ترغب بنشر مسار تعليمي؟ اضغط هنا

Broadcasted Nonparametric Tensor Regression

83   0   0.0 ( 0 )
 نشر من قبل Kejun He
 تاريخ النشر 2020
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

We propose a novel broadcasting idea to model the nonlinearity in tensor regression non-parametrically. Unlike existing non-parametric tensor regression models, the resulting model strikes a good balance between flexibility and interpretability. A penalized estimation and corresponding algorithm are proposed. Our theoretical investigation, which allows the dimensions of the tensor covariate to diverge, indicates that the proposed estimation enjoys a desirable convergence rate. We also provide a minimax lower bound, which characterizes the optimality of the proposed estimator in a wide range of scenarios. Numerical experiments are conducted to confirm the theoretical finding and show that the proposed model has advantages over existing linear counterparts.



قيم البحث

اقرأ أيضاً

In many applications there is interest in estimating the relation between a predictor and an outcome when the relation is known to be monotone or otherwise constrained due to the physical processes involved. We consider one such application--inferrin g time-resolved aerosol concentration from a low-cost differential pressure sensor. The objective is to estimate a monotone function and make inference on the scaled first derivative of the function. We proposed Bayesian nonparametric monotone regression which uses a Bernstein polynomial basis to construct the regression function and puts a Dirichlet process prior on the regression coefficients. The base measure of the Dirichlet process is a finite mixture of a mass point at zero and a truncated normal. This construction imposes monotonicity while clustering the basis functions. Clustering the basis functions reduces the parameter space and allows the estimated regression function to be linear. With the proposed approach we can make closed-formed inference on the derivative of the estimated function including full quantification of uncertainty. In a simulation study the proposed method performs similar to other monotone regression approaches when the true function is wavy but performs better when the true function is linear. We apply the method to estimate time-resolved aerosol concentration with a newly-developed portable aerosol monitor. The R package bnmr is made available to implement the method.
A simple Bayesian approach to nonparametric regression is described using fuzzy sets and membership functions. Membership functions are interpreted as likelihood functions for the unknown regression function, so that with the help of a reference prio r they can be transformed to prior density functions. The unknown regression function is decomposed into wavelets and a hierarchical Bayesian approach is employed for making inferences on the resulting wavelet coefficients.
One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We propose a Gaussi an process regression methodology that acts as a Bayesian analog to LLR for regression discontinuity designs. Our methodology provides a flexible fit for treatment and control responses by placing a general prior on the mean response functions. Furthermore, unlike LLR, our methodology can incorporate uncertainty in how units are weighted when estimating the treatment effect. We prove our method is consistent in estimating the average treatment effect at the threshold. Furthermore, we find via simulation that our method exhibits promising coverage, interval length, and mean squared error properties compared to standard LLR and state-of-the-art LLR methodologies. Finally, we explore the performance of our method on a real-world example by studying the impact of being a first-round draft pick on the performance and playing time of basketball players in the National Basketball Association.
Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are derived from models composed by an unknown function with additive gaussian noise. Although gaussian noise assumption is reasonable in several real data analysis, mainly for large sample sizes, it is not general. Contaminated data with positive noise can occur in practice and nonparametric regression models with positive noise bring challenges in wavelet shrinkage point of view. This work develops bayesian shrinkage rules to estimate wavelet coefficients from a nonparametric regression framework with additive and strictly positive noise under exponential and lognormal distributions. Computational aspects are discussed and simulation studies to analyse the performances of the proposed shrinkage rules and compare them with standard techniques are done. An application in winning times Boston Marathon dataset is also provided.
Many time-to-event studies are complicated by the presence of competing risks. Such data are often analyzed using Cox models for the cause specific hazard function or Fine-Gray models for the subdistribution hazard. In practice regression relationshi ps in competing risks data with either strategy are often complex and may include nonlinear functions of covariates, interactions, high-dimensional parameter spaces and nonproportional cause specific or subdistribution hazards. Model misspecification can lead to poor predictive performance. To address these issues, we propose a novel approach to flexible prediction modeling of competing risks data using Bayesian Additive Regression Trees (BART). We study the simulation performance in two-sample scenarios as well as a complex regression setting, and benchmark its performance against standard regression techniques as well as random survival forests. We illustrate the use of the proposed method on a recently published study of patients undergoing hematopoietic stem cell transplantation.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا