On the consistency of a random forest algorithm in the presence of missing entries

This paper tackles the problem of constructing a non-parametric predictor when the latent variables are given with incomplete information. The convenient predictor for this task is the random forest algorithm in conjunction to the so called CART criterion. The proposed technique enables a partial imputation of the missing values in the data set in a way that suits both a consistent estimation of the regression function as well as a probabilistic recovery of the missing values. A proof of the consistency of the random forest estimator that also simplifies the previous proofs of the classical consistency is given in the case where each latent variable is missing completely at random (MCAR)

Income, education, and other poverty-related variables: a journey through Bayesian hierarchical models

One-shirt-size policy cannot handle poverty issues well since each area has its unique challenges, while having a custom-made policy for each area separately is unrealistic due to limitation of resources as well as having issues of ignoring dependencies of characteristics between different areas. In this work, we propose to use Bayesian hierarchical models which can potentially explain the data regarding income and other poverty-related variables in the multi-resolution governing structural data of Thailand. We discuss the journey of how we design each model from simple to more complex ones, estimate their performance in terms of variable explanation and complexity, discuss models' drawbacks, as well as propose the solutions to fix issues in the lens of Bayesian hierarchical models in order to get insight from data. We found that Bayesian hierarchical models performed better than both complete pooling (single policy) and no pooling models (custom-made policy). Additionally, by adding the year-of-education variable, the hierarchical model enriches its performance of variable explanation. We found that having a higher education level increases significantly the households' income for all the regions in Thailand. The impact of the region in the households' income is almost vanished when education level or years of education are considered. Therefore, education might have a mediation role between regions and the income. Our work can serve as a guideline for other countries that require the Bayesian hierarchical approach to model their variables and get insight from data

CyberKnife Robotic-Assisted Stereotactic Radiosurgery for Advanced Stages of Ciliochoroidal Uveal Melanoma. Preliminary Results in Mexico

Objective: The objective of this study was to report the early results of CyberKnife® (CK®) stereotactic radiosurgery in advanced stages of ciliochoroidal (CBCh) melanoma in Mexican patients. Methods: A retrospective review of charts was performed to analyze the outcomes of patients who underwent CK® (Accuray Inc, Sunnyvale, CA, United States). Results: Four patients with CBCh melanoma were treated under this protocol. The mean age was 53.2 ± 5.3 years (range, 47-60). Median of follow-up was 9.5 ± 3.1 months (range, 5-12). Mean tumor diameter was 13.49 mm, mean thickness, 11.74 mm, and mean gross tumor volume was 1251.97 mm3. Tumors were dome- (50%) and mushroom-shaped (50%) in medium-to-large sizes. Three patients had T3b tumors, and one had a T4d tumor at the early tumor staging according to the American Joint Committee on Cancer. A mean dose of 2763 ± 181.3 cGy was prescribed to the 90% isodose line. All patients achieved local tumor control after single-session radiosurgery at the latest follow-up. One patient presented with acute toxicity (extensive serous retinal detachment associated with radiation induced tumor vasculopathy) that was promptly managed. None of the patients required secondary enucleation. Conclusions: CK® appears to be an effective therapy for medium to large-sized CBCh melanoma. A prospective comparative study with longer follow-up is needed to confirm these findings and to evaluate long-term morbidity