scholarly journals Rates of convergence for random forests via generalized U-statistics

2022 ◽  
Vol 16 (1) ◽  
Author(s):  
Wei Peng ◽  
Tim Coleman ◽  
Lucas Mentch
1980 ◽  
Vol 21 (1) ◽  
pp. 1-5 ◽  
Author(s):  
N.C. Weber

Let Un be a U-statistic whose kernel depends on the size n of the sample under consideration. It is shown that when Un is suitably normalised its distribution function differs in Lp norm from the distribution function of a standard normal variable by a term of O(n-½).


Author(s):  
P. N. Kokic ◽  
N. C. Weber

AbstractLet UNn be a U-statistic based on a simple random sample of size n selected without replacement from a finite population of size N. Rates of convergence results in the strong law are obtained for UNn, which are similar to those known for classical U-statistics based on samples of independent and identically distributed (iid) random variables.


2019 ◽  
Author(s):  
Oskar Flygare ◽  
Jesper Enander ◽  
Erik Andersson ◽  
Brjánn Ljótsson ◽  
Volen Z Ivanov ◽  
...  

**Background:** Previous attempts to identify predictors of treatment outcomes in body dysmorphic disorder (BDD) have yielded inconsistent findings. One way to increase precision and clinical utility could be to use machine learning methods, which can incorporate multiple non-linear associations in prediction models. **Methods:** This study used a random forests machine learning approach to test if it is possible to reliably predict remission from BDD in a sample of 88 individuals that had received internet-delivered cognitive behavioral therapy for BDD. The random forest models were compared to traditional logistic regression analyses. **Results:** Random forests correctly identified 78% of participants as remitters or non-remitters at post-treatment. The accuracy of prediction was lower in subsequent follow-ups (68%, 66% and 61% correctly classified at 3-, 12- and 24-month follow-ups, respectively). Depressive symptoms, treatment credibility, working alliance, and initial severity of BDD were among the most important predictors at the beginning of treatment. By contrast, the logistic regression models did not identify consistent and strong predictors of remission from BDD. **Conclusions:** The results provide initial support for the clinical utility of machine learning approaches in the prediction of outcomes of patients with BDD. **Trial registration:** ClinicalTrials.gov ID: NCT02010619.


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