scholarly journals Bayesian Optimization for Parameter of Discrete Weibull Regression

2020 ◽  
pp. 1-13
Author(s):  
Adesina, Olumide Sunday ◽  
Onanaye, Adeniyi Samson ◽  
Okewole, Dorcas Modupe
Keyword(s):  
Count Data ◽  
Optimization Problem ◽  
Likelihood Function ◽  
Bayesian Optimization ◽  
Confidence Bound ◽  
Mcmc Algorithm ◽  
Weibull Regression ◽  
Weibull Regression Model ◽  
Upper Confidence Bound ◽  
Probability Of Improvement

This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem. The choice of Discrete Weibull regression model among other models for fitting count data is due to its robustness in fitting count data. Count data of hypertensive patients visits to the doctor was obtained at Medicare Clinics Ota, Nigeria, and was used for the analysis. First, parameter θ  and β  were obtained using Metropolis Hasting Monte Carlo Markov Chain (MCMC) algorithm. Then Bayesian optimization was used to optimize the parameter the likelihood function of DW regression, given β to examine what θ would be, and making the likelihood function of DW the objective function. Upper confidence bound (UCB), Expectation of Improvement (EI), and probability of Improvement (PI) were used as acquisition functions. Results showed that fitting Bayesian DW regression to the data, there is significant relationship between the response variable, β and the covariate. On implementing Bayesian optimization to obtain parameter new parameter θ of discrete Weibull regression using the known β, the results showed promising applicability of the technique to the model, and found that EI fits the data better relative to PI and UCB in terms of accuracy and speed.

scholarly journals Bayesian Optimization using Pseudo-Points

2020 ◽  
Author(s):  
Chao Qian ◽  
Hang Xiong ◽  
Ke Xue
Keyword(s):  
Parameter Tuning ◽  
Black Box ◽  
Bayesian Optimization ◽  
Confidence Bound ◽  
Data Points ◽  
Upper Confidence Bound ◽  
Gp Model ◽  
Probability Of Improvement ◽  
And Robotics ◽  
Real World Problems

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, and robotics. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing an acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove that the cumulative regret can be generally upper bounded. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.

scholarly journals Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong
Keyword(s):  
Gaussian Process ◽  
Black Box ◽  
Bayesian Optimization ◽  
Query Point ◽  
Confidence Bound ◽  
Bayesian Optimization Algorithm ◽  
Machine Learning Model ◽  
Step Algorithm ◽  
Upper Confidence Bound ◽  
General Method

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

scholarly journals Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong
Keyword(s):  
Gaussian Process ◽  
Black Box ◽  
Bayesian Optimization ◽  
Query Point ◽  
Confidence Bound ◽  
Bayesian Optimization Algorithm ◽  
Machine Learning Model ◽  
Step Algorithm ◽  
Upper Confidence Bound ◽  
General Method

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

scholarly journals Improved Gaussian Process Acquisition for Targeted Bayesian Optimization

2021 ◽  
pp. 12-18
Author(s):  
Peter Mitic ◽  
Keyword(s):  
Gaussian Process ◽  
Optimization Problem ◽  
Bayesian Optimization ◽  
Stochastic Algorithm ◽  
Confidence Bound ◽  
Noise Component ◽  
Simple Modification ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
Long Time

A black-box optimization problem is considered, in which the function to be optimized can only be expressed in terms of a complicated stochastic algorithm that takes a long time to evaluate. The value returned is required to be sufficiently near to a target value, and uses data that has a significant noise component. Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution, and its effectiveness is measured in terms of the number of function evaluations required to attain the target. To improve results, a simple modification of the Gaussian Process ‘Lower Confidence Bound’ (LCB) acquisition function is proposed. The expression used for the confidence bound is squared in order to better comply with the target requirement. With this modification, much improved results compared to random selection methods and to other commonly used acquisition functions are obtained.

scholarly journals Computer Adaptive Testing Using Upper-Confidence Bound Algorithm for Formative Assessment

2019 ◽  
Vol 9 (20) ◽  
pp. 4303 ◽  
Author(s):  
Jaroslav Melesko ◽  
Vitalij Novickij
Keyword(s):  
Formative Assessment ◽  
Latent Trait ◽  
Corrective Feedback ◽  
Strong Support ◽  
Adaptive Testing ◽  
Computer Adaptive Testing ◽  
Confidence Bound ◽  
Question Item ◽  
E Learning ◽  
Upper Confidence Bound

There is strong support for formative assessment inclusion in learning processes, with the main emphasis on corrective feedback for students. However, traditional testing and Computer Adaptive Testing can be problematic to implement in the classroom. Paper based tests are logistically inconvenient and are hard to personalize, and thus must be longer to accurately assess every student in the classroom. Computer Adaptive Testing can mitigate these problems by making use of Multi-Dimensional Item Response Theory at cost of introducing several new problems, most problematic of which are the greater test creation complexity, because of the necessity of question pool calibration, and the debatable premise that different questions measure one common latent trait. In this paper a new approach of modelling formative assessment as a Multi-Armed bandit problem is proposed and solved using Upper-Confidence Bound algorithm. The method in combination with e-learning paradigm has the potential to mitigate such problems as question item calibration and lengthy tests, while providing accurate formative assessment feedback for students. A number of simulation and empirical data experiments (with 104 students) are carried out to explore and measure the potential of this application with positive results.

Identification of Top-K Influencers Based on Upper Confidence Bound and Local Structure

2021 ◽  
pp. 100208
Author(s):  
Mohammed Alshahrani ◽  
Fuxi Zhu ◽  
Soufiana Mekouar ◽  
Mohammed Yahya Alghamdi ◽  
Shichao Liu
Keyword(s):  
Local Structure ◽  
Confidence Bound ◽  
Upper Confidence Bound

scholarly journals Hemodialysis (HD) dose and ultrafiltration rate are associated with survival in pediatric and adolescent patients on chronic HD—a large observational study with follow-up to young adult age

2021 ◽  
Author(s):  
Verena Gotta ◽  
Olivera Marsenic ◽  
Andrew Atkinson ◽  
Marc Pfister
Keyword(s):  
Rank Test ◽  
Primary Analysis ◽  
Ultrafiltration Rate ◽  
Dialysis Dose ◽  
Dialysis Adequacy ◽  
Weibull Regression ◽  
Adult Age ◽  
Kaplan Meier ◽  
Continuous Scale ◽  
Weibull Regression Model

Abstract Background Hemodialysis (HD) dose targets and ultrafiltration rate (UFR) limits for pediatric patients on chronic HD are not known and are derived from adults (spKt/V>1.4 and <13 ml/kg/h). We aimed to characterize how delivered HD dose and UFR are associated with survival in a large cohort of patients who started HD in childhood. Methods Retrospective analysis on a cohort of patients <30 years, on chronic HD since childhood (<19 years), having received thrice-weekly HD 2004–2016 in outpatient DaVita centers. Outcome: Survival while remaining on HD. Predictors: (I) primary analysis: mean delivered dialysis dose stratified as spKt/V ≤1.4/1.4–1.6/>1.6 (Kaplan–Meier analysis), (II) secondary analyses: UFR and alternative dialysis adequacy measures [eKt/V, body-surface normalized Kt/BSA] on continuous scale (Weibull regression model). Results A total of 1780 patients were included (age at the start of HD: 0–12y: n=321, >12–18y: n=1459; median spKt/V=1.55, eKt/V=1.31, Kt/BSA=31.2 L/m2, UFR=10.6 mL/kg/h). (I) spKt/V<1.4 was associated with lower survival compared to spKt/V>1.4–1.6 (P<0.001, log-rank test), and spKt/V>1.6 (P<0.001), with 10-year survival of 69.3% (59.4–80.9%) versus 83.0% (76.8–89.8%) and 84.0% (79.6–88.5%), respectively. (II) Kt/BSA was a better predictor of survival than spKt/V or eKt/V. UFR was additionally associated with survival (P<0.001), with increased mortality <10/>18 mL/kg/h. Associations did not alter significantly following adjustment for demographic characteristics (age, etiology of kidney disease, and ethnicity). Conclusions Our results suggest usefulness of targeting Kt/BSA>30 L/m2 for best long-term outcomes, corresponding to spKt/V>1.4 (>12 years) and >1.6 (<12 years). In contrast to adults, higher UFR of 10–18 ml/kg/h was not associated with greater mortality in this population.

Sustainability Time and Its Determinant Factors of Small and Medium-scale Enterprises in East Gojjam Zone: Parametric Survival Regression Model

2021 ◽  
pp. 097215092098865
Author(s):  
Amare Wubishet Ayele ◽  
Abebaw Bizuayehu Derseh
Keyword(s):  
Regression Model ◽  
Marketing Channel ◽  
Educational Status ◽  
Weibull Regression ◽  
Service Sectors ◽  
Weibull Regression Model ◽  
Parametric Survival ◽  
Prospective Study Design ◽  
Significant Factors ◽  
Survival Regression

The contributions of small and medium-sized enterprises (SMEs) to socio-economic development are generally recognized, but they have faced several obstacles that impede their sustainability. This manuscript seeks to identify factors for the survival of SMEs in the East Gojjam Zone, Ethiopia. The prospective study design was employed. Both descriptive and inferential statistics, particularly families of parametric survival regression models, have been used. Of the 650 enterprises included in this study, 330 (50.8%) were censored (sustained enterprises) and the remaining 320 (49.2%) were events or withdrawn enterprises. The findings of this study revealed that the incidence of termination or withdrawal of SMEs in the study area is relatively common. The results from multivariable Weibull regression model revealed that woreda, sector, manger profile (gender, age, educational status, experience (in year) and source of experience), working place, marketing channel and profitability district status of enterprise were found to be statistically significant factors for the sustainability of enterprises in the study area. The bodies concerned, in particular the enterprise administrative offices at various levels, should work with collaborative organizations to develop a strong marketing platform (network), should be able to make workplaces accessible with the required infrastructure at minimal rental costs, and should prioritize the type of sector that has the highest customer needs at the onset, for instance, agriculture and service sectors.

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