  In this paper, we focus on weakly supervised learning with noisy training
data for both classification and regression problems.We assume that the
training outputs are collected from a mixture of a target and correlated noise
distributions.Our proposed method simultaneously estimates the target
distribution and the quality of each data which is defined as the correlation
between the target and data generating distributions.The cornerstone of the
proposed method is a Cholesky Block that enables modeling dependencies among
mixture distributions in a differentiable manner where we maintain the
distribution over the network weights.We first provide illustrative examples in
both regression and classification tasks to show the effectiveness of the
proposed method.Then, the proposed method is extensively evaluated in a number
of experiments where we show that it constantly shows comparable or superior
performances compared to existing baseline methods in the handling of noisy
data.
