Analysis of overfitting in the regularized Cox model

by   M Sheikh, et al.
King's College London

The Cox proportional hazards model is ubiquitous in the analysis of time-to-event data. However, when the data dimension p is comparable to the sample size N, maximum likelihood estimates for its regression parameters are known to be biased or break down entirely due to overfitting. This prompted the introduction of the so-called regularized Cox model. In this paper we use the replica method from statistical physics to investigate the relationship between the true and inferred regression parameters in regularized multivariate Cox regression with L2 regularization, in the regime where both p and N are large but with p/N O(1). We thereby generalize a recent study from maximum likelihood to maximum a posteriori inference. We also establish a relationship between the optimal regularization parameter and p/N, allowing for straightforward overfitting corrections in time-to-event analysis.


page 1

page 2

page 3

page 4


Replica analysis of overfitting in generalized linear models

Nearly all statistical inference methods were developed for the regime w...

Correction of overfitting bias in regression models

Regression analysis based on many covariates is becoming increasingly co...

Structure Learning in Inverse Ising Problems Using ℓ_2-Regularized Linear Estimator

Inferring interaction parameters from observed data is a ubiquitous requ...

Optimal regularizations for data generation with probabilistic graphical models

Understanding the role of regularization is a central question in Statis...

Complex Structure Leads to Overfitting: A Structure Regularization Decoding Method for Natural Language Processing

Recent systems on structured prediction focus on increasing the level of...

A new analytical approach to consistency and overfitting in regularized empirical risk minimization

This work considers the problem of binary classification: given training...

Please sign up or login with your details

Forgot password? Click here to reset