اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCox Point Process Regression
82
0
0.0
(
0
)
نشر من قبل
\\'Alvaro Eduardo Gajardo Cataldo
تاريخ النشر
2020
مجال البحث
الاحصاء الرياضي
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly encountered. A key object of interest is the local intensity function. It has a straightforward interpretation that allows to understand and explore point process data. We consider functional approaches for point processes, where one has a sample of repeated realizations of the point process. This situation is inherently connected with Cox processes, where the intensity functions of the replications are modeled as random functions. Here we study a situation where one records covariates for each replication of the process, such as the daily temperature for bike rentals. For modeling point processes as responses with vector covariates as predictors we propose a novel regression approach for the intensity function that is intrinsically nonparametric. While the intensity function of a point process that is only observed once on a fixed domain cannot be identified, we show how covariates and repeated observations of the process can be utilized to make consistent estimation possible, and we also derive asymptotic rates of convergence without invoking parametric assumptions.
قيم البحث
اقرأ أيضاً
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is
shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation of the change-point. A new model-based bootstrap approach is proposed and its consistency established. Simulation studies are carried out to assess the performance of various bootstrap schemes.
Gaussian process regression (GPR) model has been widely used to fit data when the regression function is unknown and its nice properties have been well established. In this article, we introduce an extended t-process regression (eTPR) model, which gi
ves a robust best linear unbiased predictor (BLUP). Owing to its succinct construction, it inherits many attractive properties from the GPR model, such as having closed forms of marginal and predictive distributions to give an explicit form for robust BLUP procedures, and easy to cope with large dimensional covariates with an efficient implementation by slightly modifying existing BLUP procedures. Properties of the robust BLUP are studied. Simulation studies and real data applications show that the eTPR model gives a robust fit in the presence of outliers in both input and output spaces and has a good performance in prediction, compared with the GPR and locally weighted scatterplot smoothing (LOESS) methods.
Recently the shape-restricted inference has gained popularity in statistical and econometric literature in order to relax the linear or quadratic covariate effect in regression analyses. The typical shape-restricted covariate effect includes monotoni
c increasing, decreasing, convexity or concavity. In this paper, we introduce the shape-restricted inference to the celebrated Cox regression model (SR-Cox), in which the covariate response is modeled as shape-restricted additive functions. The SR-Cox regression approximates the shape-restricted functions using a spline basis expansion with data driven choice of knots. The underlying minimization of negative log-likelihood function is formulated as a convex optimization problem, which is solved with an active-set optimization algorithm. The highlight of this algorithm is that it eliminates the superfluous knots automatically. When covariate effects include combinations of convex or concave terms with unknown forms and linear terms, the most interesting finding is that SR-Cox produces accurate linear covariate effect estimates which are comparable to the maximum partial likelihood estimates if indeed the forms are known. We conclude that concave or convex SR-Cox models could significantly improve nonlinear covariate response recovery and model goodness of fit.
Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical appli
cations, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an approximation to the Expectation Maximization algorithm for this model that does hard assignments to mixture groups to make optimization efficient. In each group assignment, we fit the hazard ratios within each group using deep neural networks, and the baseline hazard for each mixture component non-parametrically. We perform experiments on multiple real world datasets, and look at the mortality rates of patients across ethnicity and gender. We emphasize the importance of calibration in healthcare settings and demonstrate that our approach outperforms classical and modern survival analysis baselines, both in terms of discriminative performance and calibration, with large gains in performance on the minority demographics.
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in that data f
ollow different continuous regression models for different regions of the data with possible discontinuities between the regions. However, many conventional GP regression approaches are not designed for piecewise regression analysis. We propose a new GP modeling approach for estimating an unknown piecewise continuous regression function. The new GP model seeks for a local GP estimate of an unknown regression function at each test location, using local data neighboring to the test location. To accommodate the possibilities of the local data from different regions, the local data is partitioned into two sides by a local linear boundary, and only the local data belonging to the same side as the test location is used for the regression estimate. This local split works very well when the input regions are bounded by smooth boundaries, so the local linear approximation of the smooth boundaries works well. We estimate the local linear boundary jointly with the other hyperparameters of the GP model, using the maximum likelihood approach. Its computation time is as low as the local GPs time. The superior numerical performance of the proposed approach over the conventional GP modeling approaches is shown using various simulated piecewise regression functions.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
