scholarly journals Exploiting Structure in Weighted Model Counting Approaches to Probabilistic Inference

2011 ◽  
Vol 40 ◽  
pp. 729-765 ◽  
Author(s):  
W. Li ◽  
P. Poupart ◽  
P. Van Beek
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Large Scale ◽  
Search Algorithm ◽  
Exact Inference ◽  
Backtracking Search ◽  
Space Efficiency ◽  
Counting Approach ◽  
Model Counting ◽  
Weighted Model

Previous studies have demonstrated that encoding a Bayesian network into a SAT formula and then performing weighted model counting using a backtracking search algorithm can be an effective method for exact inference. In this paper, we present techniques for improving this approach for Bayesian networks with noisy-OR and noisy-MAX relations---two relations that are widely used in practice as they can dramatically reduce the number of probabilities one needs to specify. In particular, we present two SAT encodings for noisy-OR and two encodings for noisy-MAX that exploit the structure or semantics of the relations to improve both time and space efficiency, and we prove the correctness of the encodings. We experimentally evaluated our techniques on large-scale real and randomly generated Bayesian networks. On these benchmarks, our techniques gave speedups of up to two orders of magnitude over the best previous approaches for networks with noisy-OR/MAX relations and scaled up to larger networks. As well, our techniques extend the weighted model counting approach for exact inference to networks that were previously intractable for the approach.

scholarly journals Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

2020 ◽  
Vol 34 (04) ◽  
pp. 3097-3104
Author(s):  
Ralph Abboud ◽  
Ismail Ceylan ◽  
Thomas Lukasiewicz
Keyword(s):  
Neural Networks ◽  
Large Scale ◽  
Linear Time ◽  
Neural Model ◽  
Approximate Model ◽  
Counting Approach ◽  
Model Counting ◽  
Weighted Model ◽  
Learning To Reason ◽  
Special Case

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.

scholarly journals Learning Diverse Bayesian Networks

2019 ◽  
Vol 33 ◽  
pp. 7793-7800
Author(s):  
Cong Chen ◽  
Changhe Yuan
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Search Algorithm ◽  
Noisy Data ◽  
Local Neighborhood ◽  
Causal Ordering ◽  
True Model ◽  
Underlying Network ◽  
Novel Method

Much effort has been directed at developing algorithms for learning optimal Bayesian network structures from data. When given limited or noisy data, however, the optimal Bayesian network often fails to capture the true underlying network structure. One can potentially address the problem by finding multiple most likely Bayesian networks (K-Best) in the hope that one of them recovers the true model. However, it is often the case that some of the best models come from the same peak(s) and are very similar to each other; so they tend to fail together. Moreover, many of these models are not even optimal respective to any causal ordering, thus unlikely to be useful. This paper proposes a novel method for finding a set of diverse top Bayesian networks, called modes, such that each network is guaranteed to be optimal in a local neighborhood. Such mode networks are expected to provide a much better coverage of the true model. Based on a globallocal theorem showing that a mode Bayesian network must be optimal in all local scopes, we introduce an A* search algorithm to efficiently find top M Bayesian networks which are highly probable and naturally diverse. Empirical evaluations show that our top mode models have much better diversity as well as accuracy in discovering true underlying models than those found by K-Best.

Economic Load Dispatch Using Oppositional Backtracking Search Algorithm

2017 ◽  
Vol 6 (2) ◽  
pp. 79-97 ◽  
Author(s):  
Moumita Pradhan ◽  
Provas Kumar Roy ◽  
Tandra Pal
Keyword(s):  
Large Scale ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Economic Load Dispatch ◽  
Invasive Weed ◽  
Backtracking Search ◽  
Backtracking Search Algorithm ◽  
Test Systems ◽  
Generation Cost ◽  
Feasible Solutions

In this paper, an oppositional backtracking search algorithm (OBSA) is proposed to solve the large scale economic load dispatch (ELD) problem. The main drawback of the conventional backtracking search algorithm (BSA) is that it produces a local optimal solution rather than the global optimal solution. The proposed OBSA methodology is a highly-constrained optimization problem has to minimize the total generation cost by satisfying several constraints involving load demand, generation limits, prohibited operating zone, ramp rate limits and valve point loading effect. The proposed method is applied for three test systems and provides the unique and fast solutions. The new heuristic OBSA approach is successfully applied in three test systems consisting of 13 and 140 thermal generators. The test results are judged against various methods. The simulation results show the effectiveness and accuracy of the proposed OBSA algorithm over other methods like conventional BSA, oppositional invasive weed optimization (OIWO), Shuffled differential evolution (SDE) and oppositional real coded chemical reaction optimization (ORCCRO). This clearly suggests that the new OBSA method can achieve effective and feasible solutions of nonlinear ELD problems.

scholarly journals Cutset Sampling for Bayesian Networks

2007 ◽  
Vol 28 ◽  
pp. 1-48 ◽  
Author(s):  
B. Bidyuk ◽  
R. Dechter
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Sampling Methodology ◽  
Exact Inference ◽  
Inference Algorithms

The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the network's graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks.

scholarly journals Hardware implementation of Bayesian network building blocks with stochastic spintronic devices

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Punyashloka Debashis ◽  
Vaibhav Ostwal ◽  
Rafatul Faria ◽  
Supriyo Datta ◽  
Joerg Appenzeller ◽  
...  
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Large Scale ◽  
Hardware Implementation ◽  
Reducing Power ◽  
Perpendicular Magnetic Anisotropy ◽  
Building Blocks ◽  
Spintronic Devices ◽  
Network Building ◽  
Hardware Implementations

Abstract Bayesian networks are powerful statistical models to understand causal relationships in real-world probabilistic problems such as diagnosis, forecasting, computer vision, etc. For systems that involve complex causal dependencies among many variables, the complexity of the associated Bayesian networks become computationally intractable. As a result, direct hardware implementation of these networks is one promising approach to reducing power consumption and execution time. However, the few hardware implementations of Bayesian networks presented in literature rely on deterministic CMOS devices that are not efficient in representing the stochastic variables in a Bayesian network that encode the probability of occurrence of the associated event. This work presents an experimental demonstration of a Bayesian network building block implemented with inherently stochastic spintronic devices based on the natural physics of nanomagnets. These devices are based on nanomagnets with perpendicular magnetic anisotropy, initialized to their hard axes by the spin orbit torque from a heavy metal under-layer utilizing the giant spin Hall effect, enabling stochastic behavior. We construct an electrically interconnected network of two stochastic devices and manipulate the correlations between their states by changing connection weights and biases. By mapping given conditional probability tables to the circuit hardware, we demonstrate that any two node Bayesian networks can be implemented by our stochastic network. We then present the stochastic simulation of an example case of a four node Bayesian network using our proposed device, with parameters taken from the experiment. We view this work as a first step towards the large scale hardware implementation of Bayesian networks.

scholarly journals Weighted Model Integration with Orthogonal Transformations

2017 ◽  
Author(s):  
David Merrell ◽  
Aws Albarghouthi ◽  
Loris D'Antoni
Keyword(s):  
Satisfiability Modulo Theories ◽  
Exact Probability ◽  
Exact Inference ◽  
First Order ◽  
Probability Bounds ◽  
Model Counting ◽  
Weighted Model ◽  
Inference Techniques ◽  
Time Required ◽  
Probabilistic Programs

Weighted model counting and integration (WMC/WMI) are natural problems to which we can reduce many probabilistic inference tasks, e.g., in Bayesian networks, Markov networks, and probabilistic programs. Typically, we are given a first-order formula, where each satisfying assignment is associated with a weight---e.g., a probability of occurrence---and our goal is to compute the total weight of the formula. In this paper, we target exact inference techniques for WMI that leverage the power of satisfiability modulo theories (SMT) solvers to decompose a first-order formula in linear real arithmetic into a set of hyperrectangular regions whose weight is easy to compute. We demonstrate the challenges of hyperrectangular decomposition and present a novel technique that utilizes orthogonal transformations to transform formulas in order to enable efficient inference. Our evaluation demonstrates our technique's ability to improve the time required to achieve exact probability bounds.

scholarly journals Influence of Wind Power on Modeling of Bidding Strategy in a Promising Power Market with a Modified Gravitational Search Algorithm

2021 ◽  
Vol 11 (10) ◽  
pp. 4438
Author(s):  
Satyendra Singh ◽  
Manoj Fozdar ◽  
Hasmat Malik ◽  
Maria del Valle Fernández Moreno ◽  
Fausto Pedro García Márquez
Keyword(s):  
Wind Power ◽  
Electricity Market ◽  
Large Scale ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Optimization Methods ◽  
Bidding Strategy ◽  
Wind Speed Profile ◽  
Gravitational Search ◽  
Modified Gravitational Search Algorithm

It is expected that large-scale producers of wind energy will become dominant players in the future electricity market. However, wind power output is irregular in nature and it is subjected to numerous fluctuations. Due to the effect on the production of wind power, producing a detailed bidding strategy is becoming more complicated in the industry. Therefore, in view of these uncertainties, a competitive bidding approach in a pool-based day-ahead energy marketplace is formulated in this paper for traditional generation with wind power utilities. The profit of the generating utility is optimized by the modified gravitational search algorithm, and the Weibull distribution function is employed to represent the stochastic properties of wind speed profile. The method proposed is being investigated and simplified for the IEEE-30 and IEEE-57 frameworks. The results were compared with the results obtained with other optimization methods to validate the approach.

scholarly journals A Matheuristic Approach Combining Local Search and Mathematical Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Carolina Lagos ◽  
Guillermo Guerrero ◽  
Enrique Cabrera ◽  
Stefanie Niklander ◽  
Franklin Johnson ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Local Search ◽  
Large Scale ◽  
Search Algorithm ◽  
Facility Location Problem ◽  
Specific Information ◽  
Local Search Algorithm ◽  
Capacitated Facility Location Problem ◽  
Capacitated Facility Location ◽  
Installation Cost

A novel matheuristic approach is presented and tested on a well-known optimisation problem, namely, capacitated facility location problem (CFLP). The algorithm combines local search and mathematical programming. While the local search algorithm is used to select a subset of promising facilities, mathematical programming strategies are used to solve the subproblem to optimality. Proposed local search is influenced by instance-specific information such as installation cost and the distance between customers and facilities. The algorithm is tested on large instances of the CFLP, where neither local search nor mathematical programming is able to find good quality solutions within acceptable computational times. Our approach is shown to be a very competitive alternative to solve large-scale instances for the CFLP.

Sign in / Sign up

Export Citation Format

Share Document