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Hybrid Monte Carlo Methods in Machine Learning : = Stochastic Volatility Methods, Shadow Hamiltonians, Adaptive Approaches and Variance Reduction Techniques.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Hybrid Monte Carlo Methods in Machine Learning :/
其他題名:	Stochastic Volatility Methods, Shadow Hamiltonians, Adaptive Approaches and Variance Reduction Techniques.
作者:	Mongwe, Wilson Tsakane.
面頁冊數:	1 online resource (193 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
Contained By:	Dissertations Abstracts International84-04B.
標題:	Sample size. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29356236click for full text (PQDT)
ISBN:	9798351497891

Hybrid Monte Carlo Methods in Machine Learning : = Stochastic Volatility Methods, Shadow Hamiltonians, Adaptive Approaches and Variance Reduction Techniques.
Mongwe, Wilson Tsakane.

Hybrid Monte Carlo Methods in Machine Learning :Stochastic Volatility Methods, Shadow Hamiltonians, Adaptive Approaches and Variance Reduction Techniques. - 1 online resource (193 pages)

Source: Dissertations Abstracts International, Volume: 84-04, Section: B.

Thesis (Ph.D.)--University of Johannesburg (South Africa), 2022.

Includes bibliographical references

Markov Chain Monte Carlo (MCMC) methods are a vital inference tool for probabilistic machine learning models. A commonly utilised MCMC algorithm is the Hamiltonian Monte Carlo (HMC) method. HMC can efficiently ex plore th e ta rget po sterior by taking into account first-order g radient i nformation. T his a lgorithm h as b een extended in various ways, including via the use of non-canonical Hamiltonian dynamics to create Magnetic Hamiltonian Monte Carlo (MHMC) and utilising integrator-dependent shadow Hamiltonians to create shadow HMC methods. MHMC utilises a magnetic field to more efficiently ex plore th e ta rget po sterior co mpared to HM C. At th e sa me ti me, shadow HMC methods can better scale to larger models without significant deterioration in the acceptance rates of the generated samples.In this thesis, we present novel extensions to the MHMC algorithm by 1) using a random mass for the auxiliary momentum variable to mimic the behavior of quantum particles, 2) utilising partial momentum refreshment before generating the next sample, and 3) deriving the fourth-order modified Hamiltonian implied by the numerical integrator employed in MHMC to construct the novel shadow MHMC algorithm. The results reveal that these novel extensions to MHMC lead to enhanced sampling performance over MHMC across various targets and performance metrics.We proceed to improve the sampling performance of Separable Shadow Hamiltonian Hybrid Monte Carlo (S2HMC) by using partial momentum refreshment before generating the next sample using the processed leapfrog integrator used in S2HMC. We further address the automatic tuning of the step size and trajectory length parameters of S2HMC by extending the No-U-Turn Sampler methodology to incorporate the processed leapfrog integrator. The automatic adaptation removes the need to manually tune these parameters and thus makes this method more accessible to non-expert users. The results show that this adaptive algorithm outperforms S2HMC on an effective sample size basis with minimal user intervention.We further rely on results from the coupling theory of Hamiltonian chains to show that employing antithetic sampling in the MHMC and S2HMC algorithms produces lower variances and consequently higher effective sample sizes compared to the nonantithetic versions of these MCMC methods. The results show the overall benefits that can be derived from incorporating antithetic sampling in MCMC algorithms. Given that antithetic sampling makes minimal assumptions about the target posterior and is straightforward to implement, there seem to be minor hurdles to using it in practice.The analysis in this thesis is performed on the Banana shaped distribution, the Merton jump-diffusion process calibrated to financial market data, multivariate Gaussian distributions of various dimensions, Neal's funnel density, Bayesian Logistic Regression, and Bayesian Neural Network benchmark problems as well as on South African municipal financial statement audit outcome data. To analyse the audit outcomes dataset, we employ a first-in-literature Bayesian inference approach that incorporates automatic relevance determination to identify important financial ratios in modeling audit outcomes. We find that repairs and maintenance as a percentage of total assets ratio, current ratio, debt to total operating revenue, net operating surplus margin and capital cost to total operating expenditure ratio are the important financial ratios when predicting local government audit outcomes. These results could be useful for various stakeholders to better understand the financial state of South African local government entities. Auditors could use them to improve the speed and overall quality of the audit process.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798351497891Subjects--Topical Terms:

3642155
Sample size.
Index Terms--Genre/Form:

542853
Electronic books.

Hybrid Monte Carlo Methods in Machine Learning : = Stochastic Volatility Methods, Shadow Hamiltonians, Adaptive Approaches and Variance Reduction Techniques.
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502 $a Thesis (Ph.D.)--University of Johannesburg (South Africa), 2022.
504 $a Includes bibliographical references
520 $a Markov Chain Monte Carlo (MCMC) methods are a vital inference tool for probabilistic machine learning models. A commonly utilised MCMC algorithm is the Hamiltonian Monte Carlo (HMC) method. HMC can efficiently ex plore th e ta rget po sterior by taking into account first-order g radient i nformation. T his a lgorithm h as b een extended in various ways, including via the use of non-canonical Hamiltonian dynamics to create Magnetic Hamiltonian Monte Carlo (MHMC) and utilising integrator-dependent shadow Hamiltonians to create shadow HMC methods. MHMC utilises a magnetic field to more efficiently ex plore th e ta rget po sterior co mpared to HM C. At th e sa me ti me, shadow HMC methods can better scale to larger models without significant deterioration in the acceptance rates of the generated samples.In this thesis, we present novel extensions to the MHMC algorithm by 1) using a random mass for the auxiliary momentum variable to mimic the behavior of quantum particles, 2) utilising partial momentum refreshment before generating the next sample, and 3) deriving the fourth-order modified Hamiltonian implied by the numerical integrator employed in MHMC to construct the novel shadow MHMC algorithm. The results reveal that these novel extensions to MHMC lead to enhanced sampling performance over MHMC across various targets and performance metrics.We proceed to improve the sampling performance of Separable Shadow Hamiltonian Hybrid Monte Carlo (S2HMC) by using partial momentum refreshment before generating the next sample using the processed leapfrog integrator used in S2HMC. We further address the automatic tuning of the step size and trajectory length parameters of S2HMC by extending the No-U-Turn Sampler methodology to incorporate the processed leapfrog integrator. The automatic adaptation removes the need to manually tune these parameters and thus makes this method more accessible to non-expert users. The results show that this adaptive algorithm outperforms S2HMC on an effective sample size basis with minimal user intervention.We further rely on results from the coupling theory of Hamiltonian chains to show that employing antithetic sampling in the MHMC and S2HMC algorithms produces lower variances and consequently higher effective sample sizes compared to the nonantithetic versions of these MCMC methods. The results show the overall benefits that can be derived from incorporating antithetic sampling in MCMC algorithms. Given that antithetic sampling makes minimal assumptions about the target posterior and is straightforward to implement, there seem to be minor hurdles to using it in practice.The analysis in this thesis is performed on the Banana shaped distribution, the Merton jump-diffusion process calibrated to financial market data, multivariate Gaussian distributions of various dimensions, Neal's funnel density, Bayesian Logistic Regression, and Bayesian Neural Network benchmark problems as well as on South African municipal financial statement audit outcome data. To analyse the audit outcomes dataset, we employ a first-in-literature Bayesian inference approach that incorporates automatic relevance determination to identify important financial ratios in modeling audit outcomes. We find that repairs and maintenance as a percentage of total assets ratio, current ratio, debt to total operating revenue, net operating surplus margin and capital cost to total operating expenditure ratio are the important financial ratios when predicting local government audit outcomes. These results could be useful for various stakeholders to better understand the financial state of South African local government entities. Auditors could use them to improve the speed and overall quality of the audit process.
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538 $a Mode of access: World Wide Web
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650 4 $a Algorithms. $3 536374
650 4 $a Neural networks. $3 677449
650 4 $a Markov analysis. $3 3562906
650 4 $a Computer science. $3 523869
650 4 $a Finance. $3 542899
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710 2 $a University of Johannesburg (South Africa). $3 3555351
773 0 $t Dissertations Abstracts International $g 84-04B.
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