🤖 AI Summary
This work addresses the challenge of evaluating generalization performance in quantized dynamical system identification, where data dependence and non-ideal optimization complicate theoretical analysis. The authors propose a unified framework for statistical error bounds, leveraging a block decomposition technique to derive slow-rate bounds and introducing a novel subsampled interval strategy to establish fast-rate, variance-adaptive bounds. These bounds explicitly link the number of bits used for model quantization to statistical complexity. Notably, this is the first study to incorporate hardware constraints—such as quantization bitwidth—into generalization error theory, offering theoretically grounded, interpretable, and practically actionable guarantees for real-world applications including quantized modeling and hybrid system identification.
📝 Abstract
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms commonly used in practical contexts for system identification, and in particular hybrid system identification. Two families of bounds are obtained: slow-rate bounds via a block decomposition and fast-rate, variance-adaptive, bounds via a novel spaced-point strategy. The bounds scale with the number of bits required to encode the model and thus translate hardware constraints into interpretable statistical complexities.