Avoiding Overfitting in Variable-Order Markov Models: a Cross-Validation Approach

2025-01-24

AI Summary

Dynamic systems—such as transportation networks and corporate ownership networks—often exhibit higher-order Markov dependencies; however, conventional higher-order Markov models frequently misinterpret stochastic noise as genuine higher-order structure, leading to overfitting and degraded multi-step prediction accuracy. To address this, we propose DIVOP—the first framework that integrates cross-validation into variable-order Markov path selection. DIVOP robustly distinguishes true higher-order dependencies from spurious fluctuations via KL-divergence–based benchmarking and path significance testing, enabling sparse and interpretable dynamic structural modeling. Evaluated on synthetic and real-world datasets, DIVOP consistently outperforms state-of-the-art methods in both precision and recall. Applied to the global corporate ownership network, it identifies higher-order dependency links involving tax havens with 82% significance, uncovering their structural role in international capital flows.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Higher$ ext{-}$order Markov chain models are widely used to represent agent transitions in dynamic systems, such as passengers in transport networks. They capture transitions in complex systems by considering not only the current state but also the path of previously visited states. For example, the likelihood of train passengers traveling from Paris (current state) to Rome could increase significantly if their journey originated in Italy (prior state). Although this approach provides a more faithful representation of the system than first$ ext{-}$order models, we find that commonly used methods$-$relying on Kullback$ ext{-}$Leibler divergence$-$frequently overfit the data, mistaking fluctuations for higher$ ext{-}$order dependencies and undermining forecasts and resource allocation. Here, we introduce DIVOP (Detection of Informative Variable$ ext{-}$Order Paths), an algorithm that employs cross$ ext{-}$validation to robustly distinguish meaningful higher$ ext{-}$order dependencies from noise. In both synthetic and real$ ext{-}$world datasets, DIVOP outperforms two state$ ext{-}$of$ ext{-}$the$ ext{-}$art algorithms by achieving higher precision, recall, and sparser representations of the underlying dynamics. When applied to global corporate ownership data, DIVOP reveals that tax havens appear in 82$%$ of all significant higher$ ext{-}$order dependencies, underscoring their outsized influence in corporate networks. By mitigating overfitting, DIVOP enables more reliable multi$ ext{-}$step predictions and decision$ ext{-}$making, paving the way toward deeper insights into the hidden structures that drive modern interconnected systems.

Problem

• Markov Models
• Overfitting Prevention
• Dynamic Systems Analysis

Innovation

• DIVOP
• High-order Markov Chain
• Complex System Analysis