154,355 research outputs found
Bayesian optimization for materials design
We introduce Bayesian optimization, a technique developed for optimizing
time-consuming engineering simulations and for fitting machine learning models
on large datasets. Bayesian optimization guides the choice of experiments
during materials design and discovery to find good material designs in as few
experiments as possible. We focus on the case when materials designs are
parameterized by a low-dimensional vector. Bayesian optimization is built on a
statistical technique called Gaussian process regression, which allows
predicting the performance of a new design based on previously tested designs.
After providing a detailed introduction to Gaussian process regression, we
introduce two Bayesian optimization methods: expected improvement, for design
problems with noise-free evaluations; and the knowledge-gradient method, which
generalizes expected improvement and may be used in design problems with noisy
evaluations. Both methods are derived using a value-of-information analysis,
and enjoy one-step Bayes-optimality
Decentralized High-Dimensional Bayesian Optimization with Factor Graphs
This paper presents a novel decentralized high-dimensional Bayesian
optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms,
can exploit the interdependent effects of various input components on the
output of the unknown objective function f for boosting the BO performance and
still preserve scalability in the number of input dimensions without requiring
prior knowledge or the existence of a low (effective) dimension of the input
space. To realize this, we propose a sparse yet rich factor graph
representation of f to be exploited for designing an acquisition function that
can be similarly represented by a sparse factor graph and hence be efficiently
optimized in a decentralized manner using distributed message passing. Despite
richly characterizing the interdependent effects of the input components on the
output of f with a factor graph, DEC-HBO can still guarantee no-regret
performance asymptotically. Empirical evaluation on synthetic and real-world
experiments (e.g., sparse Gaussian process model with 1811 hyperparameters)
shows that DEC-HBO outperforms the state-of-the-art HBO algorithms.Comment: 32nd AAAI Conference on Artificial Intelligence (AAAI 2018), Extended
version with proofs, 13 page
Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models
The recently introduced class of simultaneous graphical dynamic linear models
(SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting
to higher-dimensional time series. This paper advances the methodology of
SGDLMs, developing and embedding a novel, adaptive method of simultaneous
predictor selection in forward filtering for on-line learning and forecasting.
The advances include developments in Bayesian computation for scalability, and
a case study in exploring the resulting potential for improved short-term
forecasting of large-scale volatility matrices. A case study concerns financial
forecasting and portfolio optimization with a 400-dimensional series of daily
stock prices. Analysis shows that the SGDLM forecasts volatilities and
co-volatilities well, making it ideally suited to contributing to quantitative
investment strategies to improve portfolio returns. We also identify
performance metrics linked to the sequential Bayesian filtering analysis that
turn out to define a leading indicator of increased financial market stresses,
comparable to but leading the standard St. Louis Fed Financial Stress Index
(STLFSI) measure. Parallel computation using GPU implementations substantially
advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table
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A solution to the crucial problem of population degeneration in high-dimensional evolutionary optimization
Three popular evolutionary optimization algorithms are tested on high-dimensional benchmark functions. An important phenomenon responsible for many failures - population degeneration - is discovered. That is, through evolution, the population of searching particles degenerates into a subspace of the search space, and the global optimum is exclusive from the subspace. Subsequently, the search will tend to be confined to this subspace and eventually miss the global optimum. Principal components analysis (PCA) is introduced to discover population degeneration and to remedy its adverse effects. The experiment results reveal that an algorithm's efficacy and efficiency are closely related to the population degeneration phenomenon. Guidelines for improving evolutionary algorithms for high-dimensional global optimization are addressed. An application to highly nonlinear hydrological models demonstrates the efficacy of improved evolutionary algorithms in solving complex practical problems. © 2011 IEEE
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