  Given a set of human's decisions that are observed, inverse optimization has
been developed and utilized to infer the underlying decision making problem.
The majority of existing studies assumes that the decision making problem is
with a single objective function, and attributes data divergence to noises,
errors or bounded rationality, which, however, could lead to a corrupted
inference when decisions are tradeoffs among multiple criteria. In this paper,
we take a data-driven approach and design a more sophisticated inverse
optimization formulation to explicitly infer parameters of a multiobjective
decision making problem from noisy observations. This framework, together with
our mathematical analyses and advanced algorithm developments, demonstrates a
strong capacity in estimating critical parameters, decoupling "interpretable"
components from noises or errors, deriving the denoised \emph{optimal}
decisions, and ensuring statistical significance. In particular, for the whole
decision maker population, if suitable conditions hold, we will be able to
understand the overall diversity and the distribution of their preferences over
multiple criteria, which is important when a precise inference on every single
decision maker is practically unnecessary or infeasible. Numerical results on a
large number of experiments are reported to confirm the effectiveness of our
unique inverse optimization model and the computational efficacy of the
developed algorithms.
