# The Age of Correlated Features in Supervised Learning based Forecasting

arXiv: https://arxiv.org/abs/2103.00092 · HTML: https://mlsanity.com/paper/2103.00092/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 27 Feb 2021.

## Builds on (most cited first, 8 of 8)

- [Understanding data augmentation for classification: when to warp?](https://mlsanity.com/paper/1609.08764/) (2016)
- [Spatiotemporal Relationship Reasoning for Pedestrian Intent Prediction](https://mlsanity.com/paper/2002.08945/) (2020)
- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [A Minimax Approach to Supervised Learning](https://mlsanity.com/paper/1606.02206/) (2016)
- [On Universal Features for High-Dimensional Learning and Inference](https://mlsanity.com/paper/1911.09105/) (2019)
- [Sampling for Data Freshness Optimization: Non-linear Age Functions](https://mlsanity.com/paper/1812.07241/) (2018)
- [On Timely Channel Coding with Hybrid ARQ](https://mlsanity.com/paper/1905.03238/) (2019)
- [Stochastic Control with Stale Information--Part I: Fully Observable Systems](https://mlsanity.com/paper/1810.10983/) (2018)

## Built on by (most cited first, 5 of 5)

- [Federated Learning While Providing Model as a Service: Joint Training and Inference Optimization](https://mlsanity.com/paper/2312.12863/) (2023)
- [Timely Communications for Remote Inference](https://mlsanity.com/paper/2404.16281/) (2024)
- [How Does Data Freshness Affect Real-time Supervised Learning?](https://mlsanity.com/paper/2208.06948/) (2022)
- [Multimodal Remote Inference](https://mlsanity.com/paper/2508.07555/) (2025)
- [A Survey of Freshness-Aware Wireless Networking with Reinforcement Learning](https://mlsanity.com/paper/2512.21412/) (2025)

## Abstract (arXiv)

In this paper, we analyze the impact of information freshness on supervised learning based forecasting. In these applications, a neural network is trained to predict a time-varying target (e.g., solar power), based on multiple correlated features (e.g., temperature, humidity, and cloud coverage). The features are collected from different data sources and are subject to heterogeneous and time-varying ages. By using an information-theoretic approach, we prove that the minimum training loss is a function of the ages of the features, where the function is not always monotonic. However, if the empirical distribution of the training data is close to the distribution of a Markov chain, then the training loss is approximately a non-decreasing age function. Both the training loss and testing loss depict similar growth patterns as the age increases. An experiment on solar power prediction is conducted to validate our theory. Our theoretical and experimental results suggest that it is beneficial to (i) combine the training data with different age values into a large training dataset and jointly train the forecasting decisions for these age values, and (ii) feed the age value as a part of the input feature to the neural network.