MAP-Inference on Large Scale Higher-Order Discrete Graphical Models by Fusion Moves

2015 ◽  
pp. 469-484
Author(s):  
Jörg Hendrik Kappes ◽  
Thorsten Beier ◽  
Christoph Schnörr
Keyword(s):  
Graphical Models ◽  
Large Scale ◽  
Higher Order ◽  
Map Inference

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

Efficient and High-Quality Seeded Graph Matching: Employing Higher-order Structural Information

2021 ◽  
Vol 15 (3) ◽  
pp. 1-31
Author(s):  
Haida Zhang ◽  
Zengfeng Huang ◽  
Xuemin Lin ◽  
Zhe Lin ◽  
Wenjie Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Graph Matching ◽  
Structural Information ◽  
Experimental Studies ◽  
Higher Order ◽  
Personalized Pagerank ◽  
Matching Accuracy ◽  
Approximation Techniques ◽  
Order Of Magnitude ◽  
Matching Score

Driven by many real applications, we study the problem of seeded graph matching. Given two graphs and , and a small set of pre-matched node pairs where and , the problem is to identify a matching between and growing from , such that each pair in the matching corresponds to the same underlying entity. Recent studies on efficient and effective seeded graph matching have drawn a great deal of attention and many popular methods are largely based on exploring the similarity between local structures to identify matching pairs. While these recent techniques work provably well on random graphs, their accuracy is low over many real networks. In this work, we propose to utilize higher-order neighboring information to improve the matching accuracy and efficiency. As a result, a new framework of seeded graph matching is proposed, which employs Personalized PageRank (PPR) to quantify the matching score of each node pair. To further boost the matching accuracy, we propose a novel postponing strategy, which postpones the selection of pairs that have competitors with similar matching scores. We show that the postpone strategy indeed significantly improves the matching accuracy. To improve the scalability of matching large graphs, we also propose efficient approximation techniques based on algorithms for computing PPR heavy hitters. Our comprehensive experimental studies on large-scale real datasets demonstrate that, compared with state-of-the-art approaches, our framework not only increases the precision and recall both by a significant margin but also achieves speed-up up to more than one order of magnitude.

scholarly journals Combining Bayesian Approaches and Evolutionary Techniques for the Inference of Breast Cancer Networks

2017 ◽  
Author(s):  
Stefano Beretta ◽  
Mauro Castelli ◽  
Ivo Gonçalves ◽  
Ivan Merelli ◽  
Daniele Ramazzotti
Keyword(s):  
Breast Cancer ◽  
Graphical Models ◽  
Protein Interactions ◽  
Large Scale ◽  
Small Sample Size ◽  
Small Sample ◽  
Cancer Data ◽  
Correlation Networks ◽  
Model Complex ◽  
Cancer Networks

AbstractGene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental data through computational analysis. However, this task is typically complicated by the enormously large scale of the unknowns in a rather small sample size. Furthermore, when the goal is to study causal relationships within the network, tools capable of overcoming the limitations of correlation networks are required. In this work, we make use of Bayesian Graphical Models to attach this problem and, specifically, we perform a comparative study of different state-of-the-art heuristics, analyzing their performance in inferring the structure of the Bayesian Network from breast cancer data.

scholarly journals Learning Graph Convolutional Network for Skeleton-Based Human Action Recognition by Neural Searching

2020 ◽  
Vol 34 (03) ◽  
pp. 2669-2676 ◽  
Author(s):  
Wei Peng ◽  
Xiaopeng Hong ◽  
Haoyu Chen ◽  
Guoying Zhao
Keyword(s):  
Action Recognition ◽  
Large Scale ◽  
Order Approximation ◽  
Human Action Recognition ◽  
Search Space ◽  
Human Action ◽  
Higher Order ◽  
Dynamic Graph ◽  
Convolutional Network ◽  
Representational Capacity

Human action recognition from skeleton data, fuelled by the Graph Convolutional Network (GCN) with its powerful capability of modeling non-Euclidean data, has attracted lots of attention. However, many existing GCNs provide a pre-defined graph structure and share it through the entire network, which can loss implicit joint correlations especially for the higher-level features. Besides, the mainstream spectral GCN is approximated by one-order hop such that higher-order connections are not well involved. All of these require huge efforts to design a better GCN architecture. To address these problems, we turn to Neural Architecture Search (NAS) and propose the first automatically designed GCN for this task. Specifically, we explore the spatial-temporal correlations between nodes and build a search space with multiple dynamic graph modules. Besides, we introduce multiple-hop modules and expect to break the limitation of representational capacity caused by one-order approximation. Moreover, a corresponding sampling- and memory-efficient evolution strategy is proposed to search in this space. The resulted architecture proves the effectiveness of the higher-order approximation and the layer-wise dynamic graph modules. To evaluate the performance of the searched model, we conduct extensive experiments on two very large scale skeleton-based action recognition datasets. The results show that our model gets the state-of-the-art results in term of given metrics.

Sandpiper: Scaling probabilistic inferencing to large scale graphical models

2017 ◽  
Author(s):  
Alexander Ulanov ◽  
Manish Marwah ◽  
Mijung Kim ◽  
Roshan Dathathri ◽  
Carlos Zubieta ◽  
...  
Keyword(s):  
Graphical Models ◽  
Large Scale

scholarly journals Clustered CTCF binding is an evolutionary mechanism to maintain topologically associating domains

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Elissavet Kentepozidou ◽  
Sarah J. Aitken ◽  
Christine Feig ◽  
Klara Stefflova ◽  
Ximena Ibarra-Soria ◽  
...  
Keyword(s):  
Large Scale ◽  
Evolutionary Dynamics ◽  
Computational Study ◽  
Genome Structure ◽  
Higher Order ◽  
Ctcf Binding ◽  
Natural Genetic Variation ◽  
Transcription Start Sites ◽  
Topologically Associating Domains ◽  
Species Specific

Abstract Background CTCF binding contributes to the establishment of a higher-order genome structure by demarcating the boundaries of large-scale topologically associating domains (TADs). However, despite the importance and conservation of TADs, the role of CTCF binding in their evolution and stability remains elusive. Results We carry out an experimental and computational study that exploits the natural genetic variation across five closely related species to assess how CTCF binding patterns stably fixed by evolution in each species contribute to the establishment and evolutionary dynamics of TAD boundaries. We perform CTCF ChIP-seq in multiple mouse species to create genome-wide binding profiles and associate them with TAD boundaries. Our analyses reveal that CTCF binding is maintained at TAD boundaries by a balance of selective constraints and dynamic evolutionary processes. Regardless of their conservation across species, CTCF binding sites at TAD boundaries are subject to stronger sequence and functional constraints compared to other CTCF sites. TAD boundaries frequently harbor dynamically evolving clusters containing both evolutionarily old and young CTCF sites as a result of the repeated acquisition of new species-specific sites close to conserved ones. The overwhelming majority of clustered CTCF sites colocalize with cohesin and are significantly closer to gene transcription start sites than nonclustered CTCF sites, suggesting that CTCF clusters particularly contribute to cohesin stabilization and transcriptional regulation. Conclusions Dynamic conservation of CTCF site clusters is an apparently important feature of CTCF binding evolution that is critical to the functional stability of a higher-order chromatin structure.

A Higher-Order Closure Model with an Explicit PBL Top

2010 ◽  
Vol 67 (3) ◽  
pp. 834-850 ◽  
Author(s):  
Cara-Lyn Lappen ◽  
David Randall ◽  
Takanobu Yamaguchi
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Higher Order ◽  
Entrainment Rate ◽  
Time Step ◽  
Vertical Coordinate ◽  
Second Moments ◽  
Scale Models ◽  
Vertical Grid ◽  
Flux Model

Abstract In 2001, the authors presented a higher-order mass-flux model called “assumed distributions with higher-order closure” (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higher-order closure models, are not suitable for use in large-scale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higher-order closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are “hidden” in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in large-scale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixed-layer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in large-scale models.

Cortical Circuitry Implementing Graphical Models

2009 ◽  
Vol 21 (11) ◽  
pp. 3010-3056 ◽  
Author(s):  
Shai Litvak ◽  
Shimon Ullman
Keyword(s):  
Graphical Models ◽  
Large Scale ◽  
Graphical Model ◽  
Current Model ◽  
Building Blocks ◽  
Population Based ◽  
Spiking Neurons ◽  
Inhibitory Neurons ◽  
Basket Cells ◽  
Local Circuitry

In this letter, we develop and simulate a large-scale network of spiking neurons that approximates the inference computations performed by graphical models. Unlike previous related schemes, which used sum and product operations in either the log or linear domains, the current model uses an inference scheme based on the sum and maximization operations in the log domain. Simulations show that using these operations, a large-scale circuit, which combines populations of spiking neurons as basic building blocks, is capable of finding close approximations to the full mathematical computations performed by graphical models within a few hundred milliseconds. The circuit is general in the sense that it can be wired for any graph structure, it supports multistate variables, and it uses standard leaky integrate-and-fire neuronal units. Following previous work, which proposed relations between graphical models and the large-scale cortical anatomy, we focus on the cortical microcircuitry and propose how anatomical and physiological aspects of the local circuitry may map onto elements of the graphical model implementation. We discuss in particular the roles of three major types of inhibitory neurons (small fast-spiking basket cells, large layer 2/3 basket cells, and double-bouquet neurons), subpopulations of strongly interconnected neurons with their unique connectivity patterns in different cortical layers, and the possible role of minicolumns in the realization of the population-based maximum operation.

Sign in / Sign up

Export Citation Format

Share Document