# Rethinking Remaining Useful Life Prediction with Scarce Time Series Data: Regression under Indirect Supervision

arXiv: https://arxiv.org/abs/2504.09206 · HTML: https://mlsanity.com/paper/2504.09206/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 12 Apr 2025.

## Builds on (most cited first, 4 of 4)

- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [Time-Series Regeneration with Convolutional Recurrent Generative Adversarial Network for Remaining Useful Life Estimation](https://mlsanity.com/paper/2101.03678/) (2021)
- [Deep Time Series Models for Scarce Data](https://mlsanity.com/paper/2103.09348/) (2021)
- [Learnability with Indirect Supervision Signals](https://mlsanity.com/paper/2006.08791/) (2020)

## Built on by (most cited first, 1 of 1)

- [Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations](https://mlsanity.com/paper/2606.01894/) (2026)

## Abstract (arXiv)

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.