Sparse Gaussian Process Model Research Articles

Integration Scheme for Economic Load Dispatching and Optimization Control in Coal-Fired Plants Based on Sparse Gaussian Process Model and Deep Reinforcement Learning

Integration Scheme for Economic Load Dispatching and Optimization Control in Coal-Fired Plants Based on Sparse Gaussian Process Model and Deep Reinforcement Learning

Sparse Variational Gaussian Process Based Day-Ahead Probabilistic Wind Power Forecasting

In this paper, we present a probabilistic wind power forecasting (PWPF) model via quantification of epistemic uncertainty and aleatory uncertainty. Concretely, the epistemic uncertainty is described by the statistical characteristics of function space constituted by all wind power forecasting (WPF) mappings through Gaussian process (GP) frameworks. In particular, we adopt the sparse variational Gaussian process to address inference complexity and hyperparameters determination issues, which impede the performance of existing GP-based PWPF models. It introduces inducing variables and variational inference to minimize the difference between the approximated sparse GP model and the original GP, whereby a variational distribution is introduced to explicitly represent the inducing variables. All parameters are optimized via gradient descent optimization based on likelihood maximization. Experiments based on an open dataset demonstrate that the proposed model is comparable to state-of-the-art in terms of continuous ranked probability score, and robust to overfitting.

MIXED COVARIANCE FUNCTION KRIGING MODEL FOR UNCERTAINTY QUANTIFICATION

MIXED COVARIANCE FUNCTION KRIGING MODEL FOR UNCERTAINTY QUANTIFICATION

Predicting On-axis Rotorcraft Dynamic Responses Using Machine Learning Techniques

Physical-law-based models are widely utilized in the aerospace industry. One such use is to provide flight dynamics models for use in flight simulators. For human-in-the-loop use, such simulators must run in real-time. Owing to the complex physics of rotorcraft flight, to meet this real-time requirement, simplifications to the underlying physics sometimes have to be applied to the model, leading to errors in the model's predictions of the real vehicle's response. This study investigated whether a machine-learning technique could be employed to provide rotorcraft dynamic response predictions. Machine learning was facilitated using a Gaussian process (GP) nonlinear autoregressive model, which predicted the on-axis pitch rate, roll rate, yaw rate, and heave responses of a Bo105 rotorcraft. A variational sparse GP model was then developed to reduce the computational cost of implementing the approach on large datasets. It was found that both of the GP models were able to provide accurate on-axis response predictions, particularly when the model input contained all four control inceptors and one lagged on-axis response term. The predictions made showed improvement compared to a corresponding physics-based model. The reduction of training data to one-third (rotational axes) or one-half (heave axis) resulted in only minor degradation of the sparse GP model predictions.

SOLAR-GP: Sparse Online Locally Adaptive Regression Using Gaussian Processes for Bayesian Robot Model Learning and Control

Machine learning methods have been widely used in robot control to learn inverse mappings. These methods are used to capture the entire non-linearities and non-idealities of a system that make geometric or phenomenological modeling difficult. Most methods employ some form of off-line or batch learning where training may be performed prior to a task, or in an intermittent manner, respectively. These strategies are generally unsuitable for teleoperation, where commands and sensor data are received in sequential streams and models must be learned on-the-fly. We combine sparse, local, and streaming methods to form Sparse Online Locally Adaptive Regression using Gaussian Processes (SOLAR–GP), which trains streaming data on localized sparse Gaussian Process models and infers a weighted local function mapping of the robot sensor states to joint states. The resultant prediction of the teleoperation command is used for joint control. The algorithm was adapted to perform on arbitrary link manipulators including the Baxter robot, where modifications to the algorithm are made to run training and prediction in parallel so as to keep consistent, high-frequency control loop rates. This framework allows for a user-defined cap on complexity of generated local models while retaining information on older regions of the explored state-space.

Velocities for spatio-temporal point patterns

Point patterns gathered over space and time are receiving increasing attention in the literature. Examples include incidence of disease events, incidence of insurgent activity events, or incidence of crime events. Point pattern models can attempt to explain these events. Here, a log Gaussian Cox process specification is used to learn about the behavior of the intensity over space and time.Our contribution is to expand inference by introducing the notion of the velocity of a point pattern. We develop a velocity at any location and time within the region and period of study. These velocities are associated with the evolution of the intensity driving the spatio-temporal point pattern, where this intensity is a realization of a stochastic process. Working with directional derivative processes, we are able to develop derivatives in arbitrary directions in space as well as derivatives in time. The ratio of the latter to the former provides a velocity in that direction at that location and time, i.e., speed of change in intensity in that direction. This velocity can be interpreted in terms of speed of change in chance for an event. The magnitude and direction of the minimum velocity provides the slowest speed and direction of change in chance for an event.We use a sparse Gaussian process model approximation to expedite the demanding computation for model fitting and gradient calculation. We illustrate our methodology with a simulation for proof of concept and with a spatio-temporal point pattern of theft events in San Francisco, California in 2012.

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.

A Generalized Stochastic Variational Bayesian Hyperparameter Learning Framework for Sparse Spectrum Gaussian Process Regression

While much research effort has been dedicated to scaling up sparse Gaussian process (GP) models based on inducing variables for big data, little attention is afforded to the other less explored class of low-rank GP approximations that exploit the sparse spectral representation of a GP kernel. This paper presents such an effort to advance the state of the art of sparse spectrum GP models to achieve competitive predictive performance for massive datasets. Our generalized framework of stochastic variational Bayesian sparse spectrum GP (sVBSSGP) models addresses their shortcomings by adopting a Bayesian treatment of the spectral frequencies to avoid overfitting, modeling these frequencies jointly in its variational distribution to enable their interaction a posteriori, and exploiting local data for boosting the predictive performance. However, such structural improvements result in a variational lower bound that is intractable to be optimized. To resolve this, we exploit a variational parameterization trick to make it amenable to stochastic optimization. Interestingly, the resulting stochastic gradient has a linearly decomposable structure that can be exploited to refine our stochastic optimization method to incur constant time per iteration while preserving its property of being an unbiased estimator of the exact gradient of the variational lower bound. Empirical evaluation on real-world datasets shows that sVBSSGP outperforms state-of-the-art stochastic implementations of sparse GP models.

Efficient sparsification for Gaussian process regression

Sparse Gaussian process models provide an efficient way to perform regression on large data sets. Sparsification approaches deal with the selection of a representative subset of available training data for inducing the sparse model approximation. A variety of insertion and deletion criteria have been proposed, but they either lack accuracy or suffer from high computational costs. In this paper, we present a new and straightforward criterion for successive selection and deletion of training points in sparse Gaussian process regression. The proposed novel strategies for sparsification are as fast as the purely randomized schemes and, thus, appropriate for applications in online learning. Experiments on real-world robot data demonstrate that our obtained regression models are competitive with the computationally intensive state-of-the-art methods in terms of generalization and accuracy. Furthermore, we employ our approach in learning inverse dynamics models for compliant robot control using very large data sets, i.e. with half a million training points. In this experiment, it is also shown that our approximated sparse Gaussian process model is sufficiently fast for real-time prediction in robot control.

Parallel Gaussian Process Regression for Big Data: Low-Rank Representation Meets Markov Approximation

The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in leveraging the dual computational advantages stemming from complementing a low-rank approximate representation of the full-rank GP based on a support set of inputs with a Markov approximation of the resulting residual process; the latter approximation is guaranteed to be closest in the Kullback-Leibler distance criterion subject to some constraint and is considerably more refined than that of existing sparse GP models utilizing low-rank representations due to its more relaxed conditional independence assumption (especially with larger data). As a result, our LMA method can trade off between the size of the support set and the order of the Markov property to (a) incur lower computational cost than such sparse GP models while achieving predictive performance comparable to them and (b) accurately represent features/patterns of any scale. Interestingly, varying the Markov order produces a spectrum of LMAs with PIC approximation and full-rank GP at the two extremes. An advantage of our LMA method is that it is amenable to parallelization on multiple machines/cores, thereby gaining greater scalability. Empirical evaluation on three real-world datasets in clusters of up to 32 computing nodes shows that our centralized and parallel LMA methods are significantly more time-efficient and scalable than state-of-the-art sparse and full-rank GP regression methods while achieving comparable predictive performances.

Model-Based Reinforcement Learning in Continuous Environments Using Real-Time Constrained Optimization

Reinforcement learning for robot control tasks in continuous environments is a challenging problem due to the dimensionality of the state and action spaces, time and resource costs for learning with a real robot as well as constraints imposed for its safe operation. In this paper we propose a model-based reinforcement learning approach for continuous environments with constraints. The approach combines model-based reinforcement learning with recent advances in approximate optimal control. This results in a bounded-rationality agent that makes decisions in real-time by efficiently solving a sequence of constrained optimization problems on learned sparse Gaussian process models. Such a combination has several advantages. No high-dimensional policy needs to be computed or stored while the learning problem often reduces to a set of lower-dimensional models of the dynamics. In addition, hard constraints can easily be included and objectives can also be changed in real-time to allow for multiple or dynamic tasks. The efficacy of the approach is demonstrated on both an extended cart pole domain and a challenging quadcopter navigation task using real data.

Sparse Gaussian Process regression model based on ℓ 1/2 regularization

Gaussian Process (GP) model is an elegant tool for the probabilistic prediction. However, the high computational cost of GP prohibits its practical application on large datasets. To address this issue, this paper develops a new sparse GP model, referred to as GPHalf. The key idea is to sparsify the GP model via the newly introduced l 1/2 regularization method. To achieve this, we represent the GP as a generalized linear regression model, then use the modified l 1/2 half thresholding algorithm to optimize the corresponding objective function, thus yielding a sparse GP model. We proof that the proposed model converges to a sparse solution. Numerical experiments on both artificial and real-world datasets validate the effectiveness of the proposed model.