We derive computationally tractable methods to select a small subset of
experiment settings from a large pool of given design points. The primary focus
is on linear regression models, while the technique extends to generalized
linear models and Delta's method (estimating functions of linear regression
models) as well...
The algorithms are based on a continuous relaxation of an
otherwise intractable combinatorial optimization problem, with sampling or
greedy procedures as post-processing steps. Formal approximation guarantees are
established for both algorithms, and numerical results on both synthetic and
real-world data confirm the effectiveness of the proposed methods.