  Crowdsourcing system has emerged as an effective platform for labeling data
with relatively low cost by using non-expert workers. Inferring correct labels
from multiple noisy answers on data, however, has been a challenging problem,
since the quality of the answers varies widely across tasks and workers. Many
existing works have assumed that there is a fixed ordering of workers in terms
of their skill levels, and focused on estimating worker skills to aggregate the
answers from workers with different weights. In practice, however, the worker
skill changes widely across tasks, especially when the tasks are heterogeneous.
In this paper, we consider a new model, called $d$-type specialization model,
in which each task and worker has its own (unknown) type and the reliability of
each worker can vary in the type of a given task and that of a worker. We allow
that the number $d$ of types can scale in the number of tasks. In this model,
we characterize the optimal sample complexity to correctly infer the labels
within any given accuracy, and propose label inference algorithms achieving the
order-wise optimal limit even when the types of tasks or those of workers are
unknown. We conduct experiments both on synthetic and real datasets, and show
that our algorithm outperforms the existing algorithms developed based on more
strict model assumptions.
