Financial Applications of Gaussian Processes and Bayesian Optimization

Gonzalvez, Joan; Lezmi, Edmond; Roncalli, Thierry; Xu, Jiali

doi:10.48550/arxiv.1903.04841

Cited by 8 publications

(9 citation statements)

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“…Nguyen et al [28] proposed convergence criteria for these acquisition functions in order to avoid unwanted evaluations. It has been applied with great success in machine learning applications [29], analog circuits [30], voltage failures [31], aerospace engineering [32], asset management [33], pharmaceutical products [34], laboratory gas-liquid separator [35], multi objective optimization [36], electron lasers [37], and autonomous systems [38].…”

Section: B Bayesian Optimizationmentioning

confidence: 99%

Generalized State-Feedback Controller Synthesis for Underactuated Systems through Bayesian Optimization

Solís¹,

Thomas²

2021

Preprint

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Underactuated systems pose the challenge of being able to control a plant whose degrees of freedom are not necessarily directly linked to an actuator or where such a relationship is not straightforward. Rotary inverted pendulum is an example of such systems, which on its simplest representation consists of a pendulum whose vertical angle should be taken up to the upward unstable position based on the impulse given from another bar and an appropriate control strategy, bar that is controlled by an electrical motor. This problem is often tackled by linear control theory with state-feedback controllers that is frequently obtained by means of designing a feedback gain meeting some constraints. This article reports a Bayesian Optimization approach for designing a generalized state-feedback controller, that involves more parameters than a simple statefeedback control law, but with the benefit of achieving lower control effort in terms of the signal amplitude. The source code is made publicly available to facilitate further research.

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Section: B Bayesian Optimizationmentioning

confidence: 99%

Generalized State-Feedback Controller Synthesis for Underactuated Systems through Bayesian Optimization

Solís¹,

Thomas²

2021

Preprint

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“…The proposed model could be applied to a wide range of applications in which Gaussian process regression has been used, such as finance [6], geostatistics [7], material science [8] and medical science [9,10]. The proposed model could be used to make a non-linear prediction with an explanation for an individual sample, e.g., company, country, material object, and patient in these applications.…”

Section: Broader Impactmentioning

confidence: 99%

“…They have demonstrated great success in various problem settings, such as regression [1,2], classification [1,3], time-series forecasting [4], and black-box optimization [5]. A fundamental model on GPs is Gaussian process regression (GPR) [1]; owing to its high predictive performances and versatility in using various data structures via kernels, it has been used in not only the ML community, but also in various other research areas, such as finance [6], geostatistics [7], material science [8] and medical science [9,10].…”

Section: Introductionmentioning

confidence: 99%

Gaussian Process Regression with Local Explanation

Yoshikawa,

Iwata

2020

Preprint

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Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various applications. However, in GPR, how the features of an input contribute to its prediction cannot be interpreted. Herein, we propose GPR with local explanation, which reveals the feature contributions to the prediction of each sample, while maintaining the predictive performance of GPR. In the proposed model, both the prediction and explanation for each sample are performed using an easy-to-interpret locally linear model. The weight vector of the locally linear model is assumed to be generated from multivariate Gaussian process priors. The hyperparameters of the proposed models are estimated by maximizing the marginal likelihood. For a new test sample, the proposed model can predict the values of its target variable and weight vector, as well as their uncertainties, in a closed form. Experimental results on various benchmark datasets verify that the proposed model can achieve predictive performance comparable to those of GPR and superior to that of existing interpretable models, and can achieve higher interpretability than them, both quantitatively and qualitatively.Preprint. Under review.

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“…Furthermore, due to their probabilistic nature GPs allow estimating the uncertainty at the output. They have been used extensively in many applications, including geostatistics [2], robotic modeling and control [3], [4], and finance [5]. However, the computational complexity of both learning a GP model and utilizing it for regression grows exponentially with the number of training data samples.…”

Section: Introductionmentioning

confidence: 99%

Fast Approximate Multi-output Gaussian Processes

Joukov¹,

Kulić²

2020

Preprint

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Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However, exponential computational complexity growth with the number of training samples has been a long standing challenge. During training, one has to compute and invert an N × N kernel matrix at every iteration. Regression requires computation of an m × N kernel where N and m are the number of training and test points respectively. In this work we show how approximating the covariance kernel using eigenvalues and functions leads to an approximate Gaussian process with significant reduction in training and regression complexity. Training with the proposed approach requires computing only a N × n eigenfunction matrix and a n × n inverse where n is a selected number of eigenvalues. Furthermore, regression now only requires an m × n matrix. Finally, in a special case the hyperparameter optimization is completely independent form the number of training samples. The proposed method can regress over multiple outputs, estimate the derivative of the regressor of any order, and learn the correlations between them. The computational complexity reduction, regression capabilities, and multioutput correlation learning are demonstrated in simulation examples.

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Financial Applications of Gaussian Processes and Bayesian Optimization

Cited by 8 publications

References 0 publications

Generalized State-Feedback Controller Synthesis for Underactuated Systems through Bayesian Optimization

Generalized State-Feedback Controller Synthesis for Underactuated Systems through Bayesian Optimization

Gaussian Process Regression with Local Explanation

Fast Approximate Multi-output Gaussian Processes

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