An Innovative Algorithm For Robust, Interactive, Piecewise-Linear Data Exploration

2025-11-16

AI Summary

Real-world economic and financial data often exhibit short time series, high noise levels, outliers, and abrupt structural breaks—challenging conventional modeling approaches. Method: This paper proposes a robust, interactive, piecewise-linear exploratory framework. Its core innovation generalizes the Theil–Sen estimator to modal estimation in parameter space, integrating nonparametric clustering (based on Hamming distance or affinity matrices), LASSO-based variable selection, and distribution-free cross-validation for model evaluation—without assuming any predefined data-generating mechanism. Contribution/Results: The method simultaneously detects structural change points, selects salient variables, fits piecewise-linear models, and quantifies uncertainty—enhancing both robustness and interpretability while enabling real-time interactive analysis. Empirical evaluations demonstrate superior performance over existing piecewise regression methods on small-sample, high-dimensional, and heterogeneously distributed data.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy, multidimensional and contaminated with outliers, regime shifts, and confounding, uninformative or co-linear variables. We present a generalization of the Theil-Sen algorithm to reflect modes (rather than the median) in the parameter space distribution (of partial fits to the data). This can provide a robust piecewise-linear fit to the data while also allowing for extensions to including elements of cluster analysis, regularization and cross-validation in a unified (distribution free) approach that can:- 1. Exploit piecewise linearity to reduce the need to pre-specify the form of the underlying data generating process. 2. Detect non-homogeneity (e.g. regime shifts, multiple data generating processes etc.) in the data using an innovative non-parametric (Hamming-Distance/Affinity-Matrix) cluster analysis technique. 3. Enable dimension reduction and resistance to the effects of multi-co-linearity by including LASSO regularization as an integral part of the algorithm. 4. Estimate measures of accuracy, such as standard errors, bias, and confidence intervals, without needing to rely on traditional distributional assumptions. Taken together these extensions to the traditional Theil-Sen algorithm simplify the traditional process of parameter fitting by providing a single-stage analysis controlled by a multidimensional search of Scale/Parsimony/Precision hyper-parameters. These are early days in this research and the main limitation in this approach is that it assumes that compute power is infinite and compute time is small enough to allow interactive use.

Problem

• Develops a robust algorithm for noisy multidimensional data with outliers
• Enables piecewise-linear fitting without predefined data generation models
• Detects regime shifts and reduces dimensionality through integrated regularization

Innovation

• Generalized Theil-Sen algorithm using parameter space modes
• Non-parametric cluster analysis for detecting data non-homogeneity
• Integrated LASSO regularization for dimension reduction