Tensor regression method improves robustness for complex data analysis
Partial Modal Tensor Regression
Machine Learning
Summary
Many modern studies generate data that look like multi-dimensional arrays called tensors. Understanding how these tensors relate to an outcome is tricky, especially when data have unusual patterns or outliers. The authors propose a new method that focuses on finding the most likely outcome (the mode) rather than the average, which is often more stable in complex data. They reduce the complexity of the tensor data while keeping its natural structure, making the relationship easier to understand and analyze accurately.
What this means in practice
- •For medical imaging analysts: Analyze complex imaging data to predict health outcomes more robustly by focusing on the most typical case instead of averages.
- •For financial risk analysts: Model relationships with heavy-tailed financial data robustly to reduce the impact of outliers in predicting risk metrics.
Authors
Jintao Han, Li Zhang, Xuejun Ma
Abstract
With the rapid development of modern scientific research, tensor data have become increasingly prevalent across a wide range of fields. How to effectively characterize the relationship between tensor predictors and a response while preserving the intrinsic structure of tensor data has therefore become an important problem in high-dimensional statistical analysis. Existing tensor regression methods mainly focus on conditional means or conditional quantiles. When the response distribution is asymmetric, heavy-tailed, or contaminated by outlying observations, the conditional modal provides a robust and interpretable alternative characterization. In this paper, we propose a partial modal tensor regression (PMTR) method. The proposed method constructs the partial modal tensor covariance, which incorporates information on the conditional modal to guide tensor dimension reduction, and subsequently establishes a modal tensor regression model in the reduced tensor space. This strategy alleviates the dimensionality burden caused by direct vectorization while preserving the intrinsic structural information of tensor predictors. Under suitable regularity conditions, we establish the consistency and asymptotic properties of the proposed estimators and employ a data-driven dimension-selection procedure to determine the effective dimension along each tensor mode.