An Affine-Invariant Sampler for Exoplanet Fitting and Discovery in Radial Velocity Data

Markov Chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like chi-square fitting. However, the non-linear density functions encountered in these problems can make MCMC time-consuming. In this paper, we apply an ensemble sampler respecting affine invariance to orbital parameter extraction from radial velocity data. This new sampler has only one free parameter, and it does not require much tuning for good performance, which is important for automatization. The autocorrelation time of this sampler is approximately the same for all parameters and far smaller than Metropolis-Hastings, which means it requires many fewer function calls to produce the same number of independent samples. The affine-invariant sampler speeds up MCMC by hundreds of times compared with Metropolis-Hastings in the same computing situation. This novel sampler would be ideal for projects involving large datasets such as statistical investigations of planet distribution. The biggest obstacle to ensemble samplers is the existence of multiple local optima; we present a clustering technique to deal with local optima by clustering based on the likelihood of the walkers in the ensemble. We demonstrate the effectiveness of the sampler on real radial velocity data.Comment: 24 pages, 7 figures, accepted to Ap

CIXL2: A Crossover Operator for Evolutionary Algorithms Based on Population Features

In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to test the efficiency and robustness of this crossover, we have used a set of functions to be optimized with regard to different criteria, such as, multimodality, separability, regularity and epistasis. With this set of functions we can extract conclusions in function of the problem at hand. We analyze the results using ANOVA and multiple comparison statistical tests. As an example of how our crossover can be used to solve artificial intelligence problems, we have applied the proposed model to the problem of obtaining the weight of each network in a ensemble of neural networks. The results obtained are above the performance of standard methods

Global Continuous Optimization with Error Bound and Fast Convergence

This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in machine learning, engineering design problem, and planning with a complex physics simulator. This paper proposes a new global optimization algorithm, called Locally Oriented Global Optimization (LOGO), to aim for both fast convergence in practice and finite-time error bound in theory. The advantage and usage of the new algorithm are illustrated via theoretical analysis and an experiment conducted with 11 benchmark test functions. Further, we modify the LOGO algorithm to specifically solve a planning problem via policy search with continuous state/action space and long time horizon while maintaining its finite-time error bound. We apply the proposed planning method to accident management of a nuclear power plant. The result of the application study demonstrates the practical utility of our method

Scalable Co-Optimization of Morphology and Control in Embodied Machines

Evolution sculpts both the body plans and nervous systems of agents together over time. In contrast, in AI and robotics, a robot's body plan is usually designed by hand, and control policies are then optimized for that fixed design. The task of simultaneously co-optimizing the morphology and controller of an embodied robot has remained a challenge. In psychology, the theory of embodied cognition posits that behavior arises from a close coupling between body plan and sensorimotor control, which suggests why co-optimizing these two subsystems is so difficult: most evolutionary changes to morphology tend to adversely impact sensorimotor control, leading to an overall decrease in behavioral performance. Here, we further examine this hypothesis and demonstrate a technique for "morphological innovation protection", which temporarily reduces selection pressure on recently morphologically-changed individuals, thus enabling evolution some time to "readapt" to the new morphology with subsequent control policy mutations. We show the potential for this method to avoid local optima and converge to similar highly fit morphologies across widely varying initial conditions, while sustaining fitness improvements further into optimization. While this technique is admittedly only the first of many steps that must be taken to achieve scalable optimization of embodied machines, we hope that theoretical insight into the cause of evolutionary stagnation in current methods will help to enable the automation of robot design and behavioral training -- while simultaneously providing a testbed to investigate the theory of embodied cognition

An Unsupervised Deep Learning Approach for Scenario Forecasts

In this paper, we propose a novel scenario forecasts approach which can be applied to a broad range of power system operations (e.g., wind, solar, load) over various forecasts horizons and prediction intervals. This approach is model-free and data-driven, producing a set of scenarios that represent possible future behaviors based only on historical observations and point forecasts. It first applies a newly-developed unsupervised deep learning framework, the generative adversarial networks, to learn the intrinsic patterns in historical renewable generation data. Then by solving an optimization problem, we are able to quickly generate large number of realistic future scenarios. The proposed method has been applied to a wind power generation and forecasting dataset from national renewable energy laboratory. Simulation results indicate our method is able to generate scenarios that capture spatial and temporal correlations. Our code and simulation datasets are freely available online.Comment: Accepted to Power Systems Computation Conference 2018 Code available at https://github.com/chennnnnyize/Scenario-Forecasts-GA