14,330 research outputs found
Continuous multi-task Bayesian optimisation with correlation
This paper considers the problem of simultaneously identifying the optima for a (continuous or discrete) set of correlated tasks, where the performance of a particular input parameter on a particular task can only be estimated from (potentially noisy) samples. This has many applications, for example, identifying a stochastic algorithm’s optimal parameter settings for various tasks described by continuous feature values. We adapt the framework of Bayesian Optimisation to this problem. We propose a general multi-task optimisation framework and two myopic sampling procedures that determine task and parameter values for sampling, in order to efficiently find the best parameter setting for all tasks simultaneously. We show experimentally that our methods are much more efficient than collecting information randomly, and also more efficient than two other Bayesian multi-task optimisation algorithms from the literature
Gaussian process hyper-parameter estimation using parallel asymptotically independent Markov sampling
Gaussian process emulators of computationally expensive computer codes
provide fast statistical approximations to model physical processes. The
training of these surrogates depends on the set of design points chosen to run
the simulator. Due to computational cost, such training set is bound to be
limited and quantifying the resulting uncertainty in the hyper-parameters of
the emulator by uni-modal distributions is likely to induce bias. In order to
quantify this uncertainty, this paper proposes a computationally efficient
sampler based on an extension of Asymptotically Independent Markov Sampling, a
recently developed algorithm for Bayesian inference. Structural uncertainty of
the emulator is obtained as a by-product of the Bayesian treatment of the
hyper-parameters. Additionally, the user can choose to perform stochastic
optimisation to sample from a neighbourhood of the Maximum a Posteriori
estimate, even in the presence of multimodality. Model uncertainty is also
acknowledged through numerical stabilisation measures by including a nugget
term in the formulation of the probability model. The efficiency of the
proposed sampler is illustrated in examples where multi-modal distributions are
encountered. For the purpose of reproducibility, further development, and use
in other applications the code used to generate the examples is freely
available for download at https://github.com/agarbuno/paims_codesComment: Computational Statistics \& Data Analysis, Volume 103, November 201
Hyperparameter Learning via Distributional Transfer
Bayesian optimisation is a popular technique for hyperparameter learning but
typically requires initial exploration even in cases where similar prior tasks
have been solved. We propose to transfer information across tasks using learnt
representations of training datasets used in those tasks. This results in a
joint Gaussian process model on hyperparameters and data representations.
Representations make use of the framework of distribution embeddings into
reproducing kernel Hilbert spaces. The developed method has a faster
convergence compared to existing baselines, in some cases requiring only a few
evaluations of the target objective
Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters
Bayesian optimisation has gained great popularity as a tool for optimising
the parameters of machine learning algorithms and models. Somewhat ironically,
setting up the hyper-parameters of Bayesian optimisation methods is notoriously
hard. While reasonable practical solutions have been advanced, they can often
fail to find the best optima. Surprisingly, there is little theoretical
analysis of this crucial problem in the literature. To address this, we derive
a cumulative regret bound for Bayesian optimisation with Gaussian processes and
unknown kernel hyper-parameters in the stochastic setting. The bound, which
applies to the expected improvement acquisition function and sub-Gaussian
observation noise, provides us with guidelines on how to design hyper-parameter
estimation methods. A simple simulation demonstrates the importance of
following these guidelines.Comment: 16 pages, 1 figur
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Adaptive Smoothing in fMRI Data Processing Neural Networks
Functional Magnetic Resonance Imaging (fMRI) relies on multi-step data
processing pipelines to accurately determine brain activity; among them, the
crucial step of spatial smoothing. These pipelines are commonly suboptimal,
given the local optimisation strategy they use, treating each step in
isolation. With the advent of new tools for deep learning, recent work has
proposed to turn these pipelines into end-to-end learning networks. This change
of paradigm offers new avenues to improvement as it allows for a global
optimisation. The current work aims at benefitting from this paradigm shift by
defining a smoothing step as a layer in these networks able to adaptively
modulate the degree of smoothing required by each brain volume to better
accomplish a given data analysis task. The viability is evaluated on real fMRI
data where subjects did alternate between left and right finger tapping tasks.Comment: 4 pages, 3 figures, 1 table, IEEE 2017 International Workshop on
Pattern Recognition in Neuroimaging (PRNI
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