1 research outputs found
Minimax Structured Normal Means Inference
We provide a unified treatment of a broad class of noisy structure recovery
problems, known as structured normal means problems. In this setting, the goal
is to identify, from a finite collection of Gaussian distributions with
different means, the distribution that produced some observed data. Recent work
has studied several special cases including sparse vectors, biclusters, and
graph-based structures. We establish nearly matching upper and lower bounds on
the minimax probability of error for any structured normal means problem, and
we derive an optimality certificate for the maximum likelihood estimator, which
can be applied to many instantiations. We also consider an experimental design
setting, where we generalize our minimax bounds and derive an algorithm for
computing a design strategy with a certain optimality property. We show that
our results give tight minimax bounds for many structure recovery problems and
consider some consequences for interactive sampling