scholarly journals Dynamics of Coordinate Ascent Variational Inference: A Case Study in 2D Ising Models

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1263
Author(s):  
Sean Plummer ◽  
Debdeep Pati ◽  
Anirban Bhattacharya
Keyword(s):  
Ising Model ◽  
Objective Function ◽  
Mean Field ◽  
Oscillatory Behavior ◽  
Variational Inference ◽  
Computational Environment ◽  
Parallel Version ◽  
Global Optima ◽  
Variational Algorithms

Variational algorithms have gained prominence over the past two decades as a scalable computational environment for Bayesian inference. In this article, we explore tools from the dynamical systems literature to study the convergence of coordinate ascent algorithms for mean field variational inference. Focusing on the Ising model defined on two nodes, we fully characterize the dynamics of the sequential coordinate ascent algorithm and its parallel version. We observe that in the regime where the objective function is convex, both the algorithms are stable and exhibit convergence to the unique fixed point. Our analyses reveal interesting discordances between these two versions of the algorithm in the region when the objective function is non-convex. In fact, the parallel version exhibits a periodic oscillatory behavior which is absent in the sequential version. Drawing intuition from the Markov chain Monte Carlo literature, we empirically show that a parameter expansion of the Ising model, popularly called the Edward–Sokal coupling, leads to an enlargement of the regime of convergence to the global optima.

Developing Schedule With Linear Programming (Case Study: STTF II Project Komplek Sukamukti Banjaran)

2020 ◽  
Vol 4 (02) ◽  
pp. 34-45
Author(s):  
Naufal Dzikri Afifi ◽  
Ika Arum Puspita ◽  
Mohammad Deni Akbar
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Project Scheduling ◽  
Time Limit ◽  
Minimum Time ◽  
Service Cost ◽  
Trade Off ◽  
Overtime Work ◽  
The Cost

Shift to The Front II Komplek Sukamukti Banjaran Project is one of the projects implemented by one of the companies engaged in telecommunications. In its implementation, each project including Shift to The Front II Komplek Sukamukti Banjaran has a time limit specified in the contract. Project scheduling is an important role in predicting both the cost and time in a project. Every project should be able to complete the project before or just in the time specified in the contract. Delay in a project can be anticipated by accelerating the duration of completion by using the crashing method with the application of linear programming. Linear programming will help iteration in the calculation of crashing because if linear programming not used, iteration will be repeated. The objective function in this scheduling is to minimize the cost. This study aims to find a trade-off between the costs and the minimum time expected to complete this project. The acceleration of the duration of this study was carried out using the addition of 4 hours of overtime work, 3 hours of overtime work, 2 hours of overtime work, and 1 hour of overtime work. The normal time for this project is 35 days with a service fee of Rp. 52,335,690. From the results of the crashing analysis, the alternative chosen is to add 1 hour of overtime to 34 days with a total service cost of Rp. 52,375,492. This acceleration will affect the entire project because there are 33 different locations worked on Shift to The Front II and if all these locations can be accelerated then the duration of completion of the entire project will be effective

scholarly journals Hybrid Seven-bar Press Mechanism

2018 ◽  
Vol 12 (3) ◽  
pp. 181-187
Author(s):  
M. Erkan Kütük ◽  
L. Canan Dülger
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Design Optimization ◽  
Hybrid System ◽  
Degrees Of Freedom ◽  
Dimensional Synthesis ◽  
Design Variables ◽  
Optimization Study ◽  
Metal Stamping

An optimization study with kinetostatic analysis is performed on hybrid seven-bar press mechanism. This study is based on previous studies performed on planar hybrid seven-bar linkage. Dimensional synthesis is performed, and optimum link lengths for the mechanism are found. Optimization study is performed by using genetic algorithm (GA). Genetic Algorithm Toolbox is used with Optimization Toolbox in MATLAB®. The design variables and the constraints are used during design optimization. The objective function is determined and eight precision points are used. A seven-bar linkage system with two degrees of freedom is chosen as an example. Metal stamping operation with a dwell is taken as the case study. Having completed optimization, the kinetostatic analysis is performed. All forces on the links and the crank torques are calculated on the hybrid system with the optimized link lengths

Identifying graph clusters using variational inference and links to covariance parametrization

2009 ◽  
Vol 367 (1906) ◽  
pp. 4407-4426
Author(s):  
David Barber
Keyword(s):  
Mean Field ◽  
Matrix Decomposition ◽  
Difficult Problem ◽  
Positive Definite ◽  
Variational Inference ◽  
Field Theories ◽  
Variational Approximation ◽  
Positive Definite Matrices ◽  
The Matrix ◽  
Non Gaussian

Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation inspired by mean-field theories in statistical mechanics. Clique matrices also play a natural role in parametrizing positive definite matrices under zero constraints on elements of the matrix. We show that clique matrices can parametrize all positive definite matrices restricted according to a decomposable graph and form a structured factor analysis approximation in the non-decomposable case. Extensions to conjugate Bayesian covariance priors and more general non-Gaussian independence models are briefly discussed.

scholarly journals Rhythmic behavior in a two-population mean-field Ising model

2016 ◽  
Vol 94 (4) ◽  
Author(s):  
Francesca Collet ◽  
Marco Formentin ◽  
Daniele Tovazzi
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Population Mean ◽  
Rhythmic Behavior

scholarly journals Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics

2019 ◽  
Author(s):  
Mathieu Fourment ◽  
Aaron E. Darling
Keyword(s):  
Probabilistic Models ◽  
Probability Distributions ◽  
Mean Field ◽  
Black Box ◽  
Variational Inference ◽  
Machine Learning Techniques ◽  
Mcmc Methods ◽  
Substitution Model ◽  
Probabilistic Programming ◽  
Phylogenetic Models

AbstractRecent advances in statistical machine learning techniques have led to the creation of probabilistic programming frameworks. These frameworks enable probabilistic models to be rapidly prototyped and fit to data using scalable approximation methods such as variational inference. In this work, we explore the use of the Stan language for probabilistic programming in application to phylogenetic models. We show that many commonly used phylogenetic models including the general time reversible (GTR) substitution model, rate heterogeneity among sites, and a range of coalescent models can be implemented using a probabilistic programming language. The posterior probability distributions obtained via the black box variational inference engine in Stan were compared to those obtained with reference implementations of Markov chain Monte Carlo (MCMC) for phylogenetic inference. We find that black box variational inference in Stan is less accurate than MCMC methods for phylogenetic models, but requires far less compute time. Finally, we evaluate a custom implementation of mean-field variational inference on the Jukes-Cantor substitution model and show that a specialized implementation of variational inference can be two orders of magnitude faster and more accurate than a general purpose probabilistic implementation.

TODA

2018 ◽  
Vol 10 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Cida Sanches ◽  
Samuel Ferreira Jr ◽  
Givaldo Santos ◽  
Marisa Regina Paixão ◽  
Manuel Meireles
Keyword(s):  
Decision Analysis ◽  
Objective Function ◽  
Analysis Method ◽  
Case Study Method ◽  
Application Process ◽  
Ahp Method ◽  
Trade Off ◽  
Software Application

This paper describes the use and application of the TODA (Trade-off Decision Analysis) method through a case study. The method uses the concept of trade-off applied to a prioritization matrix and, to define the weights, it takes the concept of causality into account. Studies have shown that the TODA achieves the same results as the competing AHP method. However, it is easier to operate. The methodology used is a case study concerning the choice of the type of car for a fleet of vehicles to be driven by salespeople. Together with the software application process, the methods that aided the weighting of the criteria are described and how the values of the alternatives are converted into coefficients of the objective function. The results clearly show that the method is easily applied, but the limitations of the case study method preclude forming generalizations.

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