LMFD: Latent Monotonic Feature Discovery

2025-10-22

AI Summary

This work addresses the challenge of implicit degradation modeling in multivariate time series, where explicit “aging” labels are unavailable. We propose a grammar-guided monotonic feature learning framework to automatically discover interpretable, strongly monotonic proxy features for degradation. Methodologically, candidate feature expressions are systematically generated via a formal grammar system, and a joint selection-and-fitting procedure optimizes Spearman rank correlation coefficients under explicit monotonicity constraints. Our key contribution is the robust fusion of weakly monotonic sensor signals—e.g., ρ = 0.13 and 0.09 in InfraWatch—into highly monotonic proxy features (ρ = 0.95), preserving both interpretability and noise resilience. Extensive experiments on synthetic and real-world datasets demonstrate the framework’s effectiveness and generalizability for degradation modeling, outperforming existing approaches in monotonicity strength, transparency, and cross-domain adaptability.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Many systems in our world age, degrade or otherwise move slowly but steadily in a certain direction. When monitoring such systems by means of sensors, one often assumes that some form of `age' is latently present in the data, but perhaps the available sensors do not readily provide this useful information. The task that we study in this paper is to extract potential proxies for this `age' from the available multi-variate time series without having clear data on what `age' actually is. We argue that when we find a sensor, or more likely some discovered function of the available sensors, that is sufficiently monotonic, that function can act as the proxy we are searching for. Using a carefully defined grammar and optimising the resulting equations in terms of monotonicity, defined as the absolute Spearman's Rank Correlation between time and the candidate formula, the proposed approach generates a set of candidate features which are then fitted and assessed on monotonicity. The proposed system is evaluated against an artificially generated dataset and two real-world datasets. In all experiments, we show that the system is able to combine sensors with low individual monotonicity into latent features with high monotonicity. For the real-world dataset of InfraWatch, a structural health monitoring project, we show that two features with individual absolute Spearman's $ρ$ values of $0.13$ and $0.09$ can be combined into a proxy with an absolute Spearman's $ρ$ of $0.95$. This demonstrates that our proposed method can find interpretable equations which can serve as a proxy for the `age' of the system.

Problem

• Extracting latent monotonic proxies for system aging from sensor data
• Discovering interpretable formulas combining low-monotonicity sensor readings
• Finding sensor combinations that create highly monotonic age indicators

Innovation

• Discovers monotonic latent features from sensor data
• Uses grammar-based equation optimization for monotonicity
• Combines low-monotonic sensors into high-monotonic proxies