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Maximum-entropy random graph models are random graph models used to study complex networks subject to the principle of maximum entropy under a set of structural
Maximum-entropy random graph model
Maximum-entropy_random_graph_model
Graph generated by a random process
random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph
Random_graph
Two closely related models for generating random graphs
graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random network. These models are
Erdős–Rényi_model
Set of random variables
Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties.
Markov_random_field
Average uncertainty in variable's states
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential
Entropy_(information_theory)
Measure of connection disorder in a network
network entropy is a disorder measure derived from information theory to describe the level of randomness and the amount of information encoded in a graph. It
Network_entropy
Process forming a path from many random steps
Random walk with heavy-tailed step lengths Lévy flight foraging hypothesis Loop-erased random walk – Model for a random simple path Maximal entropy random
Random_walk
Statistical models for network analysis
Exponential family random graph models (ERGMs) are a set of statistical models used to study the structure and patterns within networks, such as those
Exponential family random graph models
Exponential_family_random_graph_models
Random graph model in applied mathematics
mathematics, the soft configuration model (SCM) is a random graph model subject to the principle of maximum entropy under constraints on the expectation
Soft_configuration_model
Type of biased random walk on a graph
A maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the
Maximal_entropy_random_walk
Family of random graph models
Configuration Model is a family of random graph models designed to generate networks from a given degree sequence. Unlike simpler models such as the Erdős–Rényi
Configuration_model
Class of statistical modeling methods
theorem Maximum entropy Markov model (MEMM) Lafferty, J.; McCallum, A.; Pereira, F. (2001). "Conditional random fields: Probabilistic models for segmenting
Conditional_random_field
In graph theory, the mathematically simplest spatial network
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing
Random_geometric_graph
Probability distribution that has the most entropy of a class
In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of
Maximum entropy probability distribution
Maximum_entropy_probability_distribution
Mathematical model of ferromagnetism in statistical mechanics
S and G\S. A maximum cut size is at least the size of any other cut, varying S. For the Ising model without an external field on a graph G, the Hamiltonian
Ising_model
Structural analysis of a network
In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various
Biased_random_walk_on_a_graph
Concept in network science
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized
Stochastic_block_model
Methods of estimating differential entropy given some observations
the calculated entropy of the sample. The method gives very accurate results, but it is limited to calculations of random sequences modeled as Markov chains
Entropy_estimation
Scale-free network generation algorithm
while random graph models such as the Erdős–Rényi (ER) model and the Watts–Strogatz (WS) model do not exhibit power laws. The Barabási–Albert model is one
Barabási–Albert_model
Method of generating random small-world graphs
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and
Watts–Strogatz_model
Continuous probability distribution
distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls
Weibull_distribution
Probability distribution
N(\mu ,\sigma ^{2})} is the one with maximum entropy. To see this, let X {\displaystyle X} be a continuous random variable with probability density
Normal_distribution
Property of a thermodynamic system
thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much
Entropy
Probability distribution
p=\log(4\pi \gamma )} The Cauchy distribution is the maximum entropy probability distribution for a random variate X {\displaystyle X} for which E [ log
Cauchy_distribution
Representation of a type of random process
In statistics, an autoregressive (AR) model is a modelled representation of a type of random process. It can be used to describe time-varying processes
Autoregressive_model
Probability distribution
entropy can be negative (as it is for the beta distribution). What really matters is the relative value of entropy. Given two beta distributed random
Beta_distribution
Network whose degree distribution follows a power law
scale-free. Random graph – Graph generated by a random process Erdős–Rényi model – Two closely related models for generating random graphs Non-linear preferential
Scale-free_network
Notion in statistics
of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of
Fisher_information
Probabilistic graphical representation of causal relationships
probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one
Bayesian_network
algorithm: algorithm for constructing maximum-cardinality matching on graphs. Coloring algorithm: algorithms for graph (vertex or edge) coloring (subject
List_of_algorithms
Model describing the adsorption of a mono-layer of gas molecules on an ideal flat surface
surface dramatically reduces the entropy of the molecular system. To find the entropy decrease, we find the entropy of the molecule when in the adsorbed
Langmuir_adsorption_model
Clustering and community detection algorithm
hypothetical randomized partition of communities). In the above image, our initial collection of unsorted nodes is represented by the graph on the left
Leiden_algorithm
Agent-based segregation model
Carlo method the grid space from the random initialisations of the grid to produce a calculation of the entropy; S = k B ln Ω ( R ) . {\textstyle
Schelling's model of segregation
Schelling's_model_of_segregation
Academic field
offshoot of graph theory with Paul Erdős and Alfréd Rényi's eight famous papers on random graphs. For social networks the exponential random graph model or p*
Network_science
Statistical model for a binary dependent variable
cross-entropy loss function. Logistic regression is an important machine learning algorithm. The goal is to model the probability of a random variable
Logistic_regression
Function related to statistics and probability theory
the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters
Likelihood_function
Approximate nearest neighbor search algorithm
the model that produced the vectors. HNSW provides a way to search these vectors quickly, especially in large datasets. HNSW stores vectors in a graph. Each
Hierarchical navigable small world
Hierarchical_navigable_small_world
Sequential model-based optimization of expensive black-box functions
probabilistic model. The procedure has the following form: Choose an initial design X 0 {\displaystyle X_{0}} , often by a space-filling design or random sampling
Bayesian_optimization
of maximum entropy Probability Probability interpretations Propensity probability Random number generator Random sequence Randomization Randomness Statistical
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Threshold of percolation theory models
physics worlds it generally refers to simplified lattice models of random systems or networks (graphs), and the nature of the connectivity in them. The percolation
Percolation_threshold
Maximum entropy classifier – redirects to Logistic regression Maximum-entropy Markov model Maximum entropy method – redirects to Principle of maximum
List_of_statistics_articles
Partitioning a digital image into segments
are used in industry including the maximum entropy method, balanced histogram thresholding, Otsu's method (maximum variance), and k-means clustering.
Image_segmentation
Observation that in many real-life datasets, the leading digit is likely to be small
the dataset values are uniformly distributed on a logarithmic scale. The graph to the right shows Benford's law for base 10. Although a decimal base is
Benford's_law
Graph where most nodes are reachable in a small number of steps
than expected by random chance. Watts and Strogatz then proposed a novel graph model, currently named the Watts and Strogatz model, with (i) a small
Small-world_network
Degree of connectedness within a graph
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position
Centrality
2.71828...; base of natural logarithms
\cdots ,A_{k})} , the entropy of which is the expected information gained regarding the probability distribution by performing a random sample (or "experiment")
E_(mathematical_constant)
Notion in network science of quantum information networks
quantum random network model proposed by Perseguers et al. (2009) can be thought of as a quantum version of the Erdős–Rényi model. In this model, each node
Quantum_complex_network
Probabilistic optimization technique and metaheuristic
give some general guidelines. Simulated annealing may be modeled as a random walk on a search graph, whose vertices are all possible states, and the edges
Simulated_annealing
Network with non-trivial topological features
network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often
Complex_network
Fundamental theorem in probability theory and statistics
established for the simple random walk on a crystal lattice (an infinite-fold abelian covering graph over a finite graph), and is used for design of
Central_limit_theorem
Machine learning algorithm
IBM SPSS Modeler In a decision tree, all paths from the root node to the leaf node proceed by way of conjunction, or AND. In a decision graph, it is possible
Decision_tree_learning
Type of thermodynamic potential
equivalent Enthalpy–entropy compensation Free entropy Gibbs–Helmholtz equation Grand potential Non-random two-liquid model (NRTL model) – Gibbs energy of
Gibbs_free_energy
probability). A HGG generalizes a random geometric graph (RGG) whose embedding space is Euclidean. Mathematically, a HGG is a graph G ( V , E ) {\displaystyle
Hyperbolic_geometric_graph
NP-hard problem in combinatorial optimization
optimal tour. TSP can be modeled as an undirected weighted graph, such that cities are the graph's vertices, paths are the graph's edges, and a path's distance
Travelling_salesman_problem
Python library for graphs and networks
more graphing algorithms and functions. Classes for graphs and digraphs. Conversion of graphs to and from several formats. Ability to construct random graphs
NetworkX
Knowledge base that represents semantic relations between concepts in a network
knowledge graph the name Knowledge Graph. The Semantic Link Network was systematically studied as a social semantics networking method. Its basic model consists
Semantic_network
Mathematical theory on behavior of connected clusters in a random graph
physicists since then. In a slightly different mathematical model for obtaining a random graph, a site is "occupied" with probability p or "empty" (in which
Percolation_theory
Statistical model used in machine learning
corresponds to the entropy of the target distribution and is independent of the parameter θ {\displaystyle \theta } we want the model to learn, which only
Flow-based_generative_model
Decision support tool
when building a decision tree model with the same data the model is tested with. The ability to leverage the power of random forests can also help significantly
Decision_tree
Measure of network community structure
statistically consistent, and finds communities in its own null model, i.e. fully random graphs, and therefore it cannot be used to find statistically significant
Modularity_(networks)
Overview of and topical guide to machine learning
source Markov logic network Markov model Markov random field Markovian discrimination Maximum-entropy Markov model Multi-armed bandit Multi-task learning
Outline_of_machine_learning
Clustering and community detection algorithm
sampled from the assortative stochastic block model., it is prone to finding spurious communities in random graphs and has been shown to systematically overfit
Louvain_method
Hypothesis in neuroscience
observations under the variational density minus its entropy, it is also related to the maximum entropy principle. Finally, because the time average of energy
Free_energy_principle
Discrete set of Boolean variables
different underlying graph topologies. The homogeneous case simply refers to a grid which is simply the reduction to the famous Ising model. Scale-free topologies
Boolean_network
Sequence of data points over time
Correlation entropy Approximate entropy Sample entropy Fourier entropy [uk] Wavelet entropy Dispersion entropy Fluctuation dispersion entropy Rényi entropy Higher-order
Time_series
Model in network science
The Bianconi–Barabási model is a model in network science that explains the growth of complex evolving networks. This model can explain that nodes with
Bianconi–Barabási_model
Computer-based method for summarizing a text
language models for modeling salience. Although the system exhibited good results, the researchers wanted to explore the effectiveness of a maximum entropy (ME)
Automatic_summarization
Method of statistical inference
principle Inductive probability Information field theory Principle of maximum entropy Probabilistic causation Probabilistic programming "Bayesian". Merriam-Webster
Bayesian_inference
Particular case of the generalized extreme value distribution
type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions
Gumbel_distribution
Generalization of the concept from statistical mechanics
maximizing the entropy for a fixed expectation value of the energy; this underlies the appearance of the partition function in maximum entropy methods and
Partition function (mathematics)
Partition_function_(mathematics)
Resource problem in machine learning
Press, William H. (2009), "Bandit solutions provide unified ethical models for randomized clinical trials and comparative effectiveness research", Proceedings
Multi-armed_bandit
Basic noise model used in information theory
white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers
Additive_white_Gaussian_noise
Class of algorithms operating on data streams
graphs, and can solve interesting problems (such as connectivity) that are insoluble in o ( n ) {\displaystyle o(n)} space. In the data stream model,
Streaming_algorithm
Probability distribution
shape value (α) of log 4 5 ≈ 1.16 exhibit the Pareto principle. If X is a random variable with a Pareto (Type I) distribution, then the probability that
Pareto_distribution
Arrangement of a communication network
an application of graph theory wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines
Network_topology
Mathematical function, inverse of an exponential function
positive random variables, for example in the study of turbulence. Logarithms are used for maximum-likelihood estimation of parametric statistical models. For
Logarithm
Analysis of social structures using network and graph theory
process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of nodes (individual
Social_network_analysis
Grouping a set of objects by similarity
and just provide the grouping information. Graph-based models: a clique, that is, a subset of nodes in a graph such that every two nodes in the subset are
Cluster_analysis
Study of graphs as a representation of relations between discrete objects
science, and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network
Network_theory
Tendency for similar nodes to be connected
of networks: the random graph of Erdős and Rényi BA Model (Barabási-Albert model) In the ER model, since edges are placed at random without regard to
Assortativity
computational limitations, but suggested that copying nodes randomly is a simple, model worthy mechanism for creating Zipfian distribution networks.
Copying_network_models
Monte Carlo algorithm
regression (aka "maximum entropy models"), can be incorporated in this fashion. (BUGS, for example, allows this type of mixing of models.) There are two
Gibbs_sampling
Mixing property of Markov chains and graphs
of a directed graph, in which case it can be used to analyze how quickly random walks in the graph converge. The conductance of a graph is closely related
Conductance_(graph_theory)
Ensemble of states at a constant temperature
temperature. Maximum entropy: For a given mechanical system (fixed N, V), the canonical ensemble average −⟨log P⟩ (the entropy) is the maximum possible of
Canonical_ensemble
Set-to-real map with diminishing returns
is the entropy of the set of random variables S {\displaystyle S} , a fact known as Shannon's inequality. Further inequalities for the entropy function
Submodular_set_function
Network representing spatial objects
network is a lattice or a random geometric graph (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane;
Spatial_network
Theory of subatomic structure
In the branch of physics called statistical mechanics, entropy is a measure of the randomness or disorder of a physical system. This concept was studied
String_theory
Process in machine learning and statistics
is based on information theory, and is effectively derived via the maximum entropy principle. Other criteria are Bayesian information criterion (BIC)
Feature_selection
Method of estimating a statistical model's parameters
between 1905 and 1958 to a set containing annual maximum wind speeds. Given an Independent and identically random sample { x 1 , … , x n } {\displaystyle \{x_{1}
Maximum_spacing_estimation
Transforming data by taking the logarithm
free parameters if an entropy is assumed and the standard deviation is determined by the principle of maximum rate of entropy production. The length
Log transformation (statistics)
Log_transformation_(statistics)
principle of maximum entropy. Here, it sees as given some partially specified model complex and some specified relativity beside the model. It selects
Minimum energy performance standard
Minimum_energy_performance_standard
Concept in physics
make effective patterns in a random search for optimal solutions on graphs. An example of such an optimization problem is graph coloring. The SOC process
Self-organized_criticality
Fourth standardized moment in statistics
by using L-moments instead of the ordinary moments. Kurtosis risk Maximum entropy probability distribution Pearson, Karl (1905), "Das Fehlergesetz und
Kurtosis
Optimization algorithm
sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class of optimization algorithms modeled on the
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Theory and paradigm of statistics
Bayesian inference, probabilities can be assigned to model parameters. Parameters can be represented as random variables. Bayesian inference uses Bayes' theorem
Bayesian_statistics
Model-free reinforcement learning algorithm
possible actions based on its current state, without requiring a model of the environment (model-free). It can handle problems with stochastic transitions and
Q-learning
Method of representing systems
Königsberg, which established the foundation of graph theory. From the 1930s-1950s the study of random graphs were developed. During the mid-1990s, it was
Biological_network
Degree Preserving Randomization is a technique used in Network Science that aims to assess whether or not variations observed in a given graph could simply
Degree-preserving randomization
Degree-preserving_randomization
Concept in graph theory
community structure. Many basic network models, for example, such as the random graph and the Barabási–Albert model, do not display community structure.
Community_structure
Difficulties arising when analyzing data with many aspects ("dimensions")
difference between the minimum and the maximum distance between a random reference point Q and a list of n random data points P1,...,Pn become indiscernible
Curse_of_dimensionality
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
Boy/Male
English
Son of Rand.
Female
English
Short form of English Miranda, RANDA means "worthy of admiration."Â
Surname or Lastname
English
English : probably a variant of Crandon, a habitational name from Crandon in Somerset or Crandean in Falmer, Sussex. Compare Grandin.
Male
Scandinavian
 Scandinavian form of Old Norse Randolfr, RANDOLF means "shield-wolf." Compare with another form of Randolf.
Male
French
French form of Latin Maximus, MAXIME means "the greatest."Â
Surname or Lastname
English
English : patronymic from Rand 1.
Surname or Lastname
English
English : unexplained; perhaps a variant of Francom.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : patronymic from the Middle English personal name Rand(e) (see Rand 1).
Surname or Lastname
English
English : variant of Rand 1, from the Old French oblique case.
Surname or Lastname
English
English : variant of Ransom.
Surname or Lastname
English
English : variant of Brandon.
Female
English
Variant spelling of English Randy, RANDI means "worthy of admiration."
Boy/Male
English American
Son of Rand.
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Male
English
 Variant spelling of Middle English Randulf, RANDOLF means "shield-wolf." Compare with other forms of Randolf.
Surname or Lastname
English
English : variant spelling of Randall.Americanized spelling of Randel.
Male
Norwegian
 Norwegian form of Old Norse Arnþórr, ANDOR means "eagle of Thor." Compare with another form of Andor.
Male
Hungarian
 Variant spelling of Hungarian András, ANDOR means "man; warrior." Compare with another form of Andor.
Male
Russian
(МакÑим) Variant spelling of Russian Maksim, MAXIM means "the greatest." Compare with another form of Maxim.
Male
English
Pet form of English Randall and Randolph, both RANDY means "shield-wolf." Compare with feminine Randy.
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
Girl/Female
Arabic
Most Beautiful
Surname or Lastname
German
German : variant of Boldt.Slovenian : from Bolte, an old short form of the personal name Boltežar (see Balthazar). It may also be an Americanized form of the Slovenian surname Boljte, which has the same origin.English : variant spelling of Bolt.
Girl/Female
Latin
Prophetess.
Boy/Male
Hindu, Indian
Pronunciation
Boy/Male
British, English, Gaelic, Irish
From the Hay Meadow; Ingenious; Clever
Surname or Lastname
English
English : from a diminutive of Moore 2 or 3.English : from an unattested Old English personal name, MÅrwine.Dutch : nickname for a grumbler, from Middle Dutch murren, morren ‘to grumble or growl’.
Boy/Male
Christian & English(British/American/Australian)
A Visionary and Listener
Girl/Female
Arabic, Pashtun
Peace
Boy/Male
British, English
Spear-rule
Boy/Male
Hindu, Indian, Tamil
King of Beauty
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
MAXIMUM ENTROPY-RANDOM-GRAPH-MODEL
v. i.
To go or stray at random.
pl.
of Maximum
adv.
In a random manner.
n.
The least quantity assignable, admissible, or possible, in a given case; hence, a thing of small consequence; -- opposed to maximum.
n.
The greatest quantity or value attainable in a given case; or, the greatest value attained by a quantity which first increases and then begins to decrease; the highest point or degree; -- opposed to minimum.
n.
In a curve referred to polar coordinates, any point for which the radius vector is a maximum or minimum.
n.
Random.
n.
To exact a ransom for, or a payment on.
n.
A certain property of a body, expressed as a measurable quantity, such that when there is no communication of heat the quantity remains constant, but when heat enters or leaves the body the quantity increases or diminishes. If a small amount, h, of heat enters the body when its temperature is t in the thermodynamic scale the entropy of the body is increased by h / t. The entropy is regarded as measured from some standard temperature and pressure. Sometimes called the thermodynamic function.
n.
Anything driven at random.
n.
The release of a captive, or of captured property, by payment of a consideration; redemption; as, prisoners hopeless of ransom.
n.
A self-registering thermometer, especially one that registers the maximum and minimum during long periods.
a.
Going at random or by chance; done or made at hazard, or without settled direction, aim, or purpose; hazarded without previous calculation; left to chance; haphazard; as, a random guess.
n.
To redeem from captivity, servitude, punishment, or forfeit, by paying a price; to buy out of servitude or penalty; to rescue; to deliver; as, to ransom prisoners from an enemy.
n.
A roving motion; course without definite direction; want of direction, rule, or method; hazard; chance; -- commonly used in the phrase at random, that is, without a settled point of direction; at hazard.
a.
Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.
n.
Distance to which a missile is cast; range; reach; as, the random of a rifle ball.
a.
Having equal entropy.