5,024 research outputs found
Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, using Sparse Linear Programming
We propose new, optimal methods for analyzing randomized trials, when it is
suspected that treatment effects may differ in two predefined subpopulations.
Such sub-populations could be defined by a biomarker or risk factor measured at
baseline. The goal is to simultaneously learn which subpopulations benefit from
an experimental treatment, while providing strong control of the familywise
Type I error rate. We formalize this as a multiple testing problem and show it
is computationally infeasible to solve using existing techniques. Our solution
involves a novel approach, in which we first transform the original multiple
testing problem into a large, sparse linear program. We then solve this problem
using advanced optimization techniques. This general method can solve a variety
of multiple testing problems and decision theory problems related to optimal
trial design, for which no solution was previously available. In particular, we
construct new multiple testing procedures that satisfy minimax and Bayes
optimality criteria. For a given optimality criterion, our new approach yields
the optimal tradeoff? between power to detect an effect in the overall
population versus power to detect effects in subpopulations. We demonstrate our
approach in examples motivated by two randomized trials of new treatments for
HIV
A Survey of Monte Carlo Tree Search Methods
Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work
Bayesian inference in high-dimensional linear models using an empirical correlation-adaptive prior
In the context of a high-dimensional linear regression model, we propose the
use of an empirical correlation-adaptive prior that makes use of information in
the observed predictor variable matrix to adaptively address high collinearity,
determining if parameters associated with correlated predictors should be
shrunk together or kept apart. Under suitable conditions, we prove that this
empirical Bayes posterior concentrates around the true sparse parameter at the
optimal rate asymptotically. A simplified version of a shotgun stochastic
search algorithm is employed to implement the variable selection procedure, and
we show, via simulation experiments across different settings and a real-data
application, the favorable performance of the proposed method compared to
existing methods.Comment: 25 pages, 4 figures, 2 table
Description of research interests and current work related to automating software design
Enclosed is a list of selected and recent publications. Most of these publications concern applied research in the areas of software engineering and human-computer interaction. It is felt that domain-specific knowledge plays a major role in software development. Additionally, it is believed that improvements in the general software development process (e.g., object-oriented approaches) will have to be combined with the use of large domain-specific knowledge bases
Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
We develop a numerical approach for quantifying entanglement in mixed quantum
states by convex-roof entanglement measures, based on the optimal entanglement
witness operator and the minimax optimization method. Our approach is
applicable to general entanglement measures and states and is an efficient
alternative to the conventional approach based on the optimal pure-state
decomposition. Compared with the conventional one, it has two important merits:
(i) that the global optimality of the solution is quantitatively verifiable,
and (ii) that the optimization is considerably simplified by exploiting the
common symmetry of the target state and measure. To demonstrate the merits, we
quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of
three-qubit full-rank mixed states composed of the GHZ state, the W state, and
the white noise, the simplest mixtures of states with different genuine
multipartite entanglement, which have not been quantified before this work. We
discuss some general properties of the form of the optimal witness operator and
of the convex structure of mixed states, which are related to the symmetry and
the rank of states
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