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- W50956978 abstract "The theory of optimal experimental explains how to best select experiments in order to estimate a set of parameters. The quality of the estimation can be measured by the confidence ellipsoids of a certain estimator. This leads to concave maximization problems in which the objective function is nondecreasing with respect to the Lowner ordering of symmetric matrices, and is applied to the information describing the structure of these confidence ellipsoids. In a number of real-world applications, the variables controlling the experimental design are discrete, or binary. This paper provides approximability bounds for this NP-hard problem. In particular, we establish a matrix inequality which shows that the objective function is submodular, from which it follows that the greedy approach, which has often been used for this problem, always gives a design within $1-1/e$ of the optimum. We next study the design found by rounding the solution of the continuous relaxed problem, an approach which has been applied by several authors: When the goal is to select $n$ out of $s$ experiments, we show that the $D-$optimal design may be rounded to a random subset of $n$ experiments for which the dimension of the observable subspace is within $n/s$ of the optimum with a high probability." @default.
- W50956978 created "2016-06-24" @default.
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- W50956978 date "2010-07-23" @default.
- W50956978 modified "2023-09-27" @default.
- W50956978 title "Polynomial-time Approximability Results for combinatorial problems arising in Optimal Experimental Design" @default.
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