Consistent online Gaussian process regression without the sample complexity bottleneck

Koppel, Alec; Pradhan, Hrusikesha; Rajawat, Ketan

doi:10.1007/s11222-021-10051-5

Cited by 11 publications

(4 citation statements)

References 35 publications

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“…The state of the art in online GP includes other methods such as those based on local approximations (see e.g. [26,27]) and sparse methodologies whose strategy is based on an online reduction of the kernel matrix size through similarity criteria (prominently, the work in [28]). The first methodology is not sparse and its implementation to our applications is not direct, since its computational complexity increases indefinitely with time and, therefore, its application to our experimental setup will involve a pruning procedure to bound such complexity.…”

Section: A Experimental Setupmentioning

confidence: 99%

Adaptive Sparse Gaussian Process

Gómez-Verdejo

Parrado-Hernández

Martínez‐Ramón

2024

IEEE Trans. Neural Netw. Learning Syst.

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Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data and with the lowest possible computational cost for online parameter updating. Existing solutions only partially cover these needs. Here, we propose the first adaptive sparse Gaussian Process (GP) able to address all these issues. We first reformulate a variational sparse GP algorithm to make it adaptive through a forgetting factor. Next, to make the model inference as simple as possible, we propose updating a single inducing point of the sparse GP model together with the remaining model parameters every time a new sample arrives. As a result, the algorithm presents a fast convergence of the inference process, which allows an efficient model update (with a single inference iteration) even in highly nonstationary environments. Experimental results demonstrate the capabilities of the proposed algorithm and its good performance in modeling the predictive posterior in mean and confidence interval estimation compared to state-of-the-art approaches.

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Section: A Experimental Setupmentioning

confidence: 99%

Adaptive Sparse Gaussian Process

Gómez-Verdejo

Parrado-Hernández

Martínez‐Ramón

2024

IEEE Trans. Neural Netw. Learning Syst.

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“…The aggregation model, on the other hand, considers the predictions of most of the submodels, smoothing the discontinuous predictions between two data subsets. In conclusion, the local approximation approach allows the model to be accelerated by distributed or parallel operations, and, the submodels facilitate the identification of local features such as non-stationarity and heteroskedasticity [20].…”

Section: Local Approximationmentioning

confidence: 99%

Mechanisms influencing the learning effect of ISM network under big data regression algorithm

Zhang,

Fan

2023

Applied Mathematics and Nonlinear Sciences

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Exploring the impact mechanism of online learning effectiveness can effectively optimize and improve the impact to enhance online learning effectiveness. This paper describes a big data Gaussian process regression model under big data technology, and global a priori sparse approximation and local approximation solve the predicted distribution results. The training conditional probabilities and test conditional probabilities of the hidden variables are optimized using the induced point method and the spectral approximation method. Then, a simple analysis of the network learning behavior applied by the ISM model is introduced using the big data Gaussian process regression model, and the key, direct and fundamental factors that may affect the network learning are mined. Finally, relative data analysis was conducted based on the relevant influencing factors mined by the ISM model. From the number of course visits, 34.54% of the learners’ visits to the course are mainly concentrated between 100-199 times. Regarding the length of discussions, the per capita participation in online discussions was 37.32 minutes, and most learners mainly focused on 0-50 minutes. It indicates that using big data Gaussian regression model can analyze the influencing factors of online learning through ISM model, and the targeted improvement and optimization can enhance the effectiveness of online learning.

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“…if KSD(q W\{xj } ) 2 < α 2 + ϵ then end if 11: end while 12: Output thinned dictionary W satisfying KSD(q W ) 2 < α 2 + ϵ representing a nonparametric posterior using only most representative samples has been shown to exhibit theoretical and numerical advantages in probability density estimation Broderick 2018, 2019), Gaussian Processes (Koppel, Pradhan, and Rajawat 2021), and Monte Carlo methods (Elvira, Míguez, and Djurić 2016). Here we introduce it for the first time in model-based RL, which allows us to control the growth of the posterior complexity, which in turn permits us to obtain computationally efficient updates.…”

Section: Posterior Coreset Construction Via Ksdmentioning

confidence: 99%

Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning

Chakraborty

Bedi

Tokekar

et al. 2023

AAAI

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Model-based approaches to reinforcement learning (MBRL) exhibit favorable performance in practice, but their theoretical guarantees in large spaces are mostly restricted to the setting when transition model is Gaussian or Lipschitz, and demands a posterior estimate whose representational complexity grows unbounded with time. In this work, we develop a novel MBRL method (i) which relaxes the assumptions on the target transition model to belong to a generic family of mixture models; (ii) is applicable to large-scale training by incorporating a compression step such that the posterior estimate consists of a Bayesian coreset of only statistically significant past state-action pairs; and (iii) exhibits a sublinear Bayesian regret. To achieve these results, we adopt an approach based upon Stein's method, which, under a smoothness condition on the constructed posterior and target, allows distributional distance to be evaluated in closed form as the kernelized Stein discrepancy (KSD). The aforementioned compression step is then computed in terms of greedily retaining only those samples which are more than a certain KSD away from the previous model estimate. Experimentally, we observe that this approach is competitive with several state-of-the-art RL methodologies, and can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.

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Consistent online Gaussian process regression without the sample complexity bottleneck

Cited by 11 publications

References 35 publications

Adaptive Sparse Gaussian Process

Adaptive Sparse Gaussian Process

Mechanisms influencing the learning effect of ISM network under big data regression algorithm

Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning

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