Stochastic Gradient Descent Meets Distribution Regression
This work addresses a theoretical gap for researchers in machine learning, but it is incremental as it extends known SGD analysis to a specific problem.
The paper tackled the lack of theoretical guarantees for stochastic gradient descent (SGD) in distribution regression, a two-stage sampling problem, and provided optimal mini-max bounds under standard assumptions.
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from probability measures to real-valued responses. Secondly, we sample bags from these distributions for utilizing them to solve the overall regression problem. Recently, DR has been tackled by applying kernel ridge regression and the learning properties of this approach are well understood. However, nothing is known about the learning properties of SGD for two stage sampling problems. We fill this gap and provide theoretical guarantees for the performance of SGD for DR. Our bounds are optimal in a mini-max sense under standard assumptions.