Related papers: Computing exact $D$-optimal designs by mixed integ…
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…
We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show…
We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
Motivated by the expressive power of completely positive programming to encode hard optimization problems, many approximation schemes for the completely positive cone have been proposed and successfully used. Most schemes are based on outer…
We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this…
Optimal designs can help experimenters obtain more accurate parameter estimates with reduced experimental time and cost. In this paper, we characterize the Expected Weighted (EW) D-optimal designs as robust designs against unknown parameter…
We introduce a minor variant of the approximate D-optimal design of experiments with a more general information matrix that takes into account the representation of the design space S. The main motivation (and result) is that if S in R^d is…
Optimal designs are required to make efficient statistical experiments. D-optimal designs for some models are calculated by using canonical moments. On the other hand, integrable systems are dynamical systems whose solutions can be written…
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…
$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation.…
Elfving's Theorem is a major result in the theory of optimal experimental design, which gives a geometrical characterization of $c-$optimality. In this paper, we extend this theorem to the case of multiresponse experiments, and we show that…
We propose a method of using a Weighted second-order cone programming twin support vector machine (WSOCP-TWSVM) for imbalanced data classification. This method constructs a graph based under-sampling method which is utilized to remove…
A fundamental property of codes, the second-order weight distribution, is proposed to solve the problems such as computing second moments of weight distributions of linear code ensembles. A series of results, parallel to those for weight…
We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…
We provide a systematic treatment of $D$-optimal design for binary regression and quantal response models in toxicology studies. For the two-parameter case, we provide an analytical equation (WC equation) for computing the $D$-optimal…