1651
Author(s):  
Yuki Satake ◽  
Hiroshi Unno ◽  
Hinata Yanagi
Keyword(s):  
Graphical Models ◽  
Constraint Satisfaction ◽  
Linear Time ◽  
Predicate Logic ◽  
Probabilistic Inference ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Safety Properties ◽  
First Order ◽  
Guided Inductive

In this paper, we present a novel constraint solving method for a class of predicate Constraint Satisfaction Problems (pCSP) where each constraint is represented by an arbitrary clause of first-order predicate logic over predicate variables. The class of pCSP properly subsumes the well-studied class of Constrained Horn Clauses (CHCs) where each constraint is restricted to a Horn clause. The class of CHCs has been widely applied to verification of linear-time safety properties of programs in different paradigms. In this paper, we show that pCSP further widens the applicability to verification of branching-time safety properties of programs that exhibit finitely-branching non-determinism. Solving pCSP (and CHCs) however is challenging because the search space of solutions is often very large (or unbounded), high-dimensional, and non-smooth. To address these challenges, our method naturally combines techniques studied separately in different literatures: counterexample guided inductive synthesis (CEGIS) and probabilistic inference in graphical models. We have implemented the presented method and obtained promising results on existing benchmarks as well as new ones that are beyond the scope of existing CHC solvers.

scholarly journals Quantifying the multi-scale performance of network inference algorithms

2014 ◽  
Vol 13 (5) ◽  
Author(s):  
Chris J. Oates ◽  
Richard Amos ◽  
Simon E.F. Spencer
Keyword(s):  
Graphical Models ◽  
Network Inference ◽  
Multiple Scales ◽  
Biological Systems ◽  
Higher Order ◽  
Wisdom Of Crowds ◽  
Multi Scale ◽  
Reverse Engineer ◽  
Multiple Length Scales ◽  
Inference Algorithms

AbstractGraphical models are widely used to study complex multivariate biological systems. Network inference algorithms aim to reverse-engineer such models from noisy experimental data. It is common to assess such algorithms using techniques from classifier analysis. These metrics, based on ability to correctly infer individual edges, possess a number of appealing features including invariance to rank-preserving transformation. However, regulation in biological systems occurs on multiple scales and existing metrics do not take into account the correctness of higher-order network structure. In this paper novel performance scores are presented that share the appealing properties of existing scores, whilst capturing ability to uncover regulation on multiple scales. Theoretical results confirm that performance of a network inference algorithm depends crucially on the scale at which inferences are to be made; in particular strong local performance does not guarantee accurate reconstruction of higher-order topology. Applying these scores to a large corpus of data from the DREAM5 challenge, we undertake a data-driven assessment of estimator performance. We find that the “wisdom of crowds” network, that demonstrated superior local performance in the DREAM5 challenge, is also among the best performing methodologies for inference of regulation on multiple length scales.

Simulation of Graphical Models for Multiagent Probabilistic Inference

SIMULATION ◽  
2003 ◽  
Vol 79 (10) ◽  
pp. 545-567 ◽  
Author(s):  
Y. Xiang ◽  
X. An ◽  
N. Cercone
Keyword(s):  
Graphical Models ◽  
Probabilistic Inference
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