scholarly journals On Exchangeability in Network Models

2019 ◽  
Vol 10 (1) ◽  
pp. 85-114 ◽  
Author(s):  
Steffen Lauritzen ◽  
Alessandro Rinaldo ◽  
Kayvan Sadeghi
Keyword(s):  
Probability Distributions ◽  
Network Models ◽  
Infinite Graphs ◽  
Representation Theorems ◽  
Graph Theoretic

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size. 

Some new approaches to probability distributions

1980 ◽  
Vol 12 (04) ◽  
pp. 903-921 ◽  
Author(s):  
S. Kotz ◽  
D. N. Shanbhag
Keyword(s):  
Probability Distributions ◽  
Random Variables ◽  
Representation Theorems ◽  
Practical Applications ◽  
New Approaches ◽  
Characterization Of Distributions ◽  
Stability Theorems ◽  
Conditional Expectations

We develop some approaches to the characterization of distributions of real-valued random variables, useful in practical applications, in terms of conditional expectations and hazard measures. We prove several representation theorems generalizing earlier results, and establish stability theorems for two general characteristics introduced in this paper.

Computational Models in Developmental Psychology

2013 ◽  
pp. 476-504
Author(s):  
Thomas R. Shultz
Keyword(s):  
Neural Networks ◽  
Computational Modeling ◽  
Computational Models ◽  
Developmental Psychology ◽  
Probability Distributions ◽  
Network Models ◽  
Developmental Theory ◽  
Negative Evidence ◽  
Developmental Robotics ◽  
Neural Network Models

Computational modeling implements developmental theory in a precise manner, allowing generation, explanation, integration, and prediction. Several modeling techniques are applied to development: symbolic rules, neural networks, dynamic systems, Bayesian processing of probability distributions, developmental robotics, and mathematical analysis. The relative strengths and weaknesses of each approach are identified and examples of each technique are described. Ways in which computational modeling contributes to developmental issues are documented. A probabilistic model of the vocabulary spurt shows that various psychological explanations for it are unnecessary. Constructive neural networks clarify the distinction between learning and development and show how it is possible to escape Fodor’s paradox. Connectionist modeling reveals different versions of innateness and how learning and evolution might interact. Agent-based models analyze the basic principles of evolution in a testable, experimental fashion that generates complete evolutionary records. Challenges posed by stimulus poverty and lack of negative examples are explored in neural-network models that learn morphology or syntax probabilistically from indirect negative evidence.

scholarly journals Leavitt path algebras satisfying a polynomial identity

2016 ◽  
Vol 15 (05) ◽  
pp. 1650084 ◽  
Author(s):  
Jason P. Bell ◽  
T. H. Lenagan ◽  
Kulumani M. Rangaswamy
Keyword(s):  
Polynomial Identity ◽  
Finite Graph ◽  
Infinite Graphs ◽  
Leavitt Path Algebra ◽  
Arbitrary Graph ◽  
Graph Theoretic ◽  
Path Algebras ◽  
Leavitt Path Algebras ◽  
Dimension One ◽  
Kirillov Dimension

Leavitt path algebras [Formula: see text] of an arbitrary graph [Formula: see text] over a field [Formula: see text] satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When [Formula: see text] is a finite graph, [Formula: see text] satisfying a polynomial identity is shown to be equivalent to the Gelfand–Kirillov dimension of [Formula: see text] being at most one, though this is no longer true for infinite graphs. It is shown that, for an arbitrary graph [Formula: see text], the Leavitt path algebra [Formula: see text] has Gelfand–Kirillov dimension zero if and only if [Formula: see text] has no cycles. Likewise, [Formula: see text] has Gelfand–Kirillov dimension one if and only if [Formula: see text] contains at least one cycle, but no cycle in [Formula: see text] has an exit.

scholarly journals Sequential Monte Carlo Methods to Train Neural Network Models

2000 ◽  
Vol 12 (4) ◽  
pp. 955-993 ◽  
Author(s):  
J. F. G. de Freitas ◽  
M. Niranjan ◽  
A. H. Gee ◽  
A. Doucet
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Probability Distributions ◽  
Network Models ◽  
Computational Time ◽  
Optimization Strategy ◽  
Neural Network Models ◽  
Monte Carlo Techniques ◽  
Monte Carlo Algorithms ◽  
Importance Resampling

We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices.

Uniform conditional variability ordering of probability distributions

1985 ◽  
Vol 22 (03) ◽  
pp. 619-633 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Probability Distribution ◽  
Real Line ◽  
Convex Functions ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Queueing Network ◽  
Network Models ◽  
Scalar Multiplication ◽  
Closed Queueing Network ◽  
The Real

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.

scholarly journals Inefficiencies in network models: A graph-theoretic perspective

2018 ◽  
Vol 131 ◽  
pp. 44-50 ◽  
Author(s):  
Pietro Cenciarelli ◽  
Daniele Gorla ◽  
Ivano Salvo
Keyword(s):  
Network Models ◽  
Graph Theoretic

scholarly journals Street Network Models and Measures for Every U.S. City, County, Urbanized Area, Census Tract, and Zillow-Defined Neighborhood

Urban Science ◽  
2019 ◽  
Vol 3 (1) ◽  
pp. 28 ◽  
Author(s):  
Geoff Boeing
Keyword(s):  
Open Source ◽  
Census Tract ◽  
Morphological Characteristics ◽  
Network Models ◽  
Data Repository ◽  
Street Network ◽  
Urban Street ◽  
Graph Theoretic ◽  
Urbanized Area ◽  
Scientific Analysis

OpenStreetMap provides a valuable crowd-sourced database of raw geospatial data for constructing models of urban street networks for scientific analysis. This paper reports results from a research project that collected raw street network data from OpenStreetMap using the Python-based OSMnx software for every U.S. city and town, county, urbanized area, census tract, and Zillow-defined neighborhood. It constructed nonplanar directed multigraphs for each and analyzed their structural and morphological characteristics. The resulting data repository contains over 110,000 processed, cleaned street network graphs (which in turn comprise over 55 million nodes and over 137 million edges) at various scales—comprehensively covering the entire U.S.—archived as reusable open-source GraphML files, node/edge lists, and GIS shapefiles that can be immediately loaded and analyzed in standard tools such as ArcGIS, QGIS, NetworkX, graph-tool, igraph, or Gephi. The repository also contains measures of each network’s metric and topological characteristics common in urban design, transportation planning, civil engineering, and network science. No other such dataset exists. These data offer researchers and practitioners a new ability to quickly and easily conduct graph-theoretic circulation network analysis anywhere in the U.S. using standard, free, open-source tools.

scholarly journals Probabilistic graphlets capture biological function in probabilistic molecular networks

2020 ◽  
Vol 36 (Supplement_2) ◽  
pp. i804-i812
Author(s):  
Sergio Doria-Belenguer ◽  
Markus K. Youssef ◽  
René Böttcher ◽  
Noël Malod-Dognin ◽  
Nataša Pržulj
Keyword(s):  
Network Structure ◽  
Real World ◽  
Random Network ◽  
Probability Distributions ◽  
Network Models ◽  
Biological Information ◽  
Molecular Networks ◽  
Local Network ◽  
Supplementary Information ◽  
Probabilistic Networks

Abstract Motivation Molecular interactions have been successfully modeled and analyzed as networks, where nodes represent molecules and edges represent the interactions between them. These networks revealed that molecules with similar local network structure also have similar biological functions. The most sensitive measures of network structure are based on graphlets. However, graphlet-based methods thus far are only applicable to unweighted networks, whereas real-world molecular networks may have weighted edges that can represent the probability of an interaction occurring in the cell. This information is commonly discarded when applying thresholds to generate unweighted networks, which may lead to information loss. Results We introduce probabilistic graphlets as a tool for analyzing the local wiring patterns of probabilistic networks. To assess their performance compared to unweighted graphlets, we generate synthetic networks based on different well-known random network models and edge probability distributions and demonstrate that probabilistic graphlets outperform their unweighted counterparts in distinguishing network structures. Then we model different real-world molecular interaction networks as weighted graphs with probabilities as weights on edges and we analyze them with our new weighted graphlets-based methods. We show that due to their probabilistic nature, probabilistic graphlet-based methods more robustly capture biological information in these data, while simultaneously showing a higher sensitivity to identify condition-specific functions compared to their unweighted graphlet-based method counterparts. Availabilityand implementation Our implementation of probabilistic graphlets is available at https://github.com/Serdobe/Probabilistic_Graphlets. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Network models of massive datasets

2004 ◽  
Vol 1 (1) ◽  
pp. 75-89 ◽  
Author(s):  
Vladimir Boginski ◽  
Sergiy Butenko ◽  
Panos Pardalos
Keyword(s):  
Power Law ◽  
Network Models ◽  
Massive Datasets ◽  
Graph Theoretic ◽  
Global Organization ◽  
Standard Graph

We give a brief overview of the methodology of modeling massive datasets arising in various applications as networks. This approach is often useful for extracting non-trivial information from the datasets by applying standard graph-theoretic techniques. We also point out that graphs representing datasets coming from diverse practical fields have a similar power-law structure, which indicates that the global organization and evolution of massive datasets arising in various spheres of life nowadays follow similar natural principles.

Uniform conditional variability ordering of probability distributions

1985 ◽  
Vol 22 (3) ◽  
pp. 619-633 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Probability Distribution ◽  
Real Line ◽  
Convex Functions ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Queueing Network ◽  
Network Models ◽  
Scalar Multiplication ◽  
Closed Queueing Network ◽  
The Real

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.

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