Deep Partially Linear Transformation Model for Right-Censored Survival Data

• URL: http://arxiv.org/abs/2412.07611v1
• Date: Tue, 10 Dec 2024 15:50:43 GMT
• Title: Deep Partially Linear Transformation Model for Right-Censored Survival Data
• Authors: Junkai Yin, Yue Zhang, Zhangsheng Yu,
• Abstract summary: This paper introduces a deep partially linear transformation model (DPLTM) as a general and flexible framework for estimation, inference and prediction. Comprehensive simulation studies demonstrate the impressive performance of the proposed estimation procedure in terms of both estimation accuracy and prediction power.
• Score: 9.991327369572819
• License:
• Abstract: Although the Cox proportional hazards model is well established and extensively used in the analysis of survival data, the proportional hazards (PH) assumption may not always hold in practical scenarios. The semiparametric transformation model extends the conventional Cox model and also includes many other survival models as special cases. This paper introduces a deep partially linear transformation model (DPLTM) as a general and flexible framework for estimation, inference and prediction. The proposed method is capable of avoiding the curse of dimensionality while still retaining the interpretability of some covariates of interest. We derive the overall convergence rate of the maximum likelihood estimators, the minimax lower bound of the nonparametric deep neural network (DNN) estimator, the asymptotic normality and the semiparametric efficiency of the parametric estimator. Comprehensive simulation studies demonstrate the impressive performance of the proposed estimation procedure in terms of both estimation accuracy and prediction power, which is further validated by an application to a real-world dataset.

Related papers

• Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions [22.765095010254118]
  The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques.
  arXiv  Detail & Related papers  (2024-07-31T19:45:27Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Deep Neural Networks for Semiparametric Frailty Models via H-likelihood [0.0]
  We propose a new deep neural network based frailty (DNN-FM) for prediction of time-to-event data. Joint estimators of the new h-likelihood model provide maximum likelihood for fixed parameters and best unbiased predictors for random frailties.
  arXiv  Detail & Related papers  (2023-07-13T06:46:51Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Information Theoretic Structured Generative Modeling [13.117829542251188]
  A novel generative model framework called the structured generative model (SGM) is proposed that makes straightforward optimization possible. The implementation employs a single neural network driven by an orthonormal input to a single white noise source adapted to learn an infinite Gaussian mixture model. Preliminary results show that SGM significantly improves MINE estimation in terms of data efficiency and variance, conventional and variational Gaussian mixture models, as well as for training adversarial networks.
  arXiv  Detail & Related papers  (2021-10-12T07:44:18Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Distributionally Robust Parametric Maximum Likelihood Estimation [13.09499764232737]
  We propose a distributionally robust maximum likelihood estimator that minimizes the worst-case expected log-loss uniformly over a parametric nominal distribution. Our novel robust estimator also enjoys statistical consistency and delivers promising empirical results in both regression and classification tasks.
  arXiv  Detail & Related papers  (2020-10-11T19:05:49Z)
• Machine learning for causal inference: on the use of cross-fit estimators [77.34726150561087]
  Doubly-robust cross-fit estimators have been proposed to yield better statistical properties. We conducted a simulation study to assess the performance of several estimators for the average causal effect (ACE) When used with machine learning, the doubly-robust cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage.
  arXiv  Detail & Related papers  (2020-04-21T23:09:55Z)
• Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions [10.319367855067476]
  This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless dataset. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model.
  arXiv  Detail & Related papers  (2020-01-29T17:20:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.