Doubly Stochastic Models: Learning with Unbiased Label Noises and Inference Stability

Abstract

Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the implicit regularization effects of the label noises, under mini-batch sampling settings of stochastic gradient descent (SGD), with assumptions that label noises are unbiased. Specifically, we analyze the learning dynamics of SGD over the quadratic loss with unbiased label noises, where we model the dynamics of SGD as a stochastic differentiable equation (SDE) with two diffusion terms (namely a Doubly Stochastic Model). While the first diffusion term is caused by mini-batch sampling over the (label-noiseless) loss gradients as many other works on SGD, our model investigates the second noise term of SGD dynamics, which is caused by mini-batch sampling over the label noises, as an implicit regularizer. Our theoretical analysis finds such implicit regularizer would favor some convergence points that could stabilize model outputs against perturbation of parameters (namely inference stability). Though similar phenomenon have been investigated, our work doesn't assume SGD as an Ornstein-Uhlenbeck like process and achieve a more generalizable result with convergence of approximation proved. To validate our analysis, we design two sets of empirical studies to analyze the implicit regularizer of SGD with unbiased random label noises for deep neural networks training and linear regression.