d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response

Identifying optimal designs for generalized linear models with a binary response can be a challengingtask, especially when there are both discrete and continuous independent factors in the model. Theoreticalresults rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions.In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particleswarm optimization, to find a variety of D-optimal approximate and exact designs for experiments withdiscrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficientlyfind locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigaterobustness properties of the d-QPSO algorithm-generated designs to variousmodel assumptions andprovide real applications to design a bio-plastics odor removal experiment, an electronic static experiment,and a 10-factor car refueling experiment. Supplementary materials for the article are available online

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Best chirplet chain: near-optimal detection of gravitational wave chirps

The list of putative sources of gravitational waves possibly detected by the ongoing worldwide network of large scale interferometers has been continuously growing in the last years. For some of them, the detection is made difficult by the lack of a complete information about the expected signal. We concentrate on the case where the expected GW is a quasi-periodic frequency modulated signal i.e., a chirp. In this article, we address the question of detecting an a priori unknown GW chirp. We introduce a general chirp model and claim that it includes all physically realistic GW chirps. We produce a finite grid of template waveforms which samples the resulting set of possible chirps. If we follow the classical approach (used for the detection of inspiralling binary chirps, for instance), we would build a bank of quadrature matched filters comparing the data to each of the templates of this grid. The detection would then be achieved by thresholding the output, the maximum giving the individual which best fits the data. In the present case, this exhaustive search is not tractable because of the very large number of templates in the grid. We show that the exhaustive search can be reformulated (using approximations) as a pattern search in the time-frequency plane. This motivates an approximate but feasible alternative solution which is clearly linked to the optimal one. [abridged version of the abstract]Comment: 23 pages, 9 figures. Accepted for publication in Phys. Rev D Some typos corrected and changes made according to referee's comment

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Solving Factored MDPs with Hybrid State and Action Variables

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function by a linear combination of basis functions and optimize its weights by linear programming. We analyze both theoretical and computational aspects of this approach, and demonstrate its scale-up potential on several hybrid optimization problems

Foraging as an evidence accumulation process

A canonical foraging task is the patch-leaving problem, in which a forager must decide to leave a current resource in search for another. Theoretical work has derived optimal strategies for when to leave a patch, and experiments have tested for conditions where animals do or do not follow an optimal strategy. Nevertheless, models of patch-leaving decisions do not consider the imperfect and noisy sampling process through which an animal gathers information, and how this process is constrained by neurobiological mechanisms. In this theoretical study, we formulate an evidence accumulation model of patch-leaving decisions where the animal averages over noisy measurements to estimate the state of the current patch and the overall environment. Evidence accumulation models belong to the class of drift diffusion processes and have been used to model decision making in different contexts. We solve the model for conditions where foraging decisions are optimal and equivalent to the marginal value theorem, and perform simulations to analyze deviations from optimal when these conditions are not met. By adjusting the drift rate and decision threshold, the model can represent different strategies, for example an increment-decrement or counting strategy. These strategies yield identical decisions in the limiting case but differ in how patch residence times adapt when the foraging environment is uncertain. To account for sub-optimal decisions, we introduce an energy-dependent utility function that predicts longer than optimal patch residence times when food is plentiful. Our model provides a quantitative connection between ecological models of foraging behavior and evidence accumulation models of decision making. Moreover, it provides a theoretical framework for potential experiments which seek to identify neural circuits underlying patch leaving decisions