  Label distribution learning (LDL) trains a model to predict the relevance of
a set of labels (called label distribution (LD)) to an instance. The previous
LDL methods all assumed the LDs of the training instances are accurate.
However, annotating highly accurate LDs for training instances is
time-consuming and very expensive, and in reality the collected LD is usually
inaccurate and disturbed by annotating errors. For the first time, this paper
investigates the problem of inaccurate LDL, i.e., developing an LDL model with
noisy LDs. We assume that the noisy LD matrix is a linear combination of an
ideal LD matrix and a sparse noise matrix. Consequently, the problem of
inaccurate LDL becomes an inverse problem, where the objective is to recover
the ideal LD and noise matrices from the noisy LDs. We hypothesize that the
ideal LD matrix is low-rank due to the correlation of labels and utilize the
local geometric structure of instances captured by a graph to assist in
recovering the ideal LD. This is based on the premise that similar instances
are likely to share the same LD. The proposed model is finally formulated as a
graph-regularized low-rank and sparse decomposition problem and numerically
solved by the alternating direction method of multipliers. Furthermore, a
specialized objective function is utilized to induce a LD predictive model in
LDL, taking into account the recovered label distributions. Extensive
experiments conducted on multiple datasets from various real-world tasks
effectively demonstrate the efficacy of the proposed approach. \end{abstract}
