A graph theoretic approach to simulation and classification

Kouritzin, Michael A.; Newton, Fraser; Wu, Bi

doi:10.1016/j.csda.2013.09.026

Cited by 5 publications

(7 citation statements)

References 11 publications

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“…In Kouritzin et al (2014), there was the stronger constraint that the right hand side of (2.5) is in [0,1].…”

Section: Remarkmentioning

confidence: 99%

“…(See Kouritzin et al (2014) for examples of choices for these auxiliary pmfs.) They also appear in the conditional probability update through functions:…”

Section: Conditional Probability Updatementioning

confidence: 99%

“…The approach has been applied to Optical Character Recognition (OCR) Kouritzin et al (2014) and the generation of both black-and-white Kouritzin et al (2013) and gray-level Newton and Kouritzin (2011) CAPTCHAs ( Fig. 1 shows a new example of such a gray level CAPTCHA.)…”

Section: Introductionmentioning

confidence: 99%

“…To meet the diversity of problems in a variety of dimensions, Kouritzin et al (2014) considered random fields on a general undirected graph structure and proposed an algorithm for producing a new class of discrete correlated random field on such graphs by either one-pass simulation or Gibbs-like resampling. The approach has been applied to Optical Character Recognition (OCR) Kouritzin et al (2014) and the generation of both black-and-white Kouritzin et al (2013) and gray-level Newton and Kouritzin (2011) CAPTCHAs ( Fig.…”

Section: Introductionmentioning

confidence: 99%

“…The design portion consists of two sets of auxiliary (vertex) pmfs (theˆ's π and the 's πɶ ) that can be used in place of the 's π in portions of the algorithm to do things like improve efficiency or destroy independence (Actually, there is a wide assortment of reasonable choices for the ˆ's π and the 's πɶ discussed in Kouritzin et al (2014)). Simulating the graph then amounts to directing the graph in an acyclic manner, fixing a topological sort of the vertices and using Proposition 1 of Kouritzin et al (2014), requoted as Proposition 1 below, recursively (See Kouritzin et al (2014) for details.) Our modified algorithm, introduced herein, completes the graph by adding edges of zero covariance wherever necessary before simulation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Flexible, Real-Time Algorithm for Simulating Correlated Random Fields and Its Properties

Kouritzin¹,

Newton²,

Wu³

2017

Journal of Mathematics and Statistics

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Contemporary real-time problems like CAPTCHA generation and optical character recognition can be solved effectively using correlated random fields. These random fields should be produced on a graph in order that problems of any dimension and shape can be handled. However, traditional solutions are often too slow, inaccurate or both. Herein, the Quick Simulation Random Field algorithm to produce correlated random fields on general undirected graphs is introduced. It differs from prior algorithms by completing the graph and setting the unspecified covariances to zero, which facilitates analytic study. The Quick Simulation Random Field graph distribution is derived within and the following questions are studied: (1) For which marginal pmfs and covariances will this algorithm work? (2) When does the marginal property hold, where the sub-graph distribution of an algorithm-simulated field matches the distribution of the algorithm-simulated field on the subgraph? (3) When does the permutation property hold, where the vertex simulation order does not affect the joint distribution?

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“…In Kouritzin et al (2014), there was the stronger constraint that the right hand side of (2.5) is in [0,1].…”

Section: Remarkmentioning

confidence: 99%

“…(See Kouritzin et al (2014) for examples of choices for these auxiliary pmfs.) They also appear in the conditional probability update through functions:…”

Section: Conditional Probability Updatementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Flexible, Real-Time Algorithm for Simulating Correlated Random Fields and Its Properties

Kouritzin¹,

Newton²,

Wu³

2017

Journal of Mathematics and Statistics

Self Cite

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Performance evaluation of a petrol station queuing system: A simulation-based design of experiments study

Galankashi

Fallahiarezoudar

Moazzami

et al. 2016

Advances in Engineering Software

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VIX-linked fees for GMWBs via explicit solution simulation methods

Kouritzin

MacKay

2018

Insurance: Mathematics and Economics

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In a market with stochastic volatility and jumps, we consider a VIX-linked fee structure (see Cui et al. (2017)) for variable annuity contracts with guaranteed minimum withdrawal benefits (GMWB). Our goal is to assess the effectiveness of the VIXlinked fee structure in decreasing the sensitivity of the insurer's liability to volatility risk. Since the GMWB payoff is highly path-dependent, it is particularly sensitive to volatility risk, and can also be challenging to price, especially in the presence of the VIX-linked fee. In this paper, following Kouritzin (2018), we present an explicit weak solution for the value of the VA account and use it in Monte Carlo simulations to value the GMWB guarantee. Numerical examples are provided to analyze the impact of the VIX-linked fee on the sensitivity of the liability to changes in market volatility.

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A graph theoretic approach to simulation and classification

Cited by 5 publications

References 11 publications

A Flexible, Real-Time Algorithm for Simulating Correlated Random Fields and Its Properties

A Flexible, Real-Time Algorithm for Simulating Correlated Random Fields and Its Properties

Performance evaluation of a petrol station queuing system: A simulation-based design of experiments study

VIX-linked fees for GMWBs via explicit solution simulation methods

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