Circular local likelihood

We introduce a class of local likelihood circular density estimators, which includes the kernel density estimator as a special case. The idea lies in optimizing a spatially weighted version of the log-likelihood function, where the logarithm of the density is locally approximated by a periodic polynomial. The use of von Mises density functions as weights reduces the computational burden. Also, we propose closed-form estimators which could form the basis of counterparts in the multidimensional Euclidean setting. Simulation results and a real data case study are used to evaluate the performance and illustrate the results

A note on nonparametric estimation of circular conditional densities

The conditional density offers the most informative summary of the relationship between explanatory and response variables. We need to estimate it in place of the simple conditional mean when its shape is not well-behaved. A motivation for estimating conditional densities, specific to the circular setting, lies in the fact that a natural alternative of it, like quantile regression, could be considered problematic because circular quantiles are not rotationally equivariant. We treat conditional density estimation as a local polynomial fitting problem as proposed by \cite{Fan et al.:1996} in the euclidean setting, and discuss a class of estimators in the cases when the conditioning variable is either circular or linear. Asymptotic properties for some members of the proposed class are derived. The effectiveness of the methods for finite sample sizes is illustrated by simulation experiments and an example using real data

Nonparametric estimating equations for circular probability density functions and their derivatives

We propose estimating equations whose unknown parameters are the values taken by a circular density and its derivatives at a point. Specifically, we solve equations which relate local versions of population trigonometric moments with their sample counterparts. Major advantages of our approach are: higher order bias without asymptotic variance inflation, closed form for the estimators, and absence of numerical tasks. We also investigate situations where the observed data are dependent. Theoretical results along with simulation experiments are provided

Large Language Models for Integrating Social Determinant of Health Data: A Case Study on Heart Failure 30-Day Readmission Prediction

Social determinants of health (SDOH) $-$ the myriad of circumstances in which people live, grow, and age $-$ play an important role in health outcomes. However, existing outcome prediction models often only use proxies of SDOH as features. Recent open data initiatives present an opportunity to construct a more comprehensive view of SDOH, but manually integrating the most relevant data for individual patients becomes increasingly challenging as the volume and diversity of public SDOH data grows. Large language models (LLMs) have shown promise at automatically annotating structured data. Here, we conduct an end-to-end case study evaluating the feasibility of using LLMs to integrate SDOH data, and the utility of these SDOH features for clinical prediction. We first manually label 700+ variables from two publicly-accessible SDOH data sources to one of five semantic SDOH categories. Then, we benchmark performance of 9 open-source LLMs on this classification task. Finally, we train ML models to predict 30-day hospital readmission among 39k heart failure (HF) patients, and we compare the prediction performance of the categorized SDOH variables with standard clinical variables. Additionally, we investigate the impact of few-shot LLM prompting on LLM annotation performance, and perform a metadata ablation study on prompts to evaluate which information helps LLMs accurately annotate these variables. We find that some open-source LLMs can effectively, accurately annotate SDOH variables with zero-shot prompting without the need for fine-tuning. Crucially, when combined with standard clinical features, the LLM-annotated Neighborhood and Built Environment subset of the SDOH variables shows the best performance predicting 30-day readmission of HF patients.Comment: 36 pages including references and appendix. This is a work in progres

Kernel regression for errors-in-variables problems in the circular domain

We study the problem of estimating a regression function when the predictor and/or the response are circular random variables in the presence of measurement errors. We propose estimators whose weight functions are deconvolution kernels defined according to the nature of the involved variables. We derive the asymptotic properties of the proposed estimators and consider possible generalizations and extensions. We provide some simulation results and a real data case study to illustrate and compare the proposed methods

Local binary regression with spherical predictors

We discuss local regression estimators when the predictor lies on the -dimensional sphere and the response is binary. Despite Di Marzio et al. (2018b), who introduce spherical kernel density classification, we build on the theory of local polynomial regression and local likelihood. Simulations and a real-data application illustrate the effectiveness of the proposals

Density estimation for circular data observed with errors

Until now the problem of estimating circular densities when data are observed with errors has been mainly treated by Fourier series methods. We propose kernel‐based estimators exhibiting simple construction and easy implementation. Specifically, we consider three different approaches: the first one is based on the equivalence between kernel estimators using data corrupted with different levels of error. This proposal appears to be totally unexplored, despite its potential for application also in the Euclidean setting. The second approach relies on estimators whose weight functions are circular deconvolution kernels. Due to the periodicity of the involved densities, it requires ad hoc mathematical tools. Finally, the third one is based on the idea of correcting extra bias of kernel estimators which use contaminated data and is essentially an adaptation of the standard theory to the circular case. For all the proposed estimators we derive asymptotic properties, provide some simulation results, and also discuss some possible generalizations and extensions. Real data case studies are also included