Jiaxiang Cheng

Jiaxiang Cheng, Yipeng Pang, Guoqiang Hu

Supervised time series prediction relies on directly measured target variables, but real-world use cases such as predicting remaining useful life (RUL) involve indirect supervision, where the target variable is labeled as a function of another dependent variable. Trending temporal regression techniques rely on sequential time series inputs to capture temporal patterns, requiring interpolation when dealing with sparsely and irregularly sampled covariates along the timeline. However, interpolation can introduce significant biases, particularly with highly scarce data. In this paper, we address the RUL prediction problem with data scarcity as time series regression under indirect supervision. We introduce a unified framework called parameterized static regression, which takes single data points as inputs for regression of target values, inherently handling data scarcity without requiring interpolation. The time dependency under indirect supervision is captured via a parametrical rectification (PR) process, approximating a parametric function during inference with historical posteriori estimates, following the same underlying distribution used for labeling during training. Additionally, we propose a novel batch training technique for tasks in indirect supervision to prevent overfitting and enhance efficiency. We evaluate our model on public benchmarks for RUL prediction with simulated data scarcity. Our method demonstrates competitive performance in prediction accuracy when dealing with highly scarce time series data.

Jiaxiang Cheng, Guoqiang Hu

The Cox proportional hazards (CPH) model has been widely applied in survival analysis to estimate relative risks across different subjects given multiple covariates. Traditional CPH models rely on a linear combination of covariates weighted with coefficients as the log-risk function, which imposes a strong and restrictive assumption, limiting generalization. Recent deep learning methods enable non-linear log-risk functions. However, they often lack interpretability due to the end-to-end training mechanisms. The implementation of Kolmogorov-Arnold Networks (KAN) offers new possibilities for extending the CPH model with fully transparent and symbolic non-linear log-risk functions. In this paper, we introduce Generalized Cox Proportional Hazards (GCPH) model, a novel method for survival analysis that leverages KAN to enable a non-linear mapping from covariates to survival outcomes in a fully symbolic manner. GCPH maintains the interpretability of traditional CPH models while allowing for the estimation of non-linear log-risk functions. Experiments conducted on both synthetic data and various public benchmarks demonstrate that GCPH achieves competitive performance in terms of prediction accuracy and exhibits superior interpretability compared to current state-of-the-art methods.