Structured Adaptive Tensor Prediction for Streaming Data

Researchers have proposed new machine learning methods for streaming matrix-valued prediction and structured non-exchangeable data. The methods include an adaptive tensor regression framework and a Spectral Adaptive Conformal Prediction technique.

A new adaptive tensor regression framework has been developed for streaming matrix-valued prediction, including Matrix-on-Matrix (MoM) and Tensor-on-Matrix (ToM) formulations^[1]. The ToM formulation has been shown to achieve lower steady-state error and stronger denoising capability than MoM. Stochastic gradient descent (SGD) algorithms have been developed for online learning, and fixed-time recovery guarantees have been established for ToM under general low-dimensional structures. Additionally, a new method called Spectral Adaptive Conformal Prediction has been proposed for structured non-exchangeable data, which forms weighted conformal quantiles using local spectral similarity and updates the target miscoverage level online^[2]. This method corrects the long-run miss rate when uncertainty changes over time. Conformal prediction typically gives prediction intervals with finite-sample coverage when data are exchangeable, but many time-indexed datasets are not exchangeable due to seasons, recurring regimes, or changing frequencies.