We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions.

In label-noise learning, the noise transition matrix reveals how an instance transitions from its clean label to its noisy label. Accurately estimating an instance's noise transition matrix is crucial for estimating its clean label.