Yang Yuan

Jiaye Teng, Zeren Tan, Yang Yuan

It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence band of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP (Katzman et al., 2018; Kvamme et al., 2019)), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm WCCI, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm T-SCI, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis.

Jiaye Teng, Yang Yuan

Due to its strong interpretability, linear regression is widely used in social science, from which significance test provides the significance level of models or coefficients in the traditional statistical inference. However, linear regression methods rely on the linear assumptions of the ground truth function, which do not necessarily hold in practice. As a result, even for simple non-linear cases, linear regression may fail to report the correct significance level. In this paper, we present a simple and effective assumption-free method for linear approximation in both linear and non-linear scenarios. First, we apply a machine learning method to fit the ground truth function on the training set and calculate its linear approximation. Afterward, we get the estimator by adding adjustments based on the validation set. We prove the concentration inequalities and asymptotic properties of our estimator, which leads to the corresponding significance test. Experimental results show that our estimator significantly outperforms linear regression for non-linear ground truth functions, indicating that our estimator might be a better tool for the significance test.