Bayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function

Kiapour, Azadeh

doi:10.29252/jirss.17.1.33

Cited by 14 publications

(5 citation statements)

References 17 publications

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“…The AUC of a classifier is equivalent to the likelihood that the classifier will rank a randomly selected positive value higher than a randomly selected negative value [ 26 ]. Log loss is also essentially used as a metric for classification; it is calculated by the probability of actual and predicted classes [ 27 ]. Log loss is among the most useful evaluation metrics.…”

Section: Methodsmentioning

confidence: 99%

Machine Learning Approach to Predicting COVID-19 Disease Severity Based on Clinical Blood Test Data: Statistical Analysis and Model Development

Aktar¹,

Ahamad²,

Rashed-Al-Mahfuz³

et al. 2021

JMIR Med Inform

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Background Accurate prediction of the disease severity of patients with COVID-19 would greatly improve care delivery and resource allocation and thereby reduce mortality risks, especially in less developed countries. Many patient-related factors, such as pre-existing comorbidities, affect disease severity and can be used to aid this prediction. Objective Because rapid automated profiling of peripheral blood samples is widely available, we aimed to investigate how data from the peripheral blood of patients with COVID-19 can be used to predict clinical outcomes. Methods We investigated clinical data sets of patients with COVID-19 with known outcomes by combining statistical comparison and correlation methods with machine learning algorithms; the latter included decision tree, random forest, variants of gradient boosting machine, support vector machine, k-nearest neighbor, and deep learning methods. Results Our work revealed that several clinical parameters that are measurable in blood samples are factors that can discriminate between healthy people and COVID-19–positive patients, and we showed the value of these parameters in predicting later severity of COVID-19 symptoms. We developed a number of analytical methods that showed accuracy and precision scores >90% for disease severity prediction. Conclusions We developed methodologies to analyze routine patient clinical data that enable more accurate prediction of COVID-19 patient outcomes. With this approach, data from standard hospital laboratory analyses of patient blood could be used to identify patients with COVID-19 who are at high risk of mortality, thus enabling optimization of hospital facilities for COVID-19 treatment.

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Section: Methodsmentioning

confidence: 99%

Machine Learning Approach to Predicting COVID-19 Disease Severity Based on Clinical Blood Test Data: Statistical Analysis and Model Development

Aktar¹,

Ahamad²,

Rashed-Al-Mahfuz³

et al. 2021

JMIR Med Inform

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show abstract

“…Three attributes of the three loss functions (MSE, LogSE, and MSLE) are studied and compared in Table 2. The mean squared logarithmic error (MSLE) [Kiapour 2018, Brown 1968] is defined as the mean over the squared differences between the logarithm of real and estimated values. Actually, it measures the ratio between the true and predicted values.…”

Section: Methodsmentioning

confidence: 99%

LogSE: An Uncertainty-Based Multi-Task Loss Function for Learning Two Regression Tasks

Ghasemi-Naraghi¹,

Nickabadi²,

Safabakhsh³

2022

jucs

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Multi-task learning (MTL) is a popular method in machine learning which utilizes related information of multi tasks to learn a task more efficiently and accurately. Naively, one can benefit from MTL by using a weighted linear sum of the different tasks loss functions. Manual specification of appropriate weights is difficult and typically does not improve performance, so it is critical to find an automatic weighting strategy for MTL. Also, there are three types of uncertainties that are captured in deep learning. Epistemic uncertainty is related to the lack of data. Heteroscedas- tic aleatoric uncertainty depends on the input data and differs from one input to another. In this paper, we focus on the third type, homoscedastic aleatoric uncertainty, which is constant for differ- ent inputs and is task-dependent. There are some methods for learning uncertainty-based weights as the parameters of a model. But in this paper, we introduce a novel multi-task loss function to capture homoscedastic uncertainty in multi regression tasks models, without increasing the complexity of the network. As the experiments show, the proposed loss function aids in learning a multi regression tasks network fairly with higher accuracy in fewer training steps.

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“…Considering that the prior information may be deficient, the E-Bayesian method could be used to settle the uncertainty by introducing a class of priors. The authors in [14] demonstrated that, based on a specified prior distribution, the purpose of the E-Bayesian method is to estimate unknown parameters or to predict values of a sequence of random variables.…”

Section: E-bayesian Estimationmentioning

confidence: 99%

Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Zhang

Liu

Gui

2021

Entropy

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For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

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Bayes, E-Bayes and Robust Bayes Premium Estimation and Prediction under the Squared Log Error Loss Function

Cited by 14 publications

References 17 publications

Machine Learning Approach to Predicting COVID-19 Disease Severity Based on Clinical Blood Test Data: Statistical Analysis and Model Development

Machine Learning Approach to Predicting COVID-19 Disease Severity Based on Clinical Blood Test Data: Statistical Analysis and Model Development

LogSE: An Uncertainty-Based Multi-Task Loss Function for Learning Two Regression Tasks

Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

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